JP5208642B2 - 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.

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 at the encryption stage and a remainder operation whose modulus is a product of two prime numbers, and a prime factor by using a power root that requires a prime factor of the product in decryption. If the password is not known, the decryption becomes difficult, thereby ensuring the security of the encryption.
Furthermore, in order to ensure security in transmission / 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 daily use of an identifier in a form that is easy for the identified person to remember has the opportunity to leak personal information to others who can obtain this identifier by some means. There was a risk of occurring. In particular, in a society where a computer network has been developed, when information on an identifier that can be easily remembered is transmitted and received through the computer network without processing, the information on the identifier leaks from a communication record of a communication relay device, etc. There was a danger, and security for specific personal information could not be secured. In large corporations, etc., a common number is used for multiple personal information that requires security, such as an identifier for identifying the member, the health insurer number of the member, and an internal bank account number. When one of them leaks, there is a problem that other personal information is also exposed to the risk of leakage. Furthermore, 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, so individuals in various forms including voice or documents. There was a need for a way to hide information.

The present invention provides a method for encrypting an identifier associated with personal information under conditions that cause the computer to overflow, thereby restoring the original identifier to a third party not based on the method of the present invention. The purpose is to generate identifiers that cannot be used. Accordingly, an object of the present invention is to ensure the security of personal information transmitted and received via information communication including a computer network or the like.
Another object of the present invention is to be able to use a common identifier or the like for a plurality of pieces of personal information that need to be individually secured.

The present inventor uses a calculation procedure in which a computer intentionally generates a large number that causes an overflow in the calculation process, and performs encryption and decryption while avoiding the overflow in a predetermined procedure. A method for concealing information has been found and the present invention has been completed.
The present invention provides the following solutions.

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、整数を暗号化し復号する方法。

(1) A method in which a computer device encrypts and decrypts an integer Xi excluding 0 and 1 , wherein the computer device generates two prime numbers A and B that exceed the integer Xi with the product N input thereto , The step of storing N, A, B in the storage means, and the computer device calculates the product D of (A-1) and (B-1) and the least common multiple K of (A-1) and (B-1). Generating and storing the D and K in the storage means, and the computer device generates a number E that is prime with D or K, and the E power of the integer Xi is a digit in the integer operation of the calculation device of the computer device It is determined whether or not an overflow occurs, and the step of repeating the generation of the number E that is prime with D or K and the determination until the determination result is true, and the computer device in which the determination result is true Storing in the storage means, The computer device converts the integer Xi into M-decimal notation based on the integer M, divides the number of digits in the M-ary notation of the integer Xi into at least two, and corresponds to each of the divided digits Generating an unfolded form of the integer Xi consisting of a monomial sum consisting of a product of an integer and a power of M with the number of digits as a power exponent, and a computer device having the stored number E as a power exponent In the E-power operation of the integer Xi described in the following equation, the integer Xi is calculated by replacing the integer Xi with a calculation between integers corresponding to the respective digits using the expansion form of the integer Xi. Calculating an integer Yi modulo N by N to the power of E; and storing the integer Yi obtained by encrypting the integer Xi in a storage means ;

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 ;

The computer device calculates the integer Xn modulo N by multiplying the encrypted integer Yi described in the following equation with the stored number F as a power exponent ;
A computer device storing the integer Xn in a storage means, and decrypting the encrypted integer Yi into Xn, that is, Xi.

In the encryption and decryption method of the present invention, 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 to be input. 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, 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 the like, or has a built-in script or spreadsheet, etc. It can be a machine language program or the like called by a 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.
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。数式（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 of 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 Expression (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.

  Next, in the method for encrypting and decrypting an integer according to the present invention, an integer F represented by Formula (II) is prepared. The integer F may be any factor as long as it is a factor of the expression (m × K + 1) on the right side that can be generated based on the prime numbers A and B selected including arbitrary m.

  Next, in the method of encrypting and decrypting an integer according to the present invention, the original Xi is decrypted from the encrypted integer Yi by using Formula (III) and using F obtained as described above. sell.

In this way, in the method for encrypting and decrypting integers according to the present invention, since E in Formula (I) is selected under the condition that overflow occurs, in a computer apparatus or the like that does not use the method of the present invention Cannot accurately obtain the encrypted integer Yi, and it is possible to implement encryption with high information confidentiality.
The stages of integer encryption according to the present invention are different from the known RSA ciphers in the stages of integer encryption according to the present invention. Instead of the prime number itself, an integer obtained by subtracting 1 from the prime number is used for the remainder operation. Furthermore, the product of these integers and the least common multiple and prime integer are used for the power. Therefore, in the integer encryption according to the present invention, an unpredictable integer can be generated from a known technique using a prime number as it is. Therefore, in the present invention, high security can be ensured based on the fact that F is difficult to be known by a third party.

