JP5208797B2 - Integer encryption and decryption methods - Google Patents

Description

  The present invention relates to an integer encryption and decryption method, and in particular, the present invention relates to a method for encrypting and decrypting identification information and the like for referring to confidential information with high confidentiality.

Conventionally, it is known that an identifier including a unique integer is used to identify a member in a corporate organization or the like. For example, a number of about 8 digits is used to identify a subscriber in a national health insurance system or the like. Or, a bank branch and account are used to identify a bank account with a number of about 3 to 10 digits, or a number of about 12 digits is used to identify a credit member. A format that can be easily remembered by a person to be identified using a symbol, a character string, or other information is used as appropriate.
As a method capable of realizing encryption and digital signature, RSA encryption, which is a public key encryption based on the fact that the problem of prime factorization of a composite number having a large number of digits is difficult, is known (Patent Literature). 1 and Non-Patent Document 1). The RSA cipher uses a power of an appropriate positive number in the encryption stage and a remainder operation that uses a product of two prime numbers as a modulus, and uses a power root that requires a prime factor of the product in decryption. If the prime factor is not known, decryption becomes difficult, and thus the security of the encryption is ensured.
Furthermore, in order to ensure security in the transmission and reception of information via a computer network, an SSL protocol having encryption, authentication, and alteration detection functions is known (Non-Patent Document 2). It is known that the authentication based on the public key certificate included in the SSL protocol can use the RSA encryption.

U.S. Pat. No. 4,405,829

“RSA encryption” [online], June 12, 2008, [July 30, 2008 search], Internet, <URL: http: // ja. wikipedia. org / wiki / RSA% E6% 9A% 97% E5% 8F% B7> “Secure Sockets Layer” [online], July 29, 2008, [July 30, 2008 search], Internet, <URL: http: // ja. wikipedia. org / wiki / Secure_Sockets_Layer>

  However, in the prior art or a combination of the prior arts, the secret key paired with the public key is decrypted using the combination of the number or characters before encryption and the number or character format after decryption as a clue. However, all ciphers that use the same combination of public and private keys have the weakness of being decipherable. In RSA cryptography, the length of time required to specify a prime factor is the basis of the security of the cryptography. Therefore, by improving the performance of computer equipment and the like used for decryption, even with a certain decryption technique, There has been a problem that the possibility of leaking confidential information increases in a short time.

In addition, in the application software for personal computers, the precision of integers that can be handled by a computer as a double precision type, for example, is limited to about 15 digits due to restrictions on the range of numerical values that can be handled internally. When calculation such as power is executed, an overflow of the processor may occur, and an accurate calculation result may not be obtained. For this reason, it is necessary to divide the original integer as appropriate within the range of digits, and implement measures such as power residue calculation so that overflow does not occur during the calculation independently for each integer obtained by the division. there were. This is the same as encrypting and decrypting plaintext by dividing it by the number of unit bytes in text encryption, but in this method, a key for encryption and decryption is divided for each divided integer or phrase. In order to be linked, there was a problem that a third party gave more clues for decryption.
For example, the credit card registration number and expiration date may be represented using the 16-digit and 4-digit integer formats, respectively. If a highly confidential method capable of encrypting and decrypting a 20-digit integer consisting of these can be provided, as compared with a conventional technique in which a plurality of integers are separately encrypted by dividing the digits, Security can be ensured without increasing the amount of information used as a clue for decryption by a third party. That is, as a technique for concealing personal information, a method for encrypting and decrypting a multi-digit integer exceeding the accuracy range of a double-precision integer is required.

  In addition, information leakage via voice calls or documents such as printed materials cannot be handled by security technology such as SSL protocol for information transmitted using a computer network. Therefore, in various forms including voice or documents. There was a need for a way to conceal personal information.

  In the present invention, the processing time required for performing the steps of encryption and decryption is substantially the same as that of the prior art, and encryption using a power residue is within the range of significant figures such as application software for personal computers. An object is to provide a decoding method. That is, in the present invention, there is provided a method of accurately encrypting and decrypting an integer of about 20 digits using a power residue within the range of significant figures without increasing clues for decryption by a third party. The purpose is to provide. Accordingly, an object of the present invention is to ensure the security of personal information transmitted and received through information communication including a computer network. It is another object of the present invention to generate encrypted information that can be transmitted and received in various forms such as a computer network, voice, or document from the same identification number.

The inventor uses a calculation procedure in which a computer intentionally generates a large number that causes overflow in the calculation process, and performs encryption and decryption while avoiding overflow in a predetermined procedure. A method for concealing personal information has been found (Japanese Patent Application No. 2008-244761). Furthermore, the present inventor has completed the present invention by finding an encryption and decryption method that can use a power residue of a multi-digit integer within the range of significant digits such as application software for personal computers. It came to do.
The present invention provides the following solutions.

を含み、
前記べき剰余復号化ステップは、コンピュータ装置がｍを任意の整数として次式を成立するＦを生成し記憶手段に記憶するステップと、

コンピュータ装置が前記記憶された数Ｆをべき指数とする、次式記載の暗号化した前記整数ＹｉのＦ乗冪演算において、整数Ｙｉの前記保持した前記それぞれの整数部分の桁の情報に基づき、前記それぞれの桁に対応する整数部分間の計算に置き換えて展開し、桁ごとに積Ｎの前記生成した、前記それぞれの整数部分との差分を算出する剰余計算により、整数ＹｉをＦ乗してＮを法とする整数Ｘｎを計算するステップと、コンピュータ装置が前記整数Ｘｎを記憶手段に記憶し、暗号化した前記整数ＹｉをＸｎすなわち、Ｘｉに復号するステップと、を含むことを特徴とする整数を暗号化し復号化する方法。

(1) A power residue encryption step in which a computer device encrypts and decrypts an integer Xi excluding 0 and 1, wherein the computer device encrypts the input integer Xi into an integer Yi; decoding the integer Yi computer device is the encrypted to the integer Xi, and a remainder decoding step should remainder encrypting step should above, the integer Xi computing device, that the product N is input Generating two prime numbers A and B exceeding N, and storing the N, A, and B in a storage means, wherein the computer device converts the product N into an M-decimal notation based on the integer M, and The number of digits in the M-ary notation of the product N is divided into at least two, and the unary sum consisting of the product of the integer part corresponding to each of the divided digits and the power of M with the number of digits as the exponent Generating an expanded form of the product N, and associating each integer part consisting of a set of integer parts corresponding to each digit included in the expanded form and information on the digits of each integer part; A computer device comprising: (A-1) generating the product N; and storing in the storage means the product N and the generated information relating the respective integer parts and the respective integer parts. ) and generates a least common multiple K of (B-1) and the product D and (a-1) and (B-1), storing said D and K in the memory means, the computer device D or K To generate a number E that is prime and to determine whether the integer Xi raised to the E power causes an overflow in the integer operation of the calculation means of the computer device, and until the determination result is true, K and prime And repeating the generation and the determination of the number of E that includes the steps of computing device the determination result is stored in the storage means E that is true, the computer device, the integer Xi an integer M to M-ary notation in base Convert and divide into the same number of digits as the product N, and the integer Xi consisting of a monomial sum consisting of the product of the integer part corresponding to each of the divided digits and the power of M with the number of digits as the exponent And generating information that associates each integer part consisting of a set of integer parts corresponding to each digit included in the expanded form and information on digits of each integer part; Storing the integer Xi and the generated information associating the respective integer part and the respective integer part in a storage means; and a computer device comprising: In the E power operation of the integer Xi described in the following equation, where the generated number E is a power exponent, the integer Xi corresponds to the respective digits based on the information of the digits of the stored integer parts of the integer Xi An integer Yi modulo N by multiplying the integer Xi to the E power by performing a remainder calculation that expands by replacing the calculation between the integer parts and calculates the difference between the generated integer N and the respective integer parts for each digit. And generating an integer Yi obtained by encrypting the integer Xi and storing it in the storage means , wherein the integer Yi is converted into an M-ary notation based on the integer M, and the same number of digits as the product N To generate an expanded form of the integer Yi consisting of a monomial sum consisting of an integer part corresponding to each of the divided digits and a power of M having the number of digits as a power exponent, For each of the digits contained in And generating the information for associating a set with the respective integer part consisting of digits of information of the respective integer part of the integer part of the integer Yi that the generated, wherein each of the integer part and the respective integers Storing the information relating the part in the storage means, and

Including
The power residue decoding step includes a step in which the computer device generates F that satisfies the following expression with m as an arbitrary integer, and stores the F in the storage means ;

In the F multiplication operation of the encrypted integer Yi described in the following equation, where the computer device uses the stored number F as a power exponent, based on the information of the digits of the respective integer portions held of the integer Yi, the expanded by replacing the calculation between the integer part corresponding to each digit, and the generation of the product N for each digit, a remainder calculation for calculating a difference between the respective integer part, the integer Yi Shi multiply F calculating integer Xn modulo N Te, computing device stores the integer Xn in the storage means, and characterized in that it comprises the integer Yi encrypted Xn other words, the step of decoding the Xi, the how to encrypt and decrypt integer.

In the encryption and decryption method of the present invention, by using a computer device or the like capable of performing integer operations, an integer is input to generate an encrypted integer, and the generated encrypted integer is decrypted. The input integer can be restored.
The integer used for input may be an integer that can be processed by a computer, and may be an integer reversibly converted from a character or an image. For example, a character code or the like assigned to each computer-processable character may be handled as a hexadecimal integer such as 1 digit, 2 digits, or 4 digits. Further, for example, 26 characters included in an alphabetic alphabet may be handled as a single digit integer representing a 26-digit number. Further, for example, each pixel included in an image that can be processed by a computer may be treated as a 24-bit binary integer that is a set of 8-bit RGB RGB integers.
In one embodiment, personal information, such as a member's identification number, is reversibly converted to a computer-processable integer and used to input the method for encrypting and decrypting the integer of the present invention.

The calculation means according to the encryption and decryption method of the present invention is a program or the like that causes a computer to perform integer arithmetic, and is generated by an assembler or compiler, converted by an interpreter, or a script or spreadsheet. It can be a machine language program called by a built-in calculation routine.
In one embodiment, overflow may occur in the arithmetic register of a central processing unit (CPU) included in the computer. Therefore, an integer operation with an effective number of digits can be performed in accordance with the number of digits in the operation register of a specific CPU. For example, in the case of a CPU having a register length of 16 bits, integers that can be used for integer operations are in the range of decimal numbers 0 to 65535, for example, as unsigned 16-bit integers. In the case of a CPU having a register length of 32 bits, similarly, an unsigned 32-bit integer is in the range of decimal 0 to 4294967295.
In another embodiment, overflow can occur in an internal function that an interpreter, script, spreadsheet, etc. provides for integer arithmetic. Therefore, an integer operation with an effective number of digits can be performed in accordance with the number of digits of an integer that can be represented by an internal function of a specific interpreter, script, spreadsheet, or the like. For example, an integer that can be represented by a variable in which a type of an unsigned 16-bit integer is defined in a specific compiler or the like is in the range of 0 to 65535 in decimal.

式中、Ｍは記数法の底であり、Ｃｄは下位の桁の数であり、Ｃｄは少なくとも１である。別の実施形態において、積Ｎは２０桁の１０進数として扱われ、次式を用いて５桁の１０進数で表される４個の整数部分に分割されうる。

式中、Ｎ_１５は積Ｎの２０位から１６位、Ｎ_１０は１５位から１１位、Ｎ_５は１０位から６位、Ｎ_０は５位から１位をそれぞれ含む、５桁の１０進数である。すなわち、２０桁の１０進数として扱われうる積Ｎは、５桁の１０進数として表されるＮ_１５、Ｎ_１０、Ｎ_５及びＮ_０からなる４個の整数部分に置き換えうる。なお、積Ｎが２０桁に満たない場合には上位の桁をゼロ詰めして表してもよい。 In the method for encrypting and decrypting an integer according to the present invention, the step of generating two prime numbers A and B having a product N exceeding Xi includes dividing at least two digits of the product N into at least two from the product N An integer part may be generated. In one embodiment, the product N may be divided into an integer part Nu having a higher digit and an integer part Nd having a lower digit using the following equation:

Where M is the base of the numeration system, Cd is the number of the lower digits, and Cd is at least 1. In another embodiment, the product N is treated as a 20-digit decimal number and can be divided into four integer parts represented by a 5-digit decimal number using the following formula:

Where N ₁₅ is the 20th to 16th position of the product N, N ₁₀ is the 15th to 11th position, N ₅ is the 10th to 6th position, and N ₀ is the 5-digit decimal number including the 5th to 1st positions. It is. That is, the product N that can be treated as a 20-digit decimal number can be replaced with four integer parts consisting of N ₁₅ , N ₁₀ , N _5, and N ₀ expressed as a 5-digit decimal number. If the product N is less than 20 digits, the upper digits may be padded with zeros.

別の実施形態において、任意の整数Ｘは２０桁の１０進数として扱われ、次式を用いて５桁の１０進数で表される４個の整数部分に分割されうる。

式中、Ｘ_１５は任意の整数Ｘの２０位から１６位、Ｘ_１０は１５位から１１位、Ｘ_５は１０位から６位、Ｘ_０は５位から１位をそれぞれ含む、５桁の１０進数である。すなわち、２０桁の１０進数として扱われうる任意の整数Ｘは、５桁の１０進数として表されるＸ_１５、Ｘ_１０、Ｘ_５及びＸ_０からなる４個の整数部分に置き換えうる。なお、任意の整数Ｘが２０桁に満たない場合には上位の桁をゼロ詰めして表してもよい。 In one embodiment, as with the product N, any integer X may be divided into an upper digit Xu and a lower digit Xd using the following equation: The arbitrary integer X may be an integer that exceeds the precision range of the double precision type in the method of encrypting and decrypting an integer according to the present invention. For example, an arbitrary integer X may be an integer that can be generated by calculating a power such as a square, a third power, a fourth power, or the like of the integer Xi when the input integer Xi is a 20-digit integer. Further, for example, an arbitrary integer X may be an integer that can be generated by calculating a power such as the square, the third power, the fourth power, or the like of the integer Yi in the decoding according to the present invention.

In another embodiment, any integer X is treated as a 20-digit decimal number and can be divided into four integer parts represented by a 5-digit decimal number using the following formula:

_{Wherein, X 15} is 16 from position 20 of any integer _{X, X 10} is position 11 from position 15, _{X 5} is 6-position to 10-position, _{X 0} includes position 1 from the 5-position, 5-digit It is a decimal number. That is, an arbitrary integer X that can be treated as a 20-digit decimal number can be replaced with four integer parts consisting of X ₁₅ , X ₁₀ , X _5, and X ₀ expressed as a 5-digit decimal number. If an arbitrary integer X is less than 20 digits, the upper digits may be padded with zeros.

  In the method of encrypting and decrypting integers according to the present invention, information relating each integer part is retained. Thus, in the present invention, for the product N or any integer X, the integer parts resulting from the above-described digit division are related to each other. Thus, in the present invention, each integer part can be encrypted and decrypted as a single integer, rather than an independent integer that can be separately encrypted and decrypted. In other words, in the method for encrypting and decrypting integers according to the present invention, it is possible to conceal information without increasing clues for decryption by a third party.

  In the method of the present invention, the integer E is selected so as to generate an arbitrary overflow including the above-described overflow in the power calculation represented by the formula (I). The overflow is performed using a method known in the art, such as detection of occurrence of overflow during integer arithmetic in the CPU, or an error processing routine for overflow that is included in the integer arithmetic library appropriately provided in a compiler or the like. It can be detected.

式中、ｓは０＜ｓ＜Ｅを満たす整数である。展開した右辺のいずれかの項が桁あふれを発生する場合は適宜さらにその項を展開してもよい。式（ＩＶ）のような展開形は整数ｓの選択に計算回数が依存しうる。このように得られたＹｉは、元のＸｉを暗号化した整数でありうる。 The expanded form used in the encryption and decryption method according to the present invention includes a calculation method that substitutes an integer power that satisfies the condition for causing overflow as described above. Specifically, instead of using the formula (I) directly, in order to avoid overflow in the E power of the term Xi in the formula (I), a known method of expressing the term as a product of a plurality of integers is used. Yes, but not limited to this.

In the formula, s is an integer satisfying 0 <s <E. When any term on the expanded right side overflows, the term may be further expanded as appropriate. In the expanded form such as formula (IV), the number of calculations can depend on the selection of the integer s. Yi thus obtained may be an integer obtained by encrypting the original Xi.

  In the method of encrypting and decrypting an integer according to the present invention, the integer F represented by the formula (II) is an expression on the right side that can be generated based on the prime numbers A and B selected including any m. Any factor of (m × K + 1) may be used. The pair of integers E and F may be treated as a public key and private key pair in public key encryption technology known to those skilled in the art.

  In the method for encrypting and decrypting an integer according to the present invention, E in the formula (I) is selected under the condition that overflow occurs. Therefore, an encrypted integer Yi is used in a computer apparatus that does not use the method of the present invention. Cannot be obtained accurately, and encryption with high information confidentiality can be performed. Also, each integer part resulting from digit division can be encrypted and decrypted as a whole as a whole, rather than as an independent integer that can be separately encrypted and decrypted. Therefore, in the method of the present invention, it is possible to conceal information without increasing clues for decryption by a third party.

  (2) The method for encrypting and decrypting an integer according to (1), wherein the information that associates each integer part is information on digits of each integer part.

In the method of encrypting and decrypting integers according to the present invention as exemplified in the above formulas (V) and (VII), the product N and the arbitrary integer X are integer parts obtained by dividing the digits, respectively. Can be treated as a collection of Specifically, the product N is a collection of four integer parts consisting of N ₁₅ , N ₁₀ , N ₅ and N ₀ , and an arbitrary integer X is 4 consisting of X ₁₅ , X ₁₀ , X ₅ and X _0. It can be treated as a collection of integer parts.

Each integer part may be accompanied by information based on the mutual relationship, for example, N ₁₅ is a higher digit than N ₁₀ . The same applies to the other integer parts of the product N and the integer part of an arbitrary integer X. Therefore, in the method for encrypting and decrypting integers according to the present invention, digit information relating each integer part is retained. Thereby, in the present invention, it is possible to handle a group of divided integer parts as an integral integer.

(3) In addition, before generating the integer Yi computer device has converts the integer Xi, the steps of the computer apparatus by adding the integer T follows the integer Xi from the integers Xi replaced with the integer Xi, the computer system after There decoding the integer Yi described above converted to an integer Xn, by subtracting the integer T to the integer Xn including the step of replacing said integer Xn, encrypt and decrypt integer according to (1) Method.

The integer T is a so-called offset. In the encryption and decryption according to the present invention, in addition to the above-described substitutional encryption and decryption, the offset is applied by adding a numerical value and the offset is erased by subtracting the numerical value. Information can be concealed using.
In particular, in encryption and decryption using a power residue, 0, 1, and the original integer itself can be singularity without being converted in the conventional public key encryption technology, etc., but in the present invention, an offset is used. Thus, it is possible to change the numerical value of the singular point in the conventional method. Therefore, in the present invention, it is possible to perform encryption and decryption while avoiding the problems related to the singularities of the conventional method. Here, when the integer (Xi + T) obtained by adding the offset T exceeds the product N of the prime numbers A and B, the range of the integer Xi accepted as an input may be less than (N−T), and the product N The prime numbers A and B may be selected anew so as to exceed an integer (Xi + T), and can be appropriately designed.

(4) The method of encrypting and decrypting the integer according to (3), wherein the integer T is an integer randomly generated by the computer device .

  Like the variable E, variable F, prime number A, prime number B, prime number product N, arbitrary integer number m, etc., the integer number T is also information with the possibility or danger of being used for decryption by a third party. It can be. In the method of encrypting and decrypting an integer according to the present invention, it is difficult to decrypt the encryption by a third party by making the integer T a randomly generated integer.

(5) further comprises the step of computing devices selected by random rules a key for encryption, generation of the E, the number of computer devices is prime and D or K, i.e. a key for encryption A set of candidate numbers is generated, and the computer device generates the set of encryption key candidates from the generated encryption key candidates according to the random rule. A method for encrypting and decrypting the integer described in (1).

Both encryption and decryption keys according to the present invention may be integers. In other words, information that can be handled as an integer can be used as a key for encryption and decryption according to the present invention. For example, a specific integer that reversibly corresponds to specific character information using a character code or the like may be used as a key for encryption and decryption according to the present invention. Information that can be associated may be used.
As a random rule for selecting an encryption key according to the present invention, a random rule including generation of a random number or the like can be used. For example, an integer obtained by using a computer program for generating an integer random number may be used as the encryption key according to the present invention. The present invention is not limited to this, and a mechanism such as a random number 、 or a numerical value associated with the intensity of electrical noise at an arbitrary time may be used as a random rule, and an integer may be selected and used based on these random rules.
Specifically, in the method for encrypting an integer according to the present invention, the integer E included in the formula (I) can be selected based on a random rule. Also, in the method for decoding an integer according to the present invention, an integer F associated with the integer E can be selected according to equation (II).
In the method of encrypting an integer according to the present invention, the integer F is also selected by selecting the integer E according to this random rule. That is, the pair of integers E and F selected in the calculation of the power residue at any point in time according to the present invention is related to the other pair of integers E and F selected during the calculation of the other power residue. It can be an inexact integer. Therefore, the present invention can provide extremely high confidentiality to a third party who does not use the correct values of the integer E and the integer F used for encryption and decryption according to the present invention.

(6) In addition, the computer system to decrypt the substitution encryption step of converting the substitution cipher integers, integers computer device is the substitution cipher with substitution type decoding an integer with a substitution cipher of substitution An encryption step of encrypting an integer by performing either the power residue encryption step or the substitution encryption step first, and then executing the remaining one. In accordance with the execution order of the substitution type encryption step and the power residue encryption step, the power residue decryption step is performed first when the substitution type encryption step is executed first, and the power residue encryption step is preceded by The decryption step for decrypting the encrypted integer by executing the substitution decryption step first and then executing the other one, A method for encrypting and decrypting the integer according to (1).

  In the method for encrypting and decrypting an integer according to the present invention, in addition to the above-described encryption and decryption using a power residue, it is possible to superimpose substitution encryption and substitution decryption. .

式中、Ｒは換字式暗号化の鍵として用いる整数であり、Ｒｏｔ（）は鍵Ｒを用いて整数Ｙｉを換字式暗号化する関数である。Ｒｏｔ（）は、十進法等の記数法を用いて整数Ｙｉを記述して得られる数字の並びを文字列として扱う、公知のシーザー暗号化を用いることができる。例えば、シーザー暗号化における鍵Ｒを整数３として、十進数の数字１文字からなる集合｛０，１，２，３，４，５，６，７，８，９｝の各要素に鍵Ｒを加算し、集合｛３，４，５，６，７，８，９，０，１，２｝の各要素を同一の順番で対応させて換字することが可能である。あるいは、シーザー暗号化とは異なって、鍵Ｒはランダムな順序を用いる情報又は所定の数字の並び方の情報等と関連づけ、対応させる集合はランダムな順序又は所定の数字の並び方でもよい。またあるいは、元の集合の一部の要素に対して鍵Ｒを用いる換字式暗号化を実施してもよく、当該一部の要素の選択には乱数を用いてもよく、当該一部の要素以外の残りの要素に対して公開鍵暗号化を含む任意の暗号化を実施してもよい。これらに限定せず、記数法の桁の数字を予め用意した規則に従って、可逆的かつ一対一に対応するように換字し、整数Ｙｉを整数Ｚｉに変換してもよい。これらの換字式暗号化は、ループカウンタＬに依存せずに毎回実施してもよく、ループカウンタＬに依存して、初回のみ又は偶数回のみ等、Ｌの所定の値に基づいて実施してもよく、適宜設計しうる。 In the step of converting an integer into a substitution-encrypted integer using substitution-type encryption, substitution encryption is performed on an input integer value or a digit number in the notation system. A preferred substitution encryption is Caesar encryption, but is not limited thereto. For example, in the substitution encryption of the integer Yi and the substitution encryption to the integer Zi, the following transformation can be used.

In the equation, R is an integer used as a key for substitution encryption, and Rot () is a function for substitution-encrypting the integer Yi using the key R. Rot () can use a known Caesar encryption that handles a sequence of numbers obtained by describing an integer Yi using a notation system such as a decimal system as a character string. For example, assuming that the key R in Caesar encryption is an integer 3, the key R is assigned to each element of the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} consisting of one decimal digit. It is possible to add and replace each element of the set {3, 4, 5, 6, 7, 8, 9, 0, 1, 2} in the same order. Alternatively, unlike Caesar encryption, the key R may be associated with information using a random order or information on how to arrange a predetermined number, and the corresponding set may be in a random order or a predetermined number. Alternatively, substitution encryption using the key R may be performed on a part of the elements of the original set, and a random number may be used to select the part of the elements. Arbitrary encryption including public key encryption may be performed on the remaining elements other than. However, the present invention is not limited to this, and the integer Yi may be converted to the integer Zi by reversibly converting the numbers in the numeration system so as to correspond to each other in a one-to-one correspondence according to a rule prepared in advance. These substitutional encryption may be performed every time without depending on the loop counter L, and depending on the loop counter L, it may be performed based on a predetermined value of L, such as only the first time or only even times. It can be designed as appropriate.

式中、Ｒｏｔ^−１（）は、換字式暗号化により生成した整数Ｚｉに対して、暗号化の鍵Ｒを用いて元の整数Ｙｉに復号化する関数である。 Further, in the step of decrypting a substitution-encrypted integer using substitution decoding according to the method of the present invention, the integer before conversion is decrypted from the integer transformed using the substitution encryption described above. Is done. For example, when decoding the original integer Yi from the converted integer Zi, the substitution decoding shown in the following equation can be used.

In the equation, Rot ⁻¹ () is a function for decrypting the integer Zi generated by the substitution encryption into the original integer Yi using the encryption key R.

  The method of the present invention uses both encryption using the above power residue and substitutional encryption in encryption, and uses both in reverse order in decryption. The order of each encryption may be any, and after performing substitution-type encryption in the encryption, encryption using a power residue may be performed, or these may be replaced and encrypted. Decryption may be performed in the reverse order by the substitution procedure included in the corresponding encryption or by the power residue.

  Repeating encryption using the same method such as public key encryption according to the prior art can be equivalent to one-time encryption with another key, but in the present invention, substitution is a method different from the power residue. Including encryption and superimposing these, multiple independent encryptions can be used, and the original information can be made extremely difficult to decipher. That is, high security is ensured in the present invention based on the difficulty of deciphering because F is difficult to be known by a third party and substitution encryption and encryption using a power residue can be repeatedly used independently. Yes. Details of superposition and repetition will be described later.

  Furthermore, in the method of encrypting and decrypting integers according to the present invention, these integers are converted into other integers by substitutional encryption for 0, 1 and N which are singular points in power residue encryption. By converting, it becomes possible to encrypt to an integer that is not a singular point of a power residue. That is, in the method according to the present invention, the singular point in the prior art may be included in the original integer, and since there is no singular point that can be used as a clue by a third party, higher confidentiality can be provided. become.

(7) the key substitution cipher of the computer apparatus is an integer you select by random rules, how to encrypt and decrypt the integer of (6).

  The substitution encryption key R is information with the possibility or danger of being used for decryption by a third party, and is not inferred from any information including an integer encrypted by the present invention or an encrypted integer. It is desirable. Therefore, in the method for encrypting and decrypting an integer according to the present invention, it is possible to make it difficult for a third party to decrypt the encryption by selecting a substitution encryption key R based on a randomly generated integer. .

  In one embodiment, the substitution encryption key R prepares a set of prime numbers in advance, orders the elements of this set, generates an integer random number less than the maximum order number, and generates the generated random number. It can be selected as an element having an order. In another embodiment, the substitution encryption key R generates an integer random number less than or equal to the integer to be encrypted, and can be selected from prime numbers having the smallest difference from the generated random number. The same applies to selecting values for other variables. The values of the variables may be selected not only by these selection procedures but also by a selection procedure that can be associated with the generated random number. By doing so, in the method for encrypting and decrypting integers according to the present invention, it is possible to make it more difficult for a third party to decrypt the encryption.

(8) The substitution encryption is one of single table encryption, multi-table encryption, and automatic key encryption , and the substitution decryption corresponds to the substitution encryption. The method of encrypting and decrypting the integer according to (6), which is any one of formula decryption, multi-form decryption, and automatic key decryption.

  The substitution encryption according to the present invention can use substitution encryption including Caesar encryption known in the art. Single-table encryption may be well-known encryption including single substitution encryption, single-substitution encryption, and simple substitution encryption, and multi-table encryption includes visionnel encryption, progress key encryption, square Known encryption including encryption using a substitution table may be used, and automatic key encryption may be encryption in which the encryption key is automatically changed or updated based on the original integer and / or ciphertext. . Also in the decryption according to the present invention, substitutional decryption can be used in the same manner as encryption, and decryption procedures corresponding to various methods enumerated as encryption can be used.

(9) The encryption step for encrypting the integer performs the power residue encryption step first, and then executes the substitution encryption step to decrypt the encrypted integer. Performs the substitution decoding step first, and then executes the power residue decoding step. In the substitution encryption step, the computer device converts the integer Yi into an integer Zi. In the substitution decoding step, the computer device converts the integer Zi into the integer Yi . The method for encrypting and decrypting the integer according to (6),

  In this way, in the method for encrypting integers according to the present invention, by using different encryption methods in succession, it is possible to obtain a more confidential encryption that cannot be obtained by repeating the same encryption method. Can be realized. Even in the method for decrypting an integer according to the present invention, since accurate decryption cannot be performed without knowing the corresponding encryption procedure, more labor is required for decryption by a third party. Therefore, in the method for encrypting and decrypting an integer according to the present invention, it is possible to give extremely high confidentiality to the original integer.

(10) encrypting step of computing device continuously and substitution encrypting step and the remainder encrypting step it should said, and decoding step of computer device to continuously and remainder decoding step to said substitution decoding step, each of at least two are the same plurality of times repeated, a method for encrypting and decrypting integer according to (9).

  By doing in this way, in the encryption step, the power residue and substitution are repeated alternately. Since the adjacent encryption methods are different from each other, each encryption is performed independently of each other. That is, since two adjacent encryptions cannot be replaced with an equivalent power residue or substitution encryption, an integer encrypted using successive encryption steps according to the present invention is determined by a third party. Deciphering requires a lot of work. Similarly, since two adjacent decryptions in successive decryption steps cannot be replaced with an equivalent power residue or substitution encryption, in the method of encrypting and decrypting an integer according to the present invention, It becomes possible to give very high confidentiality to the original integer.

(11) The encryption step for encrypting the integer includes the substitution encryption step first, followed by the power residue encryption step, and the decryption step for decrypting the encrypted integer. Performs the power residue decoding step first, and then executes the substitution type decoding step, and the integer Xi is converted by the computer device executing the substitution encryption step. The method for encrypting and decrypting an integer according to (6), wherein the integer is an integer.

  In the method for encrypting and decrypting an integer according to the present invention, substitution encryption and encryption using a power residue are alternately performed as a continuous encryption step, and decryption using a power residue as a continuous decryption step And substitutional decryption may be performed alternately in reverse order corresponding to encryption. As shown in the above (2), when the encryption using the power residue in the encryption is performed first, the substitutional decryption may be performed in the decryption first, as shown in (4) When substituting encryption is performed first in encryption, decryption using a power residue in decryption may be performed first. The fact that these sequential procedures can be performed is that the encrypted integer is correctly decrypted only on the basis of accurate information when encrypted using the method according to the present invention, and the accurate information is A non-based decryption attempt means that much time is required for decryption. Therefore, in the method for encrypting and decrypting an integer according to the present invention, it is possible to give extremely high confidentiality to the original integer.

(12) decoding step for successive substitution decoding step and the power residue decoding step the substitution encryption step of continuous and remainder encrypting step to the encrypting step, and the computer unit executes the computer unit executes It is be multiple times repeated at least two or more identical respectively, a method for encrypting and decrypting integer according to (11).

  Similarly to the encryption step shown in the above (9), in the present invention, the substitution and the power residue may be repeated alternately. Since the adjacent encryption methods are different from each other, the respective encryptions can be performed independently of each other. That is, since two adjacent encryptions cannot be replaced with an equivalent power residue or substitution encryption, an integer encrypted using successive encryption steps according to the present invention is determined by a third party. Deciphering requires a lot of work. Similarly, two adjacent decodings in successive decoding steps cannot be replaced with an equivalent power residue or substitution decoding. In the present invention, these iterative procedures can be performed, and the encrypted integer is correctly decrypted only on the basis of accurate information when encrypted using the method according to the present invention. On the other hand, in a trial of decryption by a third party that is not based on the accurate information, enormous effort is required for decryption. Therefore, in the method for encrypting and decrypting an integer according to the present invention, it is possible to give extremely high confidentiality to the original integer.

(13) wherein at least two of the plurality of times of repeated the same, the predetermined positive integer, the positive computer device encrypts the predetermined positive integer integer, and positive computing device occurs at random A method for encrypting and decrypting an integer according to (9) or (11), which is any integer.

The number of times may be set as a numerical value stored in a loop counter or the like for control in the computer program. The number of times may be two or more, but a lower limit may be set in advance in order to ensure the strength of encryption. Further, an upper limit may be set in advance in order to shorten the time for calculation processing of encryption and decryption. Therefore, the value of the number of times in the method of encrypting and decrypting an integer according to the present invention is a positive integer obtained by encrypting a predetermined positive integer and a predetermined positive integer according to a preset lower limit and / or upper limit range. And a group consisting of randomly generated positive integers. Any method may be used to encrypt the number of times.
In this way, by making the number of times that can be a variable independent of both encryption using power residue and substitution-type encryption, the number of times becomes unknown to a third party. That is, the trouble of third party decoding can be further increased. Therefore, in the method for encrypting and decrypting an integer according to the present invention, it is possible to give extremely high confidentiality to the original integer.

(14) The integers Xi from some or all of the letters or numbers computing device is included in the identifier is reversibly converted integer, a method for encrypting and decrypting integer according to (1).

  The identifier according to the present invention is typically a computer-processable character (including a number as a character) or a numerical value, and the character can be converted into a unique integer by using a known technique such as a character code. Therefore, in the method for encrypting and decrypting integers according to the present invention, characters or numerical values that can be associated with unique integers can be encrypted and decrypted as original integers.

(15) The integers Xi from some or all of the 1-dimensional image reversibly converted from the computer apparatus 1-dimensional images or two-dimensional image, which is reversibly converted integer, according to (1) To encrypt and decrypt integers.

  An image according to the present invention is typically image data that can be processed by a computer. For example, one pixel has an 8-bit gradation value for each color of R (red), G (green), and B (blue). It can be an unsigned 24-bit integer. A two-dimensional image may be converted into a one-dimensional image by rearranging pixels according to a predetermined procedure. In this way, an image consisting of pixels can be treated as an integer, and a particular image is associated with a unique integer. The number of pixels included in the original integer to be encrypted can be designed as appropriate. Therefore, in the method for encrypting and decrypting integers according to the present invention, a one-dimensional or two-dimensional image that can be associated with a unique integer can be encrypted and decrypted as an original integer.

(16) Further, prior to encryption, the computer device includes a step of replacing the integer with the added digit by adding at least one digit to the original integer, and encrypting the integer according to (1) How to decrypt.

In this way, an integer obtained by adding an arbitrarily selected number of digits to the encrypted integer Xi can be generated and used for encryption input. The integer Wi with the increased number of digits can change depending on the increased number of digits and the number of each digit included in the integer of the number of digits even if the original integer Xi is the same. Therefore, different integers Wi can be generated and used for encryption based on the same Xi and an arbitrarily selected integer of digits.
In one embodiment, the encrypted integer Xi is an integer such as 4 digits, 6 digits, or 8 digits that is generated based on a character string that includes date of birth date information, and is an arbitrarily selected digit. The number can be, for example, a two-digit integer. The user of the method for encrypting and decrypting an integer according to the present invention can generate an integer Wi with an increased number of digits, which is generated from the same integer based on his / her date of birth and an arbitrarily selected two-digit integer. A plurality of encrypted integers can be generated and used by properly using the 2-digit integer as an input for encryption. Even if the integer to be encrypted is, for example, 10 digits, the user does not have to store all the digits for each purpose of use, and the two-digit integer may be used properly.
Therefore, in the method for encrypting and decrypting an integer according to the present invention, even if an integer is associated with a character string including personal information such as a date of birth, the number of digits selected arbitrarily is increased. By making it possible, a plurality of encrypted integers can be generated and used properly.

(17) The method for encrypting and decrypting an integer according to (16), further comprising the step of removing the added at least one digit from the decrypted integer after decryption by the computer device .

  By doing so, in the method for encrypting and decrypting an integer according to the present invention, it is possible to completely decrypt the original integer Xi from the integer Wi having an increased number of digits after decryption.

(18) The step of generating F and storing it in the storage means is such that a computer device generates a number F satisfying the mathematical formula [Equation 2], where m is an arbitrary integer, It is determined whether or not overflow occurs in the integer operation of the calculation means of the apparatus, the step of repeating the generation of the number F and the determination until the determination result becomes true, and the computer apparatus makes the determination result true. Storing the F in the storage means, and encrypting and decrypting the integer according to (1).

By doing so, overflow occurs in the decoding calculation process, so that correct decoding cannot be performed in a calculation means that does not use the method of the present invention.

(19) A computer program for causing a computer to execute each step of the method according to any one of (1) to (18).
Thereby, each step of the method for encrypting and decrypting an integer according to the present invention can be executed by a computer. Accordingly, each step relating to encryption and decryption can be automatically processed using a computer.

  Using the method for encrypting and decrypting integers according to the present invention, arbitrary data recorded on a storage medium and / or numerical values included in a file allocation table for referring to a specific storage area of the storage medium are encrypted. And decryption. The data or the numerical value may be anything as long as it can be regarded as an integer. That is, according to the present invention, a computer-readable medium concealed from a third party can be provided. Specifically, the computer-readable medium includes any form such as an electrical storage medium such as a flash memory, an optically readable medium such as a CD-ROM, and a magnetic storage medium such as a hard disk. The computer-readable medium that can be provided by using the method for encrypting and decrypting an integer according to the present invention does not need to go through a computer network or the like in various stages of encryption or decryption, and is in an offline state separated from the network or the like However, information encoded using the encryption and decryption methods according to the present invention can be stored. Accordingly, the present invention can provide a computer-readable medium that uses encryption and decryption methods independently, independently of security technologies that operate in cooperation with communication technologies.

前記積Ｎと前記生成した、前記それぞれの整数部分と前記それぞれの整数部分を関連づける情報、前記整数Ｘｉと前記生成した、前記それぞれの整数部分と前記それぞれの整数部分を関連づける情報、及び前記整数Ｙｉと前記生成した、前記それぞれの整数部分と前記それぞれの整数部分を関連づける情報とを保持する関連情報保持部と、
ｍを任意の整数として次式を成立するＦを生成し記憶手段に記憶する秘密鍵生成部と、

前記記憶された数Ｆをべき指数とする、次式記載の暗号化した整数ＹｉのＦ乗冪演算において、整数Ｙｉの前記保持した前記それぞれの整数部分の桁の情報に基づき、前記それぞれの桁に対応する整数部分間の計算に置き換えて展開し、桁ごとに積Ｎの前記生成した、前記それぞれの整数部分との差分を算出する剰余計算により、整数ＹｉをＦ乗してＮを法とする整数Ｘｎを生成し記憶手段に記憶することで、前記暗号化したＹｉをＸｎすなわち、Ｘｉに復号する剰余復号化実行部と

を含む、整数を暗号化し復号化する装置。
（２１） 前記秘密鍵生成部は、
ｍを任意の整数として、前記数式［数１２］を成立する数Ｆを生成して、前記整数ＹｉのＦ乗がコンピュータ装置の計算手段の整数演算に桁あふれを発生するか否かを判定し、判定結果が真となるまで、数Ｆの生成と前記判定を繰り返す手段と、前記判定結果が真となるＦを記憶手段に記憶する手段とを含む、ことを特徴とする（２０）に記載の整数を暗号化し復号化する装置。 (20) An apparatus for encrypting and decrypting an input integer Xi excluding 0 and 1, wherein the product N generates two prime numbers A and B exceeding the input integer Xi, and the N, A, A prime number generation unit for storing B in a storage means, wherein the product N is converted into an M-notation notation based on an integer M, and the number of digits in the M-notation of the product N is divided into at least two or more, An expanded form of the product N consisting of a monomial sum consisting of a product of an integer part corresponding to each of the divided digits and a power of M with the number of digits as a power exponent is generated, and is included in the expanded form A prime number generation unit that generates a set of integer parts corresponding to each digit and information that associates each integer part with information on the digits of each integer part, (A-1) and (B-1) product D and (a-1) and the least common multiple K of the (B-1) Generating D and K in the storage means, generating a number E that is prime with D or K, and the power of the integer Xi to generate an overflow in the integer operation of the calculation means of the computer device Until the determination result is true, the generation of the number E that is prime with D or K and the determination are repeated, and E where the determination result is true is stored in the storage means, and the integer Xi is stored. Convert to an M-ary notation based on an integer M, divide into the same number of digits as the product N, and the product of the integer part corresponding to each of the divided digits and the power of M with the number of digits as the exponent Generating an expanded form of the integer Xi consisting of the sum of monomials consisting of the integers, and each of the integers comprising a set of integer parts corresponding to the respective digits included in the expanded form and information on the digits of the respective integer parts A generating unit that generates information for associating the parts; In the E-power multiplication operation of the integer Xi described in the following equation using the stored number E as a power exponent, the integer Xi corresponds to each digit based on the information of the digits of the held integer part of the integer Xi An integer Yi modulo N by multiplying the integer Xi to the E power by performing a remainder calculation that expands by replacing the calculation between the integer parts and calculates the difference between the generated integer N and the respective integer parts for each digit. And the integer Yi is divided into the same number of digits as the product N, and a monomial consisting of the product of the integer part corresponding to each of the divided digits and the power of M with the number of digits as the exponent A development form consisting of a sum is generated, and a set of integer parts corresponding to each digit included in the development form and information associating each integer part consisting of information on the digits of each integer part are generated. Remainder encryption An execution unit,

The product N and the generated information associating the respective integer part and the respective integer part, the integer Xi and the generated information associating the respective integer part and the respective integer part, and the integer Yi And the generated related information holding unit for holding the respective integer parts and the information for associating the respective integer parts,
a secret key generation unit that generates F that satisfies the following expression, where m is an arbitrary integer, and is stored in the storage unit ;

In the F power multiplication operation of the encrypted integer Yi described in the following equation using the stored number F as a power exponent , each of the digits is based on the information of the digits of the held integer portions of the integer Yi. The integer Yi is raised to the F power and N is modulo by the remainder calculation for calculating the difference between the generated integers of the product N for each digit. A remainder decryption execution unit for decrypting the encrypted Yi into Xn, that is, Xi

A device that encrypts and decrypts integers, including:
(21) The secret key generation unit
By using m as an arbitrary integer, a number F that satisfies the mathematical expression [Formula 12] is generated, and it is determined whether or not the integer Yi raised to the F power causes overflow in the integer operation of the calculation means of the computer device. (20) including means for repeating generation of the number F and the determination until the determination result becomes true, and means for storing F in which the determination result is true in the storage means A device that encrypts and decrypts integers.

In the integer encryption / decryption device according to the present invention, it is only necessary to be able to detect overflow in integer arithmetic in the CPU or detection of overflow in integer arithmetic during program execution.
Further, in the integer encryption and decryption device according to the present invention, after selecting E in the above-described formula (I) under the condition that overflow occurs, for example, the above-described formula (IV) or (V) is used. Then, the product N is expanded, and further, Xi is expanded using the formula (VI) or (VII), and the integer Yi obtained by encrypting the integer Xi can be accurately obtained.
Furthermore, in the apparatus according to the present invention, it is possible to hold information on association of integer parts obtained by dividing each of the product N and the integer Xi. As a result, in the device according to the present invention, the input integer Xi can be encrypted and decrypted as one integer, and information can be concealed without increasing clues for decryption by a third party. .

  Therefore, in the device for encrypting and decrypting integers according to the present invention, it is possible to generate an encrypted integer that secures high security for the integer associated with personal information, etc., and correctly decrypt the encrypted integer. To get the original integer.

前記積Ｎと前記生成した、前記それぞれの整数部分と前記それぞれの整数部分を関連づける情報、前記整数Ｘｉと前記生成した、前記それぞれの整数部分と前記それぞれの整数部分を関連づける情報、及び前記整数Ｙｉと前記生成した、前記それぞれの整数部分と前記それぞれの整数部分を関連づける情報とを保持する関連情報保持手段と、
ｍを任意の整数として次式を成立するＦを生成し記憶手段に記憶する秘密鍵生成手段と、

前記記憶された数Ｆをべき指数とする、次式記載の暗号化した整数ＹｉのＦ乗冪演算において、整数Ｙｉの前記保持した前記それぞれの整数部分の桁の情報に基づき、前記それぞれの桁に対応する整数部分間の計算に置き換えて展開し、桁ごとに積Ｎの前記生成した、前記それぞれの整数部分との差分を算出する剰余計算により、整数ＹｉをＦ乗してＮを法とする整数Ｘｎを生成し記憶手段に記憶することで、前記暗号化したＹｉをＸｎすなわち、Ｘｉに復号する剰余復号化実行手段と

を含む、整数を暗号化し復号化するシステム。
（２３） 前記秘密鍵生成手段は、ｍを任意の整数として、前記数式［数１５］を成立する数Ｆを生成して、前記整数ＹｉのＦ乗がコンピュータ装置の計算手段の整数演算に桁あふれを発生するか否かを判定し、判定結果が真となるまで、数Ｆの生成と前記判定を繰り返す手段と、前記判定結果が真となるＦを記憶手段に記憶する手段とを含む、ことを特徴とする（２２）に記載の整数を暗号化し復号化するシステム。 A system for encrypting and decrypting an integer Xi, wherein two prime numbers A and B exceeding the integer Xi to which a product N is inputted are generated, and the prime number generating means for storing the N, A, and B in a storage means The product N is converted into an M-ary notation based on an integer M, the number of digits in the M-ary notation of the product N is divided into at least two, and the integer part corresponding to each of the divided digits A product of the monomial sum consisting of the product of M and the power of M with the number of digits as the exponent, and a set of integer parts corresponding to the respective digits included in the expansion. Prime number generating means for generating information relating the digits of the integer parts and associating the integer parts ; products D and (A-1) of (A-1) and (B-1); Generate the least common multiple K of (B-1) and write D and K Storing in the storage means, generating a number E that is prime with D or K, and determining whether the integer Xi raised to the E power causes an overflow in the integer operation of the calculation means of the computer device; Until the result becomes true, generation of the number E that is prime with D or K and the determination are repeated, and E where the determination result is true is stored in the storage means, and the integer Xi is the M base with the integer M as the base. Converted into notation, divided into the same number of digits as the product N, and consisting of a monomial sum consisting of a product of an integer part corresponding to each of the divided digits and a power of M with the number of digits as the exponent An expanded form of the integer Xi is generated, and a set of integer parts corresponding to the respective digits included in the expanded form and information that associates the respective integer parts including information on the digits of the respective integer parts are generated. Generating means and the stored number E In the E-power operation of the integer Xi described in the following equation, the exponent is replaced with a calculation between the integer parts corresponding to the respective digits based on the information of the digits of the held integer parts of the integer Xi. The integer Yi is calculated by dividing the integer Xi to the E power and calculating the integer Yi modulo N by the remainder calculation that calculates the difference between the generated integer N of the product N for each digit. Is divided into the same number of digits as the product N, and an unfolded form consisting of a monomial sum consisting of a product of an integer part corresponding to each of the divided digits and a power of M with the number of digits as the exponent is generated. , and remainder encryption means for generating an information associating said respective integer part consisting of digits of information collection and the respective integer part of the integer part corresponding to the respective digits included in the deployment shape,

The product N and the generated information associating the respective integer part and the respective integer part, the integer Xi and the generated information associating the respective integer part and the respective integer part, and the integer Yi And the generated related information holding means for holding the respective integer parts and the information relating the respective integer parts ,
a secret key generating means for generating F that holds the following expression with m as an arbitrary integer and storing it in the storing means ;

In the F power multiplication operation of the encrypted integer Yi described in the following equation using the stored number F as a power exponent , each of the digits is based on the information of the digits of the held integer portions of the integer Yi. The integer Yi is raised to the F power and N is modulo by the remainder calculation for calculating the difference between the generated integers of the product N for each digit. Generating an integer Xn to be stored and storing it in the storage means, whereby the encrypted Yi is decrypted into Xn, that is, Xi ;

A system that encrypts and decrypts integers, including
(23) The secret key generation means generates a number F that holds the mathematical expression [Expression 15], where m is an arbitrary integer, and the power of the integer Yi is a digit in the integer calculation of the calculation means of the computer device. Determining whether or not overflow occurs, and means for repeating the generation of the number F and the determination until the determination result is true, and means for storing the F in which the determination result is true in the storage means, A system for encrypting and decrypting the integer described in (22) .

In the system for encrypting and decrypting integers according to the present invention, it is only necessary to be able to detect overflow of integer operations in the CPU or detection of overflow of integer operations during program execution. The integer E included in the power calculation represented by the formula (IX) may be selected.
Further, in the system for encrypting and decrypting an integer according to the present invention, after selecting E of the above-described formula (I) under the condition that overflow occurs, for example, the above-described formula (IV) or (V) is used. Then, the product N is expanded, and further, Xi is expanded using the formula (VI) or (VII), and the integer Yi obtained by encrypting the integer Xi can be accurately obtained.
Furthermore, in the system according to the present invention, it is possible to hold information relating to the integer part obtained by dividing each of the product N and the integer Xi. As a result, in the system according to the present invention, the input integer Xi can be encrypted and decrypted as one integer, and information can be concealed without increasing clues for decryption by a third party. .

  Therefore, in the system for encrypting and decrypting integers according to the present invention, it is possible to generate an encrypted integer that secures high security for the integer associated with personal information and the like, and correctly decrypt the encrypted integer. To get the original integer.

  The method, apparatus, system, etc. for encrypting and decrypting integers according to the present invention can be combined with existing information transmission technologies, such as computer network technologies, and such combined technologies are also included in the present invention. Included in the technical scope. Similarly, an information recording system, an information management system, an information processing system and the like including the technique of the present invention are also included in the technical scope of the present invention. In addition, the technique of the present invention allows the encryption and decryption stages to be performed in FPGA (field programmable gate array), ASIC (application specific integrated circuit), equivalent hardware logic elements, programmable. The integrated circuit or a combination thereof can be provided as a program form that can be stored, that is, as a program product. Specifically, the encryption and decryption device according to the present invention can be provided as a form of a custom LSI (large scale integrated circuit) including an input / output, a data bus, a memory bus, a system bus, etc. The form of the program product stored in the circuit is also included in the technical scope of the present invention.

According to the present invention, an integer obtained by encrypting an identification number or the like for identifying an individual using a method for encrypting and decrypting the integer within a range of significant digits under the condition that the computer overflows. Can be generated. In the present invention, a third party is provided by providing a method of calculating a power residue using division of integer parts having correlation with each other even for a multi-digit integer exceeding the range of precision of a double precision type. It is possible to keep information secret without increasing clues for decryption. That is, the present invention can provide a form that can be concretely implemented and commercialized for a target to which random numbers can be applied, and has the effect of dramatically improving the difficulty of decoding compared to simple logic. is there.
Therefore, according to the present invention, there is an effect that the identification number can be concealed by making it extremely difficult to estimate the identification number or the like from the integer generated for a third party. Further, according to the present invention, in addition to the method of encrypting and decrypting the integer within the range of significant digits, by performing superimposition of substitutional encryption and performing encryption and decryption, Decryption becomes extremely difficult, and the confidentiality of the identification number and the like can be improved. Further, according to the present invention, an integer representing a character string including the same personal information such as date of birth and an integer selected arbitrarily are used, a randomly generated key, or an integer with an increased number of digits is used. Thus, by encrypting and decrypting, a plurality of different encrypted integers can be generated from the same personal information and used separately. Furthermore, according to the present invention, it is possible to conceal personal information in various forms including a voice call or a document such as a printed matter.

FIG. 3 is a flow diagram of a method for encrypting an integer, according to one embodiment of the invention. FIG. 4 is a flow diagram of a method for decrypting an encrypted integer, according to one embodiment of the invention. FIG. 5 is a flow diagram of another embodiment of a method for encrypting integers according to the present invention. FIG. 4 is a flow diagram of another embodiment of a method for decrypting an encrypted integer, in accordance with the present invention. FIG. 4 is a diagram illustrating an example of a personal information hiding procedure using a method for encrypting an integer according to an embodiment of the present invention. It is a figure which shows another example of the personal information concealment procedure using the method which encrypts an integer based on one Embodiment of this invention. It is a figure which shows another example of the personal information concealment procedure using the method which encrypts an integer based on one Embodiment of this invention. FIG. 4 is a diagram illustrating an example of an encrypted integer decryption procedure according to an embodiment of the present invention. FIG. 6 illustrates an example of implementing steps of an encryption method according to an embodiment of the present invention using a spreadsheet-style calculation application package. FIG. 6 is a diagram illustrating an example of calculating and implementing the steps of the decryption method in a spreadsheet-type calculation application package according to an embodiment of the present invention.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings.

[Flow diagram of encryption and decryption]
1 and 2 show a flow chart of a method for encrypting and decrypting an integer according to an embodiment of the present invention. FIG. 1 is an example of a flowchart of a method for encrypting an integer according to the present invention, and FIG. 2 is an example of a flowchart of a method for decrypting the encrypted integer.

[Encryption stages]
First, the encryption steps will be described with reference to FIG. The method for encrypting an integer according to the present invention secures a variable area in step S100 of FIG. Specifically, a memory area of a computer device or the like is appropriately secured for calculation using the variables listed in the following Table 1.

The integer to be encrypted includes an unsigned integer that can be included in an identifier or the like, but is not limited to this, and an integer in any format can be used in the method according to the present invention. Preferably, the integer to be encrypted can be any integer greater than or equal to zero.
In one embodiment, word lengths of integers Xi, Yi, Zi, Xn, and Yn in a computer device or the like used for calculation are register bits that can be used to represent one integer in an internal instruction of a CPU included in the computer device or the like. Can be within maximum width. For example, in a computer device equipped with a CPU that can execute an integer operation included in an internal instruction using a 16-bit register, the word lengths of integers Xi, Yi, Zi, Xn, and Yn are 16 bits or less. The variable may be 0 or more and 65535 or less in decimal notation.

  Next, the method for encrypting an integer according to the present invention may generate two prime numbers A and B having a product N exceeding Xi in step S110. The prime numbers A and B may be selected as appropriate by preparing a set of prime numbers in advance.

式中、Ｍは記数法の底であり、Ｃｄは下位の桁の数であり、Ｃｄは少なくとも１である。別の実施形態において、積Ｎは２０桁の１０進数として扱われ、次式を用いて５桁の１０進数で表される４個の整数部分に分割されうる。

式中、Ｎ_１５は積Ｎの２０位から１６位、Ｎ_１０は１５位から１１位、Ｎ_５は１０位から６位、Ｎ_０は５位から１位をそれぞれ含む、５桁の１０進数である。すなわち、２０桁の１０進数として扱われうる積Ｎは、５桁の１０進数として表されるＮ_１５、Ｎ_１０、Ｎ_５及びＮ_０からなる４個の整数部分に置き換えうる。なお、積Ｎが２０桁に満たない場合には上位の桁をゼロ詰めして表してもよい。 In one embodiment, step S110 may divide the digit of product N into at least two to generate at least two integer parts from product N. For example, the product N may be divided into an integer part Nu having an upper digit and an integer part Nd having a lower digit using the following equation.

Where M is the base of the numeration system, Cd is the number of the lower digits, and Cd is at least 1. In another embodiment, the product N is treated as a 20-digit decimal number and can be divided into four integer parts represented by a 5-digit decimal number using the following formula:

Where N ₁₅ is the 20th to 16th position of the product N, N ₁₀ is the 15th to 11th position, N ₅ is the 10th to 6th position, and N ₀ is the 5-digit decimal number including the 5th to 1st positions. It is. That is, the product N that can be treated as a 20-digit decimal number can be replaced with four integer parts consisting of N ₁₅ , N ₁₀ , N _5, and N ₀ expressed as a 5-digit decimal number. If the product N is less than 20 digits, the upper digits may be padded with zeros.

Next, in the method for encrypting an integer according to the present invention, in step S120, the product of (A-1) and (B-1) is substituted into D, and (A-1) and (B-1) Substitute the least common multiple for K.
Next, the method for encrypting an integer according to the present invention generates a number E that is prime to D or K in step S130.
Next, in the method for encrypting an integer according to the present invention, in step S140, whether the term on the right side of the following equation (XII) (Xi raised to the E power) causes overflow in the integer operation of the calculation means. Determine. If the determination result is true, the process proceeds to step S150, and if it is false, the process returns to step S130.

  The overflow detection is performed by using a flag included in a specific register of the CPU (for example, an overflow flag included in the status register or the condition register) for storing the internal operation status of the CPU included in the calculation means. You may refer to the value, register exception handling in the operating system in advance using the compiler language, etc., and refer to the operation of the exception handling, or an overflow provided by a library attached to the script language or compiler language, etc. • You may refer to error handling and design accordingly.

式中、Ｍは記数法の底であり、Ｃｄは前記下位の桁の数であり、Ｃｄは少なくとも１でありうる。すなわち、このようにして置き換えたＸｕ又はＸｄを用いて、式（ＸＩＩＩ）の剰余計算を実施しうる。このようにすることで、本発明に係る整数を暗号化し復号化する方法においては、桁あふれを発生する条件で前述の式（ＸＩＩＩ）のＥを選択した後に、式（ＸＩＶ）を用いてＸｉを展開し、桁あふれを避けて、暗号化した整数であるＹｉを正確に得ることができる。 Next, in step S150, the method for encrypting an integer according to the present invention can generate an integer Yi obtained by encrypting the integer Xi using the expansion form of the formula (XIII). For example, the following expression can be used as a developed form of the expression (XIII).

Where M is the base of the numeration system, Cd is the number of the lower digits, and Cd can be at least 1. That is, the remainder calculation of the formula (XIII) can be performed using Xu or Xd thus replaced. In this way, in the method for encrypting and decrypting an integer according to the present invention, after selecting E in the above-mentioned formula (XIII) under the condition that overflow occurs, Xi is used using the formula (XIV). Yi that is an encrypted integer can be obtained accurately by avoiding overflow.

In one embodiment, similar to the product N, the method according to the invention divides in step S150 into an upper digit Xu and a lower digit Xd for any integer X including the integer Xi using the following equation: Generated integer parts. Xu and Xd are the same as in the above formula (XIV). The arbitrary integer X may be an integer that exceeds the precision range of the double precision type in the method of encrypting and decrypting an integer according to the present invention. For example, an arbitrary integer X may be an integer that can be generated by calculating a power such as a square, a third power, a fourth power, or the like of the integer Xi when the input integer Xi is a 20-digit integer. Further, for example, an arbitrary integer X may be an integer that can be generated by calculating a power such as the square, the third power, the fourth power, or the like of the integer Yi in the decoding according to the present invention.

For example, when M, which is the base of the notation system, is 2, the number of digits of Xi is 16 digits, and the number of lower digits Ct is 8 digits, the formula (IX) is expressed as the following equation.

For example, when the implementation means of the method for encrypting and decrypting an integer according to the present invention is a computer device including a CPU having a 16-bit width register, the value of the original integer Xi is a decimal number 65532, etc. If there is, in the calculation of a power to an arbitrary integer X, when 2 which can be the smallest integer power number is used, it exceeds the upper limit 65535 of the integer that can be expressed using the 16-bit width register provided in the CPU. End up. That is, if the calculation of the Ei power of Xi included in the right side of the formula (XIII) is performed according to a normal calculation method that simply powers the original integer as it is, an accurate power value may not be obtained.
In the method according to the present invention, for example, the upper digit and the lower digit can be divided as integer parts by using the digit division represented by the formula (XVI). For example, a decimal number 65532 is used as an arbitrary integer X, which is expressed as a binary number 1111111111111100 (2), divided into upper 8 digits, lower 8 digits, etc., and an integer 11111111 (2) (10 Using the integer number 111111100 (2) (decimal number 252) included in the lower 8 digits of the decimal number 255) and calculating the square of 255, the product of 255 and 252 and the square of 252 respectively, the product of these integers Is clearly within the range of integers that can be represented using the 16-bit wide registers of the CPU. The same applies to 32-bit wide registers, 64-bit wide registers, and the like. In particular, an integer having a data length of 64 bits is in the precision range of the double precision type, and the method according to the present invention avoids an error due to overflow when it is a calculation result such as a power that can exceed the precision range. Is possible.
Therefore, for example, in the calculation of the power of Xi expressed as the above formula (XIII), in the case of the square of Xi that is the smallest number of times, the square of the right side of the formula (XV) is changed to the square of Xu, Since Xu · Xd and the square of Xd are generated, both of which can be integers less than the number of digits of the original Xi, overflow is avoided. That is, it is possible to avoid overflow in the power calculation process by repeating the procedure of the equation (XV) at an arbitrary power of Xi.

式中、Ｘ_１５は任意の整数Ｘの２０位から１６位、Ｘ_１０は１５位から１１位、Ｘ_５は１０位から６位、Ｘ_０は５位から１位をそれぞれ含む、５桁の１０進数である。すなわち、２０桁の１０進数として扱われうる任意の整数Ｘは、５桁の１０進数として表されるＸ_１５、Ｘ_１０、Ｘ_５及びＸ_０からなる４個の整数部分に置き換えうる。なお、任意の整数Ｘが２０桁に満たない場合には上位の桁をゼロ詰めして表してもよい。 In another embodiment, any integer X, including the input integer Xi, is treated as a 20-digit decimal number and can be divided into four integer parts represented by a 5-digit decimal number using the following formula:

_{Wherein, X 15} is 16 from position 20 of any integer _{X, X 10} is position 11 from position 15, _{X 5} is 6-position to 10-position, _{X 0} includes position 1 from the 5-position, 5-digit It is a decimal number. That is, an arbitrary integer X that can be treated as a 20-digit decimal number can be replaced with four integer parts consisting of X ₁₅ , X ₁₀ , X _5, and X ₀ expressed as a 5-digit decimal number. If an arbitrary integer X is less than 20 digits, the upper digits may be padded with zeros.

  The number of digits to be divided can be appropriately set based on the bit width of a register for integer arithmetic operation of the CPU provided in the calculation means or the like. Preferably, as shown in the equation (XV), the number of upper digits and the number of lower digits obtained by equally dividing the bit width of the register for unsigned integer arithmetic can be used as divided digits. More preferably, as shown in the formula (XVII), the input integer Xi is represented as a 20-digit integer, and each integer part obtained by dividing this into four 5-digit integers is used as the divided digits. sell.

  Through the above steps, Yi which is an integer encrypted using a power residue is obtained from the original integer Xi. The word length required to represent the integer Yi may be the same as the word length to represent the original integer Xi, but is not limited thereto, depending on the use of the encrypted integer Yi, etc. A number or the like that increases the number of digits may be added by combining security means or methods, or an integer Yi may be converted into a character and a character including a symbol or the like may be arbitrarily added.

Next, in step S160, the method for encrypting an integer according to the present invention retains information relating each integer part divided for the above-described purpose. Specifically, the information of the digits of each integer part with respect to the integer before division is held. For example, with respect to the integer X before the division, the integer parts X ₁₅ , X ₁₀ , X ₅ , and X ₀ are the 20th to 16th, 15th to 11th, and 10th positions of the arbitrary integer X, respectively. The information indicating that it is 6th from 5th and 1st from 5th is held.

  In the method of encrypting and decrypting integers according to the present invention, information relating the product N and each integer part included in the expanded form is held. Thus, in the present invention, for the product N or any integer X, the integer parts resulting from the above-described digit division are related to each other. Thus, in the present invention, each integer part can be encrypted and decrypted as a single integer, rather than an independent integer that can be separately encrypted and decrypted. In other words, in the method for encrypting and decrypting integers according to the present invention, it is possible to conceal information without increasing clues for decryption by a third party.

  In this way, in the method for encrypting and decrypting integers according to the present invention, since E in formula (XIII) is selected under the condition that overflow occurs, a computer apparatus that does not use the method of the present invention, etc. The encrypted integer Yi cannot be obtained accurately and encryption with high information confidentiality can be performed.

Ｐ又はＱはいずれも、上述の積Ｎでもよく、入力の整数Ｘｉでもよく、任意の整数Ｘでもよい。式（ＸＶＩＩＩ）のように展開することにより、分割された整数部分どうしの積である式中の各項に含まれるＰ_１５Ｑ_１５、Ｐ_１５Ｑ_１０等はいずれも倍精度型の精度の範囲にある。 In one embodiment, the product of any two integers in the encryption method according to the present invention can be expanded and replaced as: As an example, the integers P and Q are shown as two integers. In the formula, P and Q are each expressed as a 20-digit decimal number, and may be zero-padded when there is no number in the upper digit.

Either P or Q may be the product N described above, the input integer Xi, or an arbitrary integer X. By expanding as in the formula (XVIII), P ₁₅ Q ₁₅ , P ₁₅ Q _10, etc. included in each term in the formula that is the product of the divided integer parts are both in the double precision type accuracy range. It is in.

Similarly to the formula (XVIII), N which is the product of two prime numbers may be expressed as the following formula. In the formula, the prime numbers A and B are each expressed as a 20-digit decimal number, and may be padded with zeros when there are no digits in the upper digits.

In the method for encrypting an integer according to the present invention, a remainder for N may be obtained by calculating a difference for each digit. As an example, the following equation shows the remainder for N of the product of two integers PQ. In calculating the remainder, a known calculation technique can be arbitrarily used. For example, the remainder when the difference (PQ−AB) in the second equation is negative can be PQ.

[Decoding stages]
Next, the decoding steps will be described. The method for decoding an integer according to the present invention reserves a variable area in step S200 of FIG. The securing of the variable area may be the same as that in step S100 in the above-described encryption stages. The encryption and decryption stages are built in a single computer device, and both the common variable area is encrypted and decrypted. It may be used in these stages.

Next, in step S410, the method for decoding an integer according to the present invention restores information relating the integer part. This association is information for associating integer parts held in step S160 of encryption according to the present invention shown in FIG. Therefore, by the operation in step S410, the digit information associated with each of the plurality of integer parts is restored. For example, each of the integer parts X ₁₅ , X ₁₀ , X ₅ , and X ₀ is 20th to 16th, 15th to 11th, 10th to 6th, and 5th to 1st of any integer X. Is restored, and the digits of the integer X before division can be correctly reproduced.

式（ＸＸＩ）において、整数Ｆは、任意のｍを含んで選択された素数Ａ及びＢに基づいて生成しうる右辺の式（ｍ×Ｋ＋１）の因数であれば何でもよい。
次いで、本発明に係る暗号化した整数を復号化する方法は、ステップＳ２２０において、次の式（ＸＸＩＩ）を用いて前記暗号化したＹｉをＸｎに復号化する。

Next, the method for decoding an integer according to the present invention generates F that satisfies the following expression (XVI) in step S210, where m is an arbitrary integer.

In the formula (XXI), the integer F may be any factor as long as it is a factor of the formula (m × K + 1) on the right side that can be generated based on the prime numbers A and B selected including any m.
Next, in the method for decrypting an encrypted integer according to the present invention, in step S220, the encrypted Yi is decrypted into Xn using the following equation (XXII).

  In this way, in the method for encrypting and decrypting integers according to the present invention, since E in formula (XIII) is selected under the condition that overflow occurs, a computer apparatus that does not use the method of the present invention, etc. The encrypted integer Yi cannot be obtained accurately and encryption with high information confidentiality can be performed. Furthermore, in the method for encrypting and decrypting an integer of the present invention, the integer F included in the formula (XXI) and the formula (XXII) that are not included in the formula (XIII) that is the process of decryption is included High security can be secured based on the fact that it is difficult to be known or estimated by a third party.

  The calculation of the product of any two integers included in the formula (XXI) may be performed using the expansion of the product for each integer part obtained by dividing digits as shown in the above formula (XVIII) or the formula (XIX). Good. For the remainder calculation included in the formula (XXII), the expansion of the product for each integer part obtained by dividing the digits shown in the above formula (XX) may be used. That is, in the method for encrypting and decrypting integers according to the present invention, it is possible to correctly obtain an integer product or remainder exceeding the double precision type accuracy range in decryption as well as encryption. Furthermore, in the present invention, the type and number of encryption and decryption keys that use integer products or remainders that exceed the precision of the double precision type are the encryption and decryption of integers that are within the precision range of the double precision type. It is equivalent to the type and number of keys. Therefore, in the present invention, it is possible to encrypt and decrypt an integer exceeding the precision of the double precision type without increasing clues for decryption by a third party.

  In the method of encrypting and decrypting an integer according to the present invention shown in FIGS. 1 and 2, an identifier for identifying an individual can be received as an integer identifier and encrypted. However, the present invention is not limited to this, and in the method for encrypting and decrypting integers according to the present invention, various data that can be received by a computer device or the like capable of performing integer power and remainder calculation can also be used for encryption. For example, by encrypting an image converted into an integer using the method of the present invention, the concealed image can be transmitted to a third party. Further, for example, a file storage table or the like for referring to a specific storage area of the storage medium is encrypted using the method of the present invention, thereby providing a storage medium or the like hidden from a third party. These storage media that can be provided using the method for encrypting integers according to the present invention do not need to go through a computer network or the like at various stages of encryption, and can be encrypted even in an offline state separated from the network or the like. And decoding can be performed. Therefore, in the present invention, independent encryption and decryption methods can be provided independently of the security technology operating in cooperation with the communication technology.

[Another embodiment of encryption and decryption]
3 and 4, another embodiment of encryption and decryption according to another embodiment of the present invention will be described. First, the encryption steps will be described with reference to FIG. The description of the portions common to the embodiment shown in FIG. 1 and the above-described Table 1 will be omitted. The method for encrypting an integer according to the present invention secures a variable area in step S105 of FIG. Specifically, in addition to the variables shown in Table 1 above, a memory area of a computer device or the like is appropriately secured for the calculation in which the variables shown in Table 2 below are added.

At this time, initial setting of the loop counter L and the like may be appropriately performed.
For example, when the combination of encryption using power remainder and substitution encryption is repeated three times as a whole, the integer 3 may be set in the loop counter L in step S105. The loop counter L may be selected from the group consisting of a predetermined positive integer, a positive integer obtained by encrypting the predetermined positive integer, and a randomly generated positive integer.
The loop counter L is an independent variable for both encryption using power remainder and substitution-type encryption, affects the strength of secrecy by encryption, and may affect calculation time for encryption and decryption. .
In order to ensure the strength of confidentiality for the loop counter L, a lower limit may be set in advance. Furthermore, an upper limit may be set in advance in order to shorten the time for calculation processing of encryption and decryption. Therefore, the value of the loop counter L in the method for encrypting and decrypting an integer according to the present invention is a predetermined positive integer according to a preset lower limit and / or upper limit range, and the predetermined positive integer is encrypted. Selected from the group consisting of a positive integer and a randomly generated positive integer. By keeping the loop counter L secret from a third party, in addition to the secrecy of each encryption method, the effort of the third party to decrypt can be further increased. Therefore, in the method for encrypting and decrypting an integer according to the present invention, it is possible to give extremely high confidentiality to the original integer.

  Similarly, the offset T and the arbitrary integer m included in the encryption using the power residue and the key R which is the variable included in the substitution encryption are also selected so as to be secret from a third party. May be.

  Subsequent step S10 is equivalent to the stages of encryption according to the present invention shown using FIG. By the operations from step S110 to step S160 included in step S10, information that correlates the encrypted integer Yi and a plurality of integer parts used in the calculation process is held. Further, the encrypted integer Yi may be offset using the offset T arbitrarily. Specifically, instead of Yi generated by the operation in step S150, an offset (Yi + T) may be used.

式中、Ｒは換字式暗号化の鍵として用いる整数であり、Ｒｏｔ（）は鍵Ｒを用いて整数Ｙｉを換字式暗号化する関数である。具体的には、Ｒｏｔ（）は、十進法等の記数法を用いて整数Ｙｉを記述して得られる数字の並びを文字列として扱う、公知のシーザー暗号化を用いることができる。例えば、シーザー暗号化における鍵Ｒを整数３として、十進数の数字１文字からなる集合｛０，１，２，３，４，５，６，７，８，９｝の各要素に鍵Ｒを加算し、集合｛３，４，５，６，７，８，９，０，１，２｝の各要素を同一の順番で対応させて換字することが可能である。あるいは、シーザー暗号化とは異なって、鍵Ｒはランダムな順序を用いる情報又は特定の数字の並び方の情報等と関連づけ、対応させる集合は｛８，０，２，４，６，３，７，９，５，１｝のように昇順ではない順序でもよい。これらに限定せず、記数法の桁の数字を予め用意した規則に従って、可逆的かつ一対一に対応するように換字し、整数Ｙｉを整数Ｚｉに変換してもよい。
例えば、英字アルファベットを２６進数の１桁の数字として扱い、ｕｎｉｘ（登録商標）オペレーティング・システムが備える文字列をシーザー暗号化するためのｒｏｔ１３関数等を利用してもよい。また例えば、このｒｏｔ１３関数が有する鍵である、整数の１３に換えて任意の１桁の整数を鍵に用い、同様の関数を１０進数の整数に対するシーザー暗号化の関数として定義して用いてもよい。 Next, the method for encrypting an integer according to the present invention sequentially performs the steps of substitutional encryption included in step S30. Step S30 includes the following steps S310 and S320. First, in the method for encrypting an integer according to the present invention, in step S310, the integer Yi is substitution-encrypted with the key R to generate the integer Zi. For example, the integer Zi is expressed by the following formula.

In the equation, R is an integer used as a key for substitution encryption, and Rot () is a function for substitution-encrypting the integer Yi using the key R. Specifically, Rot () can use a known Caesar encryption that handles a sequence of numbers obtained by describing an integer Yi using a notation system such as a decimal system as a character string. For example, assuming that the key R in Caesar encryption is an integer 3, the key R is assigned to each element of the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} consisting of one decimal digit. It is possible to add and replace each element of the set {3, 4, 5, 6, 7, 8, 9, 0, 1, 2} in the same order. Alternatively, unlike Caesar encryption, the key R is associated with information using a random order or information on the arrangement of specific numbers, and the corresponding set is {8, 0, 2, 4, 6, 3, 7, An order other than ascending order such as 9, 5, 1} may be used. However, the present invention is not limited to this, and the integer Yi may be converted to the integer Zi by reversibly converting the numbers in the numeration system so as to correspond to each other in a one-to-one correspondence according to a rule prepared in advance.
For example, an alphabetic alphabet may be treated as a one-digit number of 26 hexadecimal numbers, and a rot13 function or the like for Caesar encryption of a character string provided in a unix (registered trademark) operating system may be used. Further, for example, an arbitrary one-digit integer may be used as a key instead of the integer 13 which is the key of the rot13 function, and the same function may be defined and used as a Caesar encryption function for a decimal integer. Good.

  Next, the method for encrypting an integer according to the present invention retains information on the number of digits in step S320 if necessary. For example, when the most significant integer Zi generated by substitutional encryption is zero, this information may be held as the number of digits of the integer Yi before conversion. The information on the number of digits held may be used for confirmation of an integer generated at various stages of decoding to be described later. That is, unlike the operation of step S160 described above, the operation of step S320 can be used to hold information such as a change in the number of digits caused by substitutional encryption.

After performing step S10 and step S30 in succession, the method for encrypting an integer according to the present invention decrements the loop counter L in step S180. In step S190, it is determined whether the loop counter L is 0 or less. If the determination result is true, the process is terminated. If the determination result is false, the process proceeds to step S195, and the steps of step S10 are repeated with the integer Zi generated from the above-described equation (XII) as Xi.
In the repetition, the same values may be reused for the variables A, B, D, and K. The same value may be reused for the pair of variables E and F, but more preferably, the pair of variables E and F is changed depending on the value of the loop counter L so that the decryption by a third party is possible. It becomes possible to make it more difficult.
In this way, the above-described steps are repeated until the determination in step S190 becomes true, and an encrypted integer Zi is obtained. For example, when the loop counter L is set to 3, the steps including the above-described steps S10 and S30 are repeated three times.

  Therefore, in the method for encrypting an integer according to the present invention, the stages of encryption using the remainder to be included in step S10 and the substitution encryption included in step S30 until the loop counter L becomes 0 or less. These steps are performed repeatedly in succession. The stages of encryption using a power residue and the stages of substitutional encryption may be interchanged. That is, after the variable initialization in step S100, the substitutional encryption steps included in step S30 are performed, and thereafter, the encryption steps using the remainder to be included in step S10 are performed. S190 and step S195 may be performed as appropriate.

  Thus, in the method for encrypting an integer according to the present invention, only one of the encryptions can be performed by superimposing the steps of encryption using a power residue and the steps of substitutional encryption. Compared with the case of using it, it becomes possible to ensure extremely high secrecy.

  Next, the steps of decryption of another embodiment of the method for encrypting and decrypting an integer according to the present invention will be described.

The method for encrypting an integer according to the present invention secures a variable area and initializes the loop counter L in step S205 of FIG. The securing of the variable area may be the same as that in step S105 in the above-described encryption stages, and the encryption and decryption stages are built in one computer device and the common variable area is encrypted and decrypted. It may be used in both stages. The initialization of the loop counter L can repeatedly use the value of the loop counter L in the encryption corresponding to the decryption. For example, when the loop counter L is set to 3 in encryption, the loop counter L is set to 3 in decryption as well.
Next, the method for decrypting an encrypted integer according to the present invention implements the steps of decrypting the substitution cipher included in step S40 and the steps of decryption using the remainder to be included in step S20. . Here, the number to be decrypted is the encrypted integer Zi described above with reference to FIG.

式中、Ｒｏｔ^−１（）は、換字式暗号化により生成した整数Ｚｉを、鍵Ｒを用いて元の整数Ｙｉに復号化する関数である。 Step S40 includes the steps of S410 and S420. In step S410, information on the number of digits of the integer Zi is restored if necessary. This may be performed simply for verification with the information held in step S320 of the encryption process. In step S420, the substitution cipher is decrypted, and an integer Yi is generated from the encrypted integer Zi. For example, the integer Yi is decoded by the following equation.

In the equation, Rot ⁻¹ () is a function for decrypting the integer Zi generated by the substitution encryption into the original integer Yi using the key R.

  Next, in the method for decoding an integer according to the present invention, steps of decoding using a power residue are performed. Step S410, step S210, and step S220 included in step S20 are common to the decoding stages described above with reference to FIG. When (Yi + T) that is offset in step S150 is used, prior to the operation in step S220, (Yi-T) in which the offset is deleted is used instead of the integer Yi in the decoding of Xn.

  After performing step S40 and step S20 in succession, the method for decoding an integer according to the present invention decrements the loop counter L in step S280. In step S290, it is determined whether the loop counter L is 0 or less. If the determination result is true, the process is terminated. If the determination result is false, the process proceeds to step S295, and the steps of step S40 are repeated with the integer Xn generated from the above equation (XV) as Zi. In this way, the above-described steps are repeated until the determination in step S290 becomes true, and a decoded integer Xn is obtained. For example, when the loop counter L is set to 3, the steps consisting of the above steps S40 and S20 are repeated three times.

  Therefore, in the method for decrypting an integer according to the present invention, the stages for decrypting the substitution cipher included in step S40 and the remainder to be included in step S20 are used until the loop counter L becomes 0 or less. The decryption steps are performed repeatedly in succession. The steps of decrypting the substitution cipher and the steps of decoding using a power residue may be in the reverse order of the steps of encryption, and the whole may be exchanged. That is, after the variable initialization in step S200, the various stages of decryption using the remainder to be included in step S20 are performed, and then the various stages of decrypting the substitution cipher included in step S40 are performed, and step S280 is performed. Step S290 and step S295 may be performed as appropriate.

  Thus, in the method of decrypting an integer according to the present invention, the stages of decrypting the substitution cipher and the stages of decryption using a power residue are used in an overlapping manner, and the corresponding stages of encryption are used. It is possible to decrypt the encrypted integer Zi into an integer Xn equal to the original integer Xi.

[Personal information hiding procedure]
FIG. 5 shows an example of a personal information concealment procedure using an integer encryption method according to an embodiment of the present invention.
The encryption unit 100 is a unit that generates an encrypted integer from the input integer according to the present invention. The encryption unit 100 accepts an identifier including numbers and / or characters for identification possessed by a specific individual 20 as an integer type identifier 30. For example, the individual 20 is one of the members belonging to the business entity, etc., and the integer type identifier 30 includes a plurality of digits of integers that are used appropriately to identify a plurality of members in the business entity. It may be a member identifier. Further, for example, the integer type identifier 30 may be personal information associated with a specific individual 20 such as a credit card number. Typically, a specific individual 20 and an integer type identifier 30 are associated one-to-one, and are not associated with other members. In addition, when the member identifier includes English characters, the integer identifier 30 treats all or part of the English characters and numbers as a set of computer-processable character codes, and converts each character code to hexadecimal. The integer type identifier 30 may be configured as a modulo integer. In the method of encrypting and decrypting an integer according to the present invention, the thus converted hexadecimal integer is encrypted, and a set of original computer-processable character codes from the encrypted hexadecimal integer. Can be decrypted. Even in the case where the member identifier or the like is image data, the original image data is handled as a collection of hexadecimal integers, so that encryption and decryption are possible in the same manner.

The encryption unit 100 generates an integer part 32 or 34 by appropriately dividing based on the digit of the received integer type identifier 30. FIG. 5 shows that two integer parts 32 and 34 are generated from the integer type identifier 30, but the present invention is not limited to this, and the number of integer parts to be generated is two or more. But you can. Preferably, each integer portion 32, 34 is in the range of double precision type precision and may be an integer represented using a 64-bit binary number. For example, the integer-type identifier 30 is a 20-digit decimal number, and the encryption unit 100 can divide the identifier into four decimal numbers every five digits and hold the digit information 35 of each integer part. For such digit division, for example, the operation of step S150 of the embodiment shown with reference to FIG. 1 and the digit division method shown in Expression (XVII) may be used. As shown in the formula (XVII), each integer part digit information 35 has an integer part X ₁₅ , X ₁₀ , X ₅ , and X ₀ , with respect to the integer X before division. It can be information that the arbitrary integer X is 20th to 16th, 15th to 11th, 10th to 6th, and 5th to 1st.

  Identification application A (122), identification application B (124), and identification application C (126) can be any application that requires identification of a particular individual 20 using an integer type identifier 30. Although these three identification uses are illustrated in FIG. 1, the type, number, etc. of the identification uses can be appropriately set. It may be a computer network use within the business entity including transmission / reception or the like, an online banking business associated with the business entity, an insurance service, etc., or a recording act related to a business of a specific individual 20 by the business entity. Each identification application A (122), identification application B (124), and identification application C (126) may include information for distinguishing each other from each other in the encryption unit 100. That is, the unique information (62) for the identification application A, the unique information (64) for the identification application B, the unique information (66) for the identification application C, and the like may be different from each other. For example, the specific information for identification use may be a specific integer value, and different values may be used independently as the values of N or E included in the above formula (XIII).

  The encryption unit 100 uses the unique information (62) for the identification application A, the unique information (64) for the identification application B, or the unique information (66) for the identification application C for the received integer type identifier 30, respectively. The encryption calculation A (72), the encryption calculation B (74), or the encryption calculation C (76) can be performed independently for each unique information of the identification use. As described above, the encryption calculation is performed using the expanded form of the formula (XIII) under the condition that overflow occurs in the computer apparatus or the like used by the encryption unit 100 for the calculation including the power of the integer. Steps to generate a generalized integer. As a result of the encryption calculation, an encrypted integer A (42), an encrypted integer B (44), or an encrypted integer C (46) is generated.

Each of the generated encrypted integer A (42), encrypted integer B (44) or encrypted integer C (46) is independently associated with the corresponding identification application A (122), identification application B. (124) or for identification application C (126).
For example, when the identification application A (122) is the use of a computer network inside the business entity, the encryption unit 100 according to the present invention encrypts the identifier instead of the integer identifier 30 for identifying the specific individual 20. The converted integer A (42) can be provided to the computer network 132 of the entity through the information transmission path A (82). The information transmission path A (82) can be, for example, a local area network in the business entity.
Further, for example, when the identification use B (124) is a recording act or the like related to the business of the specific individual 20 by the business entity, the encryption unit 100 according to the present invention is an integer type for identifying the specific individual 20 The integer B (44) encrypted in place of the identifier 30 can be provided to the work management storage device 134 or the like of the business entity via the information transmission path B (84). The information transmission path B (84) can be, for example, a terminal device and a storage device for recording a visitor provided appropriately at the entrance and exit of the business entity.

The encryption unit 100 is not limited to the numerical data that can be processed by the computer, and the encryption unit 100 converts the encrypted integer C (46) in place of the integer identifier 30 for identifying the specific individual 20 into the information transmission path C ( 86) to an unspecified other person 136 or the like. The information transmission path C (86) may be in any form including oral or document. For example, the unspecified other person 136 is a person in charge of accepting a group insurance service business operated independently of the business entity, and the specific individual 20 who is a member of the business entity is informed of the information transmission path C ( 86), an encrypted integer C (46) can be transmitted as information for identifying itself in the group health service using a telephone of a general public line. This transmission includes any form such as a telephone call, a facsimile, and an electronic mail. Therefore, even if the voice of a telephone call or the like is heard by a third party around, the content of this transmission is intercepted by an irrelevant third party, the encryption means 100 according to the present invention. Since the integer C (46) encrypted by the above is an integer different from the integer identifier 30 for identifying the specific individual 20, the third party knows the integer identifier 30 from the intercepted content. I can't. That is, the personal information can be concealed by using the encryption means 100 according to the present invention.
In this way, in the encryption means 100 according to the present invention, an encrypted integer that is different for each identification purpose is generated from the integer type identifier 30 associated with the specific individual 20, and the individual of the specific individual 20 is generated. Information can be hidden.

Furthermore, the encryption unit 100 according to the present invention may collectively encrypt the identifiers of a plurality of members in a specific identification application.
The encryption means 100 according to the present invention can conceal specific personal information for specific identification applications. Since the integer type identifiers 30 received by the encryption unit 100 are different for each specific individual 20, an encrypted integer is generated for each individual integer type identifier 30. Therefore, even if the identification application A (122), the identification information A unique information (62), and the encryption calculation A (72) are constant, a plurality of members in the business entity having different integer type identifiers 30 , Each can obtain a different encrypted integer A (72).
For example, the network administrator of the business entity selects the specific information (62) of the identification use A according to the specific conditions such as the date and time of network maintenance, and thereby the network account information of a plurality of members of the business entity Each of these can be encrypted separately and collectively. The network administrator or the like can manage the conditions for selecting the unique information (62) for the identification use A, thereby collectively storing and managing the account information of a plurality of members. Furthermore, by concealing explicit account information from a third party who does not know this value because the integer F included in the formula (XVI) and formula (XVII) is difficult to be known or estimated by a third party. Is possible.

  In FIG. 5, the encryption means 100 according to the present invention is used from a specific individual 20 toward the computer network 132 of the business entity, the work management storage device 134 of the business entity, or an unspecified other person 136. Although the integer type identifier 30 is encrypted and transmitted, the encryption unit 100 according to the present invention can be used even if the subject of transmission and reception is switched. That is, the integer type identifier 30 stored by a server device (not shown) connected to the computer network 132 of the business entity is encrypted as an input to the encryption means 100 according to the present invention according to the above-described procedure. An integer A (42) or the like may be generated and transmitted to the specific individual 20. By doing so, the business entity can encrypt the identification information of the member or information related to the business, etc., and urge the employee to use the encrypted identifier, etc., to increase security. become.

  Specifically, the encryption unit 100 according to the present invention can be implemented using an integer calculation library or the like built in an application such as a general-purpose worksheet that can be executed by a personal computer or the like. Therefore, in the method of encrypting and decrypting integers according to the present invention, it is possible to encrypt and decrypt employee numbers and the like using an existing computer without preparing a dedicated computer or the like. is there. Furthermore, in the present invention, if the method for encrypting and decrypting an integer according to the present invention is not used, overflow in any stage of encryption or decryption occurs, and accurate encryption and / or decryption is performed. Therefore, it is possible to conceal personal information such as member identifiers from a third party who does not implement the method of the present invention.

[Another form of personal information hiding procedure]
FIG. 6 shows another example of the personal information hiding procedure using the method of encrypting an integer according to an embodiment of the present invention. Descriptions of parts common to those in FIG. 5 are omitted.

In FIG. 6, the encryption unit 100 can appropriately add an additional digit 37 to the integer type identifier 30 received from a specific individual 20. This additional digit may be an integer, similar to the integer type identifier 30. The number of digits of the additional digit 37 may be any number, for example, 2 digits, 3 digits, or 4 digits. The additional digit 37 may be added to the integer type identifier 30 from the left side or from the right side. Alternatively, the integer type identifier 30 may be divided at a predetermined digit and an additional digit 37 may be inserted, and an additional mode of the additional digit 37 may be set as appropriate. Further, the value of the additional digit 37 may be any value, and may be arbitrarily prepared by an entity or system using integer encryption and decryption according to the present invention, or may be determined in advance from the integer identifier 30. It may be generated by a procedure. For example, the lower two digits of the value obtained by calculating the sum of the digits of the integer type identifier 30 may be used as the additional digits 37. Further, the additional digit 37 may be prepared independently for each identification application depending on the identification application A (122), the identification application B (124), the identification application C (126), and the like.
By adding the additional digit 37, the identifier 38 with an additional digit, which is a new integer including the integer type identifier 30 and the number of each digit included in the additional digit 37, can be generated.

式中、Ｗ_３８は桁増しした識別子３８の値、Ｗ_３０は整数型の識別子３０の値、Ｗ_３７は追加の桁３７の値であり、Ｍは記数法の底である。例えば、これらの整数が１０進法の整数であるときには、Ｗ_３８の値はＷ_３０を１００００倍してＷ_３７を加えた値でありうる。記数法は１０進法に限らず、２進法、８進法又は１６進法等を任意に用いうる。桁増しする桁の数は４桁に限らず適宜設定しうる。 In one embodiment, the digitized identifier 38 is generated as an integer with an additional digit 37 added to the right of the integer type identifier 30. For example, when the integer type identifier 30 is a 16-digit integer and the additional digit 37 is a 4-digit integer, the identifier 38 with an additional digit is an integer with 20 digits, and the identifier 38 with an additional digit is expressed.

Where W ₃₈ is the value of identifier 38 incremented by digits, W ₃₀ is the value of integer type identifier 30, W ₃₇ is the value of additional digits 37, and M is the base of numeration. For example, when an integer of these integers are _decimal, the value of _{W 38} can be a value obtained by adding the _{W 37} by the _{W 30} 10000 times. The number system is not limited to the decimal system, and a binary system, an octal system, a hexadecimal system, or the like can be arbitrarily used. The number of digits to be added is not limited to four digits and can be set as appropriate.

  The stages of encryption for the increased identifier 38 including the additional digits 37 are performed depending on the flow diagram of the embodiment shown in FIGS. 1 and 3 or the identification application of the embodiment shown in FIG. This is similar to the encryption procedure that can be used. That is, the identifier 38 with the digit increased is represented as, for example, a 20-digit integer in the encryption unit 100, and is divided into four decimal numbers every five digits, and information that associates each divided integer part is held. Is done. Next, encryption using the remainder shown in Formula (XIII) is performed, and the offset and superposition of substitutional encryption can be used as appropriate to perform encryption. The encrypted integer generated by the various stages of encryption shown in FIG. 6 may be generated as computer-processable data using the computer network 132 or the work management storage device 134, etc. You may produce | generate with the form of the audio | voice or publication which the other person 136 can know.

  In one embodiment, an entity that uses a number or the like included in a member's date of birth as an identifier is included in the date of birth of the member using the method of encrypting and decrypting an integer according to the present invention. Arbitrary 4-digit numbers can be combined as additional digits 37 in addition to the numbers to be displayed. As a result, even if there are multiple members with the same date of birth, if any four-digit numbers are different from each other, the generated encrypted numbers are different from each other. The business entity or the like can identify the member using the encrypted integer.

  In this way, by adding the additional digits 37 having a predetermined number of digits, the integer input to the various stages of encryption of the encryption means 100 according to the present invention is the identification that the specific individual 20 or the like has. Is no longer the information for itself. By encrypting the integer obtained by adding digits, the encryption of the integer according to the present invention enables the encryption in which the personal information of the specific individual 20 or the like is further concealed.

[Another form of personal information hiding procedure]
FIG. 7 shows still another example of the personal information hiding procedure using the method of encrypting an integer according to an embodiment of the present invention. Descriptions of parts common to those in FIG. 5 are omitted.

  In the personal information concealment procedure shown in FIG. 7, it is shown that the encryption unit 100 according to the present invention can include the random number generation unit 39 and the offset information 40.

  In one embodiment, the encryption unit 100 according to the present invention can generate a random number using the random number generation unit 39 and encrypt the integer type identifier 30 based on the generated random number. Specifically, the generated random number can be used to select the substitution encryption key R included in step S30 described above with reference to FIG. Specifically, the selection of the substitution encryption key R may be performed by selecting a prime number nearest to the generated random number. That is, a prime number having the smallest difference from the generated random number may be selected from a set including prime numbers without duplication. Alternatively, the selection of the key R for substitution-type encryption is performed by preparing a number sequence in which respective elements (that is, prime numbers) are arranged in ascending or descending order from a set including prime numbers without duplication, and using the upper limit of random numbers as the number of elements of the set, An element (that is, a prime number) having the generated random number as a term number may be selected from the number sequence. Not limited to these, the association between random numbers and prime numbers can be designed as appropriate.

  In another embodiment, the encryption means 100 according to the present invention may perform the steps of encryption shown in FIG. 1 or FIG. 3 after offsetting the integer identifier 30 using the offset information 40. . That is, the encryption unit 100 according to the present invention can add or subtract a predetermined integer type constant to the integer type identifier 30. The predetermined constant to be added or subtracted is subtracted or added at the stage of decoding into the original integer, whereby the integer type identifier 30 can be correctly restored. The offset information 40 is not limited to a constant, and a different value may be selected and used each time the encryption unit 100 according to the present invention operates by accepting one integer type identifier 30. In selecting the different values, the random number generating means 39 described above may be used.

In another embodiment, the encryption unit 100 according to the present invention generates a random number using the random number generation unit 39, and selects the loop counter L in step S190 shown in FIG. 3 based on the generated random number. May be. The loop counter L in step S290 shown in FIG. 4 can have the same value as the loop counter L in step S190 shown in FIG. That is, the loop counter L can be selected from the group consisting of a predetermined positive integer, a positive integer obtained by encrypting the predetermined positive integer, and a positive integer that is randomly generated.
The loop counter L may set a lower limit in advance in order to ensure the strength of encryption. Further, an upper limit may be set in advance in order to shorten the time for calculation processing of encryption and decryption. Therefore, the value of the loop counter L in the method for encrypting and decrypting an integer according to the present invention is a predetermined positive integer according to a preset lower limit and / or upper limit range, and the predetermined positive integer is encrypted. Selected from the group consisting of a positive integer and a randomly generated positive integer. Thus, by making the loop counter L, which can be a variable independent of both the encryption using the power residue and the substitutional encryption, the trouble of decryption by a third party can be further increased.

  In still another embodiment, the encryption unit 100 according to the present invention may generate a public key that is offset using the offset information 40 with respect to the public key in the public key encryption technology. Specifically, after determining the variable E included in the formula (I), a predetermined integer constant may be added to or subtracted from the variable E to obtain the public key. Therefore, it is a useless procedure for a third party who does not know that this predetermined integer type constant is added or subtracted to use the public key for decryption. Therefore, by applying the offset information 40 to the public key, the confidentiality of information such as an encrypted integer is further enhanced.

  In another embodiment, the encryption unit 100 according to the present invention may encrypt the integer identifier 30 using both the random number generation unit 39 and the offset information 40 described above.

  In FIG. 7, the encryption process is represented as one arrow for each of the identification application A (122), the identification application B (124), the identification application C (126), etc., but FIG. As described above, in the encryption method according to the present invention, for each identification application, encryption using a power residue and substitution-type encryption can be alternately superimposed for a predetermined number of repetitions. The encrypted integer A (42), the encrypted integer B (44) or the encrypted integer C (46) generated for each identification application is information on random numbers generated using the random number generating means 39, If all of the encryption information using the power residue and the substitutional encryption information are not used accurately, neither can be decrypted correctly. Therefore, the personal information concealment procedure according to the embodiment of the present invention requires more types of information for accurate decryption, which further enhances the secrecy compared to known public key encryption technology and the like. Can be increased.

[Example of decryption procedure]
FIG. 8 shows an example of an encrypted integer decryption procedure according to an embodiment of the present invention. In FIG. 8, with respect to numerical values that can be processed by a computer for simplification of explanation, an encrypted integer A (42) and / or an encrypted integer B (generated by the encryption means 100 shown in FIG. 44), the same applies to decryption of an encrypted integer that can be transmitted in the form of a call or a document. Descriptions of portions common to FIG. 5 or FIG. 6 are omitted.

FIG. 8 shows that the decryption means 110 according to the present invention accepts an encrypted integer A ′ (52) and / or an encrypted integer B ′ (54), and generates an integer-type decrypted identifier 41. Indicates. Here, the encrypted integer A ′ (52) is the information obtained by the encrypted integer A (42) generated by the encryption unit 100 using the encryption calculation A (72) for the integer type identifier 30. After being transmitted to the computer network 132 or the like via the transmission path A (82), it may be further transmitted to the decoding means 110 according to the present invention via the information transmission path A ′ (102). Therefore, as an integer type numerical value, the encrypted integer A ′ (52) may be the same as the corresponding encrypted integer A (42).
Similarly, the encrypted integer B ′ (54) may be the same as the encrypted integer B (44).

The decryption means 110 according to the present invention performs the steps from step S200 to step S220 shown in FIG. 1 or FIG. 3 on the encrypted integer A ′ (52) and the encrypted integer B ′ (54). In practice, an integer-type decrypted identifier 41 may be generated.
The encrypted integer A ′ (52) is an encrypted integer A (42) generated by using the unique information (62) of the identification application A (122) in the encryption calculation A (72) by the encryption unit 100. It is possible. Since the specific information (62) can be the value of N or E and the value of K included in the above formula (VIII), for example, the value of E and the value of K used in the encryption calculation A (72) Can be used as the specific information (92) in the decoding calculation A (112).
Similarly, the value of E and the value of K used in the encryption calculation B (74) can be used as the unique information (94) in the decryption calculation B (114).
The unique information (92) and / or the unique information (94) may be stored in advance by the decryption means 110, and generated by one or both of the encryption means 100 and the decryption means 110 according to a predetermined procedure. It can be set as appropriate.

FIG. 8 shows a network or the like that can transmit computer-processable numerical values as the information transmission path A (82), the information transmission path B (84), the information transmission path A ′ (102), and the information transmission path B ′ (104). Although an information transmission path is shown, the encrypted integer can be transmitted from the encryption means 100 to the decryption means 110 via any transmission path or transmission means including, but not limited to, audio or a document.
In the method of encrypting and decrypting integers according to the present invention, the integers transmitted through these transmission paths or means are encrypted, and used for encryption under conditions that cause overflow. The original integer cannot be decoded unless the method of the present invention for decoding with a specific numerical value is used. Accordingly, in the present invention, personal information is concealed from a third party who may access a transmission path or a transmission means, and predetermined specific information and predetermined encryption and decryption methods are used. Only the implementation means of the present invention can correctly decrypt the personal information.

  Although FIG. 8 shows the encryption unit 100 and the decryption unit 110 separately, the present invention is not limited to this, and the encryption unit 100 and the decryption unit 110 may be integrated. The form of the transmission path or means for transmitting the encrypted integer may be a computer network, a telephone call including a public telephone line, a facsimile, an electronic mail, or the like, and can be arbitrarily set. Depending on the respective transmission path or means of transmission, a separate encrypted integer may be generated independently from one integer type identifier 30 and the additional digits 37 shown in FIG. The random number generator 39, the offset information 40, or a combination thereof shown in the figure may be used as appropriate to process the integer identifier 30 and then encrypt it. In this way, in the method of encrypting and decrypting an integer according to the present invention, an integer that conceals personal information is identified from one identifier such as a member identifier for each of various information transmission means using the identifier. Can be provided instead. Since the steps of encryption or decryption can be automatically performed using a computer device or the like, the user of the method according to the present invention can set an integer that conceals his / her personal information without being particularly conscious of these procedures. It can be used instead of its own identifier.

  FIG. 8 shows that the integer identifier 30 can be encrypted and transmitted to the entity's computer network 132 or the entity's work management storage device 134, etc., and then decrypted for the purposes described above. As shown, the decoding means 110 according to the present invention can be used even if the subject of transmission and reception is switched. That is, the integer identifier 30 stored in a server device (not shown) connected to the computer network 132 of the business entity is encrypted by the encryption means 100 according to the present invention and transmitted to the members, etc. The member or the like may decrypt the integer type identifier 30 using the decryption means 110 according to the present invention in accordance with the above-described procedure.

[Example 1: Example of encrypting integer using internal function of worksheet]
FIG. 9 shows an example of implementing the stages of encryption using a spreadsheet-type calculation application package according to an embodiment of the present invention. As a spreadsheet application software package, Microsoft Excel 2007 or the like can be used. However, the present invention is not limited to this, and package software that can perform integer power and remainder calculation can be arbitrarily used.
The integer cryptographic calculation worksheet 200 shown in FIG. 9 may be spreadsheet application data including cells arranged in a plurality of rows and columns. Individual cells included in the integer cryptographic calculation worksheet 200 may be identified using a set of row and column numbers.

The region of 2 rows and 1 column to 15 rows and 1 column and the region of 2 rows and 2 columns to 15 rows (2n + 1) columns included in the integer encryption calculation worksheet 200 are represented by steps S105 to S195 shown in FIG. Can be used for calculations related to encryption stages in
Specifically, the area from 2 rows and 1 column to 15 rows and 1 column is used to secure a variable area in step S105 shown in FIG. The region of 2 rows and 2 columns to 15 rows (2n + 1) columns is used for repeating step S10 and step S30 shown in FIG. FIG. 9 shows an example in which the same values are repeatedly used for the variables A, B, D, and K, and the variables E, F, and T change at each repetition depending on the loop counter.

  In an exemplary embodiment, a 2 × 1 cell may be used to store the encryption input Xi. The other cells in one column are a pair of prime numbers A and B, a product D of (A-1) and (B-1) and a least common multiple K, a public key and a secret key in decoding using a power residue. Integers Ei and Fi, substitution type encryption key Ri, offset Ti, loop counter L, and the like can be appropriately defined.

  That is, a cell of 3 rows and 1 column and a cell of 4 rows and 2 columns can be used to store two prime numbers A and B. The determination that the product of A and B exceeds the input Xi may be displayed using, for example, a cell with 3 rows and 2 columns. The product of A and B is the product N in the above-described formula (XIII), and N may be the base of the remainder calculation included in the integer encryption according to the present invention.

Furthermore, the integer encryption calculation worksheet 200 according to the embodiment of the present invention may store the expanded form of the product N in 3 rows and 2 columns using an array form. For example, the product N is treated as a 20-digit integer, and the 20th to 16th, 15th to 11th, 10th to 6th, and 5th to 1st positions of the product N are each represented as a 5-digit decimal number. It may be expanded into four integer parts consisting of N ₁₅ , N ₁₀ , N ₅ and N ₀ represented. These sets {N ₁₅ , N ₁₀ , N ₅ , N ₀ } may be stored in the form of an array in a 3 × 2 cell.

  The cell in 7 rows and 1 column can be used to store a D value that is the product of (A-1) and (B-1). The cell of 8 rows and 1 column can be used to store a K value that is the least common multiple of (A-1) and (B-1). The D value and / or K value may be a set of expanded integer parts, like the product N described above. A cell of 9 rows and 1 column can be used to store a D value or K value and a prime integer Ei. This integer Ei can be used as a public key in public key encryption technology. The cell of 11 rows and 1 column can be used to store the integer F that satisfies the above formula (XVI). This integer Fi can be used as a secret key in public key encryption technology. The cell of 13 rows and 1 column can be used to store the substitution encryption key Ri, the cell of 14 rows and 1 column can store the offset Ti, and the 15 rows and 1 column can store the loop counter L.

  Each cell in the 10 rows can be used to display whether or not the power of the integer Ei has caused an overflow in the integer operation incorporated in the worksheet. For example, the occurrence of the overflow may be represented by characters such as “error” indicating that the power value of the integer Ei exceeds the range that can be handled in the spreadsheet-type calculation application package. Alternatively, a numerical value or the like representing a false logical value may be displayed in response to the error. Similarly, each cell in the 12th row can be used to display whether or not the power of the integer Fi has overflowed in the integer operation built in the worksheet. On the condition that the power of the integer Ei or the power of the integer Fi generates an overflow, the encryption method using the power residue according to the present invention should be accurate using the expansion shown in the formula (XX). You can get a surplus. Specifically, it is possible to obtain an integer Y1 in 2 rows and 2 columns as an encrypted integer from an integer offset using an offset T1 of 14 rows and 2 columns with respect to the original integer Xi of 1 row and 2 columns. . At this time, the public key E1 and the secret key F1 resulting from the encryption using the power residue are stored in 9 rows and 2 columns and 11 rows and 2 columns, respectively.

  The variable with the subscript i may be an array. That is, each of Ei, Fi, Ri, and Ti assigned to one cell is {E1, E2,..., En}, {F1, F2,..., Fn}, {R1, R2,. {T1, T2, ..., Tn}, etc., or a sequence using an array format (each term may be defined by a recurrence formula or an arbitrary function as appropriate) may be included in these arrays for each row. Individual integers may be extracted and used.

In a further exemplary embodiment, two columns are used for encryption with a power residue. In FIG. 9, an integer Y1 obtained by performing encryption using a power residue once is stored in 2 rows and 2 columns. Three columns are used for substitution encryption. In FIG. 9, a converted integer Z1 generated by substitution encryption from Y1 is stored in two rows and three columns.
The values of variables resulting from the various stages of encryption are stored appropriately in the other two columns of cells. For example, the public key E1 is stored in the 9th and 2nd column, the secret key F1 is stored in the 11th and 2nd column, and the offset T1 is stored in the 14th and 2nd column. Similarly, for the other three columns of cells, the substitution encryption key R1 is stored in row 13 and column 3, and the loop counter (L-1) decremented once is stored in row 15 and column 3.
In this way, the converted integer Y1 and other variables E1, F1, and T1 in the encryption using the power residue are stored in the second column from the input Xi, and the third column is an integer converted from the integer Y1. Z1, the other variable R1, and the decremented loop counter (L-1) are stored.

  It is known in the art that an array or the like can be defined in one cell and a plurality of constants, variables, or calculation formulas can be arbitrarily included. That is, a cell of 2 rows and 1 column may store one integer Xi, or may store a number sequence {X1, X2, X3,..., Xk} using an array format. Here, Xk is the number of encryptable integers defined depending on the absolute value of the key in encryption using a power residue, and the number of integers included in this sequence is the same value as the least common multiple K Alternatively, the number may be K-1, K-2, K-3, or the like, and can be arbitrarily set. The first term X1 of the sequence {X1, X2, X3,..., Xk} may be 0, 1 or an integer of 2 or more. For example, when the value of the first term is an integer 2 and the number of integers included in the number sequence is K-1, the number sequence can include K-2 integers as a whole. In the method for encrypting integers according to the present invention, each of such K-2 integers can be separately encrypted to obtain an encrypted sequence of numbers, but the present invention is not limited to this. The number of integers included in the number sequence can be designed as appropriate. Therefore, the user of the present invention can also use an integer that is encrypted by appropriately extracting from a previously calculated encrypted sequence.

Next, the method of encrypting an integer according to the present invention converts the integer Y1 stored in 2 rows and 2 columns into an integer Z1 of 2 rows and 3 columns using substitution-type encryption. This conversion can use R1 in 13 rows and 3 columns as a key for substitutional encryption.
After the integer Z1 is obtained by substitutional encryption, the method of encrypting an integer according to the present invention is the value obtained by decrementing the loop counter L of 15 rows and 1 column and decrementing it to 15 rows and 3 columns (L -1) is stored. If the decremented value is less than or equal to zero, the encryption steps are terminated. If the value of the decremented loop counter is greater than zero, the value of Z1 in 2 rows and 3 columns is treated like the value of Xi in 2 rows and 1 column, the various stages of encryption using the power residue, and the substitution cipher By repeating the steps, the encrypted integer is obtained as Z2 in 2 rows and 5 columns.

  In this way, the method for encrypting an integer according to the present invention repeatedly performs a combination of encryption using a power residue and substitution-type encryption, and the condition that the loop counter becomes zero or less is 2 lines ( In the 2n + 1) column, an integer encrypted as an integer Zn is obtained.

[Example 2: Decoding an integer using an internal function of a worksheet]
FIG. 10 illustrates an example of implementing the decryption stages using a spreadsheet-style calculation application package according to one embodiment of the present invention. The integer decoding calculation worksheet 220 shown in FIG. 10 may be spreadsheet application data including cells arranged in a plurality of rows and columns. Individual cells included in the integer decryption calculation worksheet 220 may be identified using a set of row and column numbers.

The region of 2 rows and 1 column to 15 rows and 1 column and the region of 2 rows and 2 columns to 15 rows (2n + 1) columns included in the integer decryption calculation worksheet 220 are the steps S205 to S295 shown in FIG. Can be used for calculations related to encryption stages in
Specifically, the area from 2 rows 1 column to 15 rows 1 column is used for securing the variable area and initializing the loop counter L in step S205 shown in FIG. The region from 2 rows and 2 columns to 15 rows (2n + 1) columns is used for repeating step S40 and step S20 shown in FIG.

  In an exemplary embodiment, a 2 × 1 cell may be used to store the decoding input Zi. The other cells in one column are the same as the variables in the decoding using the remainder shown in FIG. That is, in the process of encryption corresponding to the decryption input Zi, the values already used can be used for the respective variables A, B, D, K, Ei, Fi, Ri, Ti. Therefore, in decryption, the value of the corresponding encryption variable may be reused to initialize the loop counter L corresponding to the input Zi.

  In the decryption of the integer according to the present invention, the original integer is decrypted from the encrypted integer by a procedure reverse to the corresponding encryption. For example, when power residue and substitution encryption are repeated in this order combination, the corresponding decryption repeats substitution and power residue decryption the same number of times in this order.

  First, a procedure for converting the input Zi using substitution decoding will be described. In substitution decoding, the integer Zn stored in 2 rows and 1 column is converted into an integer Yn in 2 rows and 2 columns. The key for substitution encryption for this conversion is Rn in 13 rows and 2 columns, and the Rn is 13 rows (2n + 1) in the integer encryption calculation worksheet 200 of FIG. 9 used for the corresponding encryption. Can be the same as the Rn in the column.

  Next, in the decoding of the integer according to the present invention, decoding using a power residue is performed on Yn of 2 rows and 2 columns, and the offset is eliminated to obtain the integer Xn-1 in 2 rows and 3 columns. . Fn of 11 rows and 3 columns is used as the exponent of the power residue, and Tn of 14 rows and 3 columns is used as the offset value. The decoding method using the power residue according to the present invention can obtain an accurate power residue by using the expanded form shown in Expression (XX).

  After the integer Xn−1 is obtained by decoding using the power residue, the method of decoding the integer according to the present invention decrements the loop counter L of 15 rows and 1 column, and the value decremented to 15 rows and 3 columns. (L-1) is stored. If the decremented value is less than or equal to zero, the decoding steps are terminated. If the value of the decremented loop counter is greater than zero, the value of Xn-1 in 2 rows and 3 columns is treated like the value of Zi in 2 rows and 1 column, and the stages of substitution decoding and the power residue are determined. The decoding steps used are repeated to obtain an integer decoded as Xn-2 in 2 rows and 5 columns.

  Each cell in the 10th and 12th rows can be used to display whether or not the power of the integer Ei and the integer Fi has overflowed in the integer operation incorporated in the worksheet, as in the encryption. On the condition that the power by the integer Ei or the power by the integer Fi generates an overflow, the decoding method using the power residue according to the present invention uses the expansion form shown in Equation (VII) before conversion. You can expand integers to get the exact power remainder.

In a further exemplary embodiment, two columns are used for decoding with a power residue. In FIG. 10, in 2 rows and 2 columns, an integer Y1 obtained by performing decoding using a power residue once is stored. Three columns are used for substitution decoding. In FIG. 10, a converted integer Z1 generated by substitution decoding from Y1 is stored in 2 rows and 3 columns.
In the other two columns of cells, the values of variables resulting from the various stages of decoding are stored as appropriate. For example, the public key E1 is stored in the 9th and 2nd column, the secret key F1 is stored in the 11th and 2nd column, and the offset T1 is stored in the 14th and 2nd column. Similarly, for the other three columns of cells, the substitution encryption key R1 is stored in row 13 and column 3, and the loop counter (L-1) decremented once is stored in row 15 and column 3.
In this way, the converted integer Y1 and other variables E1, F1, and T1 in the encryption using the power residue are stored in the second column from the input Xi, and the third column is an integer converted from the integer Y1. Z1, the other variable R1, and the decremented loop counter (L-1) are stored.

  In this way, the method for decoding an integer according to the present invention repeatedly executes a combination of substitution decoding and decoding using a power residue, on the condition that the loop counter becomes zero or less. An integer decoded as an integer X1 in 2n + 1) columns is obtained. By performing these decryption steps in the reverse order of the corresponding encryption steps, the integer X1 obtained in 2 rows (2n + 1) columns of the integer decryption calculation worksheet 220 shown in FIG. , Which is equal to the original integer Xi input in 2 rows and 1 column of the integer encryption calculation worksheet 200 shown in FIG.

  By using the steps of the integer encryption and decryption method according to the present invention, it is possible to generate an overflow in the calculation process at any of the steps of encryption and decryption using a power residue. In a calculation means that does not use the method of the invention, neither correct encryption nor decryption can be performed. Furthermore, by superimposing substitutional encryption and decryption in addition to the power residue, it is possible to dramatically improve the confidentiality of information in the method of the present invention. As a result, the method of encrypting and decrypting integers according to the present invention and the means for implementing the method can provide high confidentiality to information in the form of integers related to personal information and the like. .

[Time required for decoding]
The time required in the case of searching for the possibility of a decipherment with respect to the integer produced | generated using the method which encrypts the integer based on this invention is illustrated. This can be the computation time for decrypting the secret information using a so-called brute force attack.
Assuming that the computing power of the computer is 1 petaflop per second, that is, 10 15 instructions per second, the computer can execute approximately 10 22 instructions per year.
In the method for encrypting an integer according to the present invention, it is assumed that the original integer is a 6-digit decimal number, and encryption using a power residue and substitution-type encryption are continuously executed. In the case of encryption, when this continuously executed encryption is repeated five times, the total number of independent five-fold substitutional encryption combinations included in the five-time repeated encryption is 10 30 ( That is, 10 6 to the 5th power), and the time required for the brute force calculation by the computer can be calculated to be about 10 8 years (that is, about 100 million years). In the encryption method according to the present invention, encryption using a quintuple independent power residue is further performed, and the keys used for these encryptions can be randomly selected by random number generation means. The time required for decoding can be astronomical figures well over 100 million years. Therefore, the present invention can provide a form that can be concretely implemented and commercialized for a target to which random numbers can be applied, and has the effect of dramatically improving the difficulty of decoding compared to simple logic. is there.
In this way, in the present invention, it is possible to generate an encrypted integer with extremely high secrecy from the original integer by repeatedly performing encryption using a remainder and substitution-type encryption a plurality of times in succession. Is possible. In the present invention, it is possible to encrypt and decrypt identification information or the like for referring to confidential information with high confidentiality by enlarging the effort of decryption by a third party.

  As mentioned above, although demonstrated using embodiment of this invention, the technical scope of this invention is not limited to the range as described in the said embodiment. Various modifications or improvements can be added to the above embodiment. It is apparent from the scope of the claims that the embodiments added with such changes or improvements can be included in the technical scope of the present invention.

20 Specific Individual 30 Integer Type Identifier 32, 34 Integer Part 35 Integer Part Digit Information 37 Additional Digit 39 Random Number Generator 40 Offset Information 41 Integer Type Decoded Identifier 42, 44, 46, 52, 54 Encryption Integer 62, 64, 66, 92, 94 Specific information 72, 74, 76 Encryption calculation 82, 84, 102, 104 Information transmission path 100 Encryption means 110 Decoding means 112, 114 Decryption calculation 122, 124, 126 Identification applications

Claims (23)

A method in which a computer device encrypts and decrypts an integer Xi excluding 0 and 1 ,
A power residue encryption step in which the computer device encrypts the input integer Xi into an integer Yi;
A power residue decrypting step, wherein the computing device decrypts the encrypted integer Yi into the integer Xi;
The power residue encryption step includes:
Computing device, the method comprising the product N exceeds the integer Xi input to generate two prime numbers A and B, and stores the N, A, and B in the storage means,
The computer device converts the product N into an M-ary notation based on an integer M, divides the number of digits in the M-ary notation of the product N into at least two, and an integer corresponding to each of the divided digits Generating an expanded form of the product N consisting of a monomial sum consisting of a product of a part and a power of M with the number of digits as a power exponent, and a set of integer parts corresponding to the respective digits included in the expanded form Generating information for associating the respective integer parts comprising information of digits of the respective integer parts;
Storing the product N and the generated information relating the respective integer parts and the respective integer parts in a storage means, and
A computer generating a product D of (A-1) and (B-1) and a least common multiple K of (A-1) and (B-1), and storing the D and K in a storage means; ,
The computer device generates a number E that is prime with D or K, and determines whether or not the integer Xi raised to the E power causes an overflow in the integer operation of the calculation means of the computer device. Repeating the generation of the number E that is prime with D or K and the determination until
A step in which the computer stores E in which the determination result is true in a storage means ;
The computer device converts the integer Xi into an M-ary notation based on the integer M, divides it into the same number of digits as the product N, and converts the integer part corresponding to each of the divided digits and the number of digits into a power exponent Generating an expanded form of the integer Xi consisting of a monomial sum of products of the powers of M and a set of integer parts corresponding to the respective digits included in the expanded form and the digits of the respective integer parts Generating information associating each of said integer portions of information;
Storing in the storage means the integer Xi and the generated information relating the integer part and the integer part;
In the E power multiplication operation of the integer Xi described in the following equation, in which the computer apparatus uses the generated number E as a power exponent, each of the integer Xi based on the information of the digits of the stored integer part of the integer Xi The integer Xi is raised to the E power and N is calculated by the remainder calculation for calculating the difference between the generated integers of the product N for each digit. Calculating a modulo integer Yi, generating an integer Yi obtained by encrypting the integer Xi, and storing it in a storage means ;
The integer Yi is converted to an M-ary notation based on the integer M, divided into the same number of digits as the product N, and an integer part corresponding to each of the divided digits and the number of digits as an exponent Generates an expanded form of the integer Yi consisting of a monomial sum consisting of a product with a power, and includes a set of integer parts corresponding to the respective digits included in the expanded form and information on the digits of the respective integer parts Generating information associating the respective integer parts ;
Storing the integer Yi and the generated information associating the respective integer part and the respective integer part in a storage means, and

Including
The power residue decoding step includes:
A step in which the computer device generates F that satisfies the following expression with m as an arbitrary integer and stores it in the storage means ;

In the F multiplication operation of the encrypted integer Yi described in the following equation, where the computer device uses the stored number F as a power exponent, based on the information of the digits of the respective integer portions held of the integer Yi, the expanded by replacing the calculation between the integer part corresponding to each digit, and the generation of the product N for each digit, a remainder calculation for calculating a difference between the respective integer part, the integer Yi Shi multiply F Calculating an integer Xn modulo N;
And a computer device storing the integer Xn in a storage means and decrypting the encrypted integer Yi into Xn, that is, Xi. A method for encrypting and decrypting an integer.

  The method for encrypting and decrypting an integer according to claim 1, wherein the information relating the respective integer parts is information of digits of the respective integer parts. Furthermore, before generating the integer Yi computer device has converts the integer Xi, the steps of the computer apparatus by adding the integer T follows the integer Xi from the integers Xi replaced with the integer Xi,
After the computer device decodes the converted integer Yi into an integer Xn, subtracts the integer T from the integer Xn to replace the integer Xn;
A method of encrypting and decrypting an integer according to claim 1 comprising: The method of claim 3, wherein the integer T is an integer generated randomly by a computer device . And further comprising the step of the computer device selecting a key for encryption according to a random rule,
The generation of E generates a set of numbers for which the computer device is prime with D or K, that is, a number of key candidates for encryption, and the computer device generates the key candidates for encryption generated above. The method for encrypting and decrypting an integer according to claim 1, wherein the integer is generated by the step of selecting according to the random rule from the set . further,
A substitution encryption step where the computer device converts the integer to a substitution-encrypted integer using substitution encryption ;
A substitution decoding step wherein the computing device decrypts the substitution-encrypted integer using substitution decoding ;
An encryption step of encrypting an integer by executing either the power residue encryption step or the substitution encryption step first, and then executing the remaining one;
Corresponding to the execution order of the substitution type encryption step and the power residue encryption step, the power residue decryption step is executed first when the substitution type encryption step is executed first, and the power residue encryption step is given first. If executed, the substituting decryption step is executed first, and then the remaining one is executed to decrypt the encrypted integer, and
A method of encrypting and decrypting an integer according to claim 1 comprising: The key of substitution cipher of the computer apparatus is an integer you select by random rules, how to encrypt and decrypt integer of claim 6. The substitution cipher reduction are either single expressions encryption, multi expressions encryption and automated key encryption,
The substitutional decryption is one of single table decryption, multi-table decryption and automatic key decryption corresponding to the substitutional encryption .
A method for encrypting and decrypting an integer according to claim 6. The encryption step for encrypting the integer performs the power residue encryption step first, followed by the substitution encryption step,
The decryption step of decrypting the encrypted integer is to perform the substitutional decryption step first, and then perform the power residue decryption step,
In the substitution encryption step, the computer device converts the integer Yi into an integer Zi;
7. The method of encrypting and decrypting an integer according to claim 6, wherein in the substitution decoding step, the computer device converts the integer Zi into the integer Yi . Encrypting step of computing device continuously and substitution encrypting step and the remainder encrypting step should said, and decoding step of computer device to continuously and remainder decoding step to said substitution decoding step, each of at least two The method for encrypting and decrypting an integer according to claim 9, wherein the integer is repeated a plurality of times. The encryption step for encrypting the integer performs the substitution encryption step first, followed by the power residue encryption step,
The decryption step for decrypting the encrypted integer is to perform the power residue decryption step first, and then perform the substitutional decryption step,
7. The method of encrypting and decrypting an integer according to claim 6, wherein the integer Xi is an integer converted by the computer device performing the substitution encryption step. An encryption step in which the substitution encryption step and the power residue encryption step executed by the computer device are consecutive, and a decryption step in which the power residue decoding step and the substitution decryption step are executed by the computer device , respectively. At least 2 or more you practice the same plurality of times repeatedly, a method for encrypting and decrypting integer of claim 11. Wherein at least two of the plurality of times of repeated the same, predetermined positive integer, any computer device said predetermined positive integer encrypted positive integer, and a positive integer computing device occurs at random it is either a method of encrypting and decrypting integer of claim 9 or 11. The integer Xi from some or all of the letters or numbers computing device is included in the identifier is reversibly converted integer, a method for encrypting and decrypting integer of claim 1. The integer Xi from some or all of the 1-dimensional image reversibly converted from the computer apparatus 1-dimensional images or two-dimensional image, which is reversibly converted integer, an integer of claim 1 How to encrypt and decrypt. 2. The method of claim 1, further comprising: prior to encryption, the computer device replacing at least one digit with the integer with the added digits by adding at least one digit to the original integer. Method. The method of claim 16, further comprising the step of removing the added at least one digit from the decrypted integer after decryption by the computing device . The step of generating F and storing it in the storage means includes:
Whether the computer apparatus generates a number F satisfying the mathematical expression [Expression 33], where m is an arbitrary integer, and whether or not the integer Yi raised to the F power causes overflow in the integer operation of the calculation means of the computer apparatus Repeating the generation of the number F and the determination until the determination result is true;
The method for encrypting and decrypting an integer according to claim 1, further comprising a step of storing, in a storage unit, F for which the determination result is true. A computer program for causing a computer to execute the steps of the method according to claim 1. A device for encrypting and decrypting an input integer Xi excluding 0 and 1 ,
It generates two prime numbers A and B exceeds the integer Xi which the product N is input, the N, A, a prime generating unit for storing a B in the storage means, the product N integers M and base M The number of digits in M notation of the product N is divided into at least two, an integer part corresponding to each of the divided digits, and a power of M with the number of digits as a power exponent; Generating an expanded form of the product N consisting of a monomial sum consisting of products of the above, and each of the integer parts corresponding to each digit included in the expanded form and each digit part information of the integer part A prime number generator for generating information relating the integer part of
A product D of (A-1) and (B-1) and a least common multiple K of (A-1) and (B-1) are generated, the D and K are stored in a storage means, and the D or K To generate a number E that is prime and to determine whether the integer Xi raised to the E power causes an overflow in the integer operation of the calculation means of the computer device, and until the determination result is true, The generation of the number E that is prime with K and the above determination are repeated, and E for which the determination result is true is stored in the storage means,
The integer Xi is converted into an M-ary notation based on the integer M, divided into the same number of digits as the product N, and the integer part corresponding to each of the divided digits and the power of M with the number of digits as the exponent Generating an expanded form of the integer Xi consisting of a monomial sum consisting of a product of and a set of integer parts corresponding to the respective digits included in the expanded form and the digits information of the respective integer parts A generator that generates information that associates each integer part;
In the E-power operation of the integer Xi described in the following equation using the stored number E as a power exponent, it corresponds to each digit based on the information of the digits of the integer part held in the integer Xi An integer Yi modulo N by multiplying the integer Xi to the E power by performing a remainder calculation that expands by replacing the calculation between the integer parts and calculates the difference between the generated integer N and the respective integer parts for each digit. And the integer Yi is divided into the same number of digits as the product N, and a monomial consisting of the product of the integer part corresponding to each of the divided digits and the power of M with the number of digits as the exponent A development form consisting of a sum is generated, and a set of integer parts corresponding to each digit included in the development form and information associating each integer part consisting of information on the digits of each integer part are generated. Remainder encryption An execution unit,

The product N and the generated information associating the respective integer part and the respective integer part, the integer Xi and the generated information associating the respective integer part and the respective integer part, and the integer Yi And the generated related information holding unit for holding the respective integer parts and the information for associating the respective integer parts,

a secret key generation unit that generates F that satisfies the following expression, where m is an arbitrary integer, and is stored in the storage unit ;

In the F power multiplication operation of the encrypted integer Yi described in the following equation using the stored number F as a power exponent , each of the digits is based on the information of the digits of the held integer portions of the integer Yi. The integer Yi is raised to the F power and N is modulo by the remainder calculation for calculating the difference between the generated integers of the product N for each digit. A remainder decryption execution unit for decrypting the encrypted Yi into Xn, that is, Xi

A device that encrypts and decrypts integers, including: The secret key generation unit
By using m as an arbitrary integer, a number F that satisfies the mathematical formula [Equation 36] is generated, and it is determined whether or not the integer Yi raised to the F power causes overflow in the integer operation of the calculation means of the computer device. Means for repeating the generation of the number F and the determination until the determination result is true;
21. The apparatus for encrypting and decrypting an integer according to claim 20, further comprising: means for storing in the storage means F for which the determination result is true. A system for encrypting and decrypting an integer Xi,
Generates two prime numbers A and B exceeds the integer Xi which the product N is input, the N, A, a prime number generating means for storing the B in the storage means, the product N integers M and base M The number of digits in M notation of the product N is divided into at least two, an integer part corresponding to each of the divided digits, and a power of M with the number of digits as a power exponent; Generating an expanded form of the product N consisting of a monomial sum consisting of products of the above, and each of the integer parts corresponding to each digit included in the expanded form and each digit part information of the integer part Prime number generating means for generating information relating the integer part of
A product D of (A-1) and (B-1) and a least common multiple K of (A-1) and (B-1) are generated, the D and K are stored in a storage means, and the D or K To generate a number E that is prime and to determine whether the integer Xi raised to the E power causes an overflow in the integer operation of the calculation means of the computer device, and until the determination result is true, The generation of the number E that is prime with K and the above determination are repeated, and E for which the determination result is true is stored in the storage means,
The integer Xi is converted into an M-ary notation based on the integer M, divided into the same number of digits as the product N, and the integer part corresponding to each of the divided digits and the power of M with the number of digits as the exponent Generating an expanded form of the integer Xi consisting of a monomial sum consisting of a product of and a set of integer parts corresponding to the respective digits included in the expanded form and the digits information of the respective integer parts Generating means for generating information relating each integer part;
In the E-power operation of the integer Xi described in the following equation using the stored number E as a power exponent, it corresponds to each digit based on the information of the digits of the integer part held in the integer Xi An integer Yi modulo N by multiplying the integer Xi to the E power by performing a remainder calculation that expands by replacing the calculation between the integer parts and calculates the difference between the generated integer N and the respective integer parts for each digit. And the integer Yi is divided into the same number of digits as the product N, and a monomial consisting of the product of the integer part corresponding to each of the divided digits and the power of M with the number of digits as the exponent A development form consisting of a sum is generated, and a set of integer parts corresponding to each digit included in the development form and information associating each integer part consisting of information on the digits of each integer part are generated. Remainder encryption And means,

The product N and the generated information associating the respective integer part and the respective integer part, the integer Xi and the generated information associating the respective integer part and the respective integer part, and the integer Yi And the generated related information holding means for holding the respective integer parts and the information relating the respective integer parts ,
a secret key generating means for generating F that holds the following expression with m as an arbitrary integer and storing it in the storing means ;

In the F power multiplication operation of the encrypted integer Yi described in the following equation using the stored number F as a power exponent , each of the digits is based on the information of the digits of the held integer portions of the integer Yi. The integer Yi is raised to the F power and N is modulo by the remainder calculation for calculating the difference between the generated integers of the product N for each digit. Generating an integer Xn to be stored and storing it in the storage means, whereby the encrypted Yi is decrypted into Xn, that is, Xi ;

A system that encrypts and decrypts integers, including The secret key generation means includes
By using m as an arbitrary integer, a number F that holds the mathematical formula [Equation 39] is generated, and it is determined whether or not the integer Yi raised to the F power causes overflow in the integer operation of the calculation means of the computer device. Means for repeating the generation of the number F and the determination until the determination result is true;
23. The system for encrypting and decrypting an integer according to claim 22, further comprising: means for storing in the storage means F for which the determination result is true .

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