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、コンピュータ装置が、前記置き換えたＸｕ又はＸｄを用いて剰余計算を実施する、（１）に記載の整数を暗号化し復号する方法。 (2) In the expanded form, the computer device divides the Xi digit into two, and generates the integer Xu represented by the upper digit of the divided digit and the integer Xd represented by the divided lower digit And expand by replacing Xi using the following equation:

Where M is the base of the numeration system, Cd is the number of the lower digits, Cd is at least 1, and the computing device performs a remainder calculation using the replaced Xu or Xd. A method for encrypting and decrypting the integer described in (1).

In this way, in the method of encrypting and decrypting an integer according to the present invention, after selecting E in the above formula (I) under the condition that overflow occurs, Xi is calculated using the formula (IV). Yi that is an encrypted integer can be obtained accurately by expanding and avoiding overflow.
Therefore, in the calculation of the power of Xi expressed as the above-described mathematical formula (I), the power integer calculation process is performed by appropriately dividing the original integer Xi into upper and lower digits using the mathematical formula (IV). It becomes possible to avoid overflowing digits.

(3) wherein said integer Xi, the computer device, the part or all of a character or number included in the identifier is reversibly converted integer, for decrypting encrypted integers described in (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.

(4) The integer Xi is an integer reversibly converted by a computer device from a part or the whole of a one-dimensional image reversibly converted from a one-dimensional image or a two-dimensional image. 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.

(5) The computer device further includes the step of replacing the integer Xi with an integer Wi increased in number by adding at least one digit to the integer Xi prior to encryption. (1) To the method of encrypting and decrypting the integer according to any one of (4).

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 encrypts the 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. By using the two-digit integer properly as an input for the conversion, a plurality of encrypted integers can be generated and used. 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 an integer associated with a character string including personal information such as a date of birth is encrypted with an arbitrarily selected number of digits. By doing so, a plurality of encrypted integers can be generated and used properly.

(6) The method for encrypting and decrypting an integer according to (5), further comprising the step of the computer device removing the added at least one digit from the decrypted integer Wi after decryption.

  In this way, in the method for encrypting and decrypting an integer according to the present invention, it becomes possible to completely decrypt the original integer Xi from the integer Wi with the digit increased after decryption.

(7) The step of generating F and storing it in the storage means is such that a computer device generates a number F that satisfies the mathematical formula [Equation 12], where m is an arbitrary integer, and the integer Yi raised to the F power is a computer 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 F in the storage means,
The step of calculating the integer Xn is such that the computer device converts the integer Yi into an M-decimal notation based on the integer M, and divides the number of digits in the M-ary notation of the integer Yi into at least two or more. Generating a development form of the integer Yi consisting of a monomial sum consisting of a product of an integer corresponding to each of the divided digits and a power of M with the number of digits as a power exponent; In the power multiplication operation of the integer Yi with the generated number F as a power exponent, by using the expansion form of the integer Yi and replacing the calculation between integers corresponding to the respective digits, the remainder calculation is performed. The method of encrypting and decrypting an integer according to any one of (1) to (6), further comprising: calculating an integer Xn modulo N by raising the integer Yi to the power of F.

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.

(8) A computer program for causing a computer device to execute each step of the method according to any one of (1) to (7).
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, any data to be recorded on a storage medium and / or numerical values included in a file allocation table or the like for referring to a specific storage area of the storage medium are encrypted And can be decrypted. 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. Information encoded using the encryption and decryption methods according to the above can be stored. Therefore, 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.

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復号準備部と、

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に復号する復号部と、を含む、整数の暗号化及び復号装置。

（１０） 前記復号準備部は、ｍを任意の整数として、前記［数１７］を成立する前記Ｆを生成して、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の生成と前記判定とを繰り返す手段と、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み、前記復号部は、暗号化された整数Ｙｉを整数Ｍを基数とするＭ進表記に変換し、前記ＹｉのＭ進表記の桁数を、少なくとも２つ以上に分割し、前記分割したそれぞれの桁に対応する整数と当該桁数をべき指数とするＭのべき乗との積からなる単項式の和からなる前記Ｙｉの展開形を生成する手段と、前記生成した数Ｆをべき指数とする、整数ＹｉのＦ乗冪演算において、整数Ｙｉの前記展開形を用いて、前記それぞれの桁に対応する整数間の計算に置き換えて展開した剰余計算により、整数ＹｉをＦ乗してＮを法とする整数Ｘｎを計算する手段とを含むことを特徴とする、（９）に記載の整数の暗号化及び復号装置。 (9) An apparatus for encrypting and decrypting an input integer Xi different from 0 and 1, and generating two prime numbers A and B having a product N exceeding the integer Xi , and storing the N, A, and B A prime number generation unit that stores data, and a product D of (A-1) and (B-1) and a least common multiple K of (A-1) and (B-1), and stores said D and K And generating a number E that is prime with D or K, and determining whether the integer Xi raised to the E power generates an overflow in the integer operation of the computing means of the computer device. Until it becomes true, the generation of the number E that is prime with D or K and the determination are repeated, E that is the determination result is stored in the storage means, and the integer Xi is expressed in M-ary notation with the integer M as the base. Convert and divide the number of digits in X notation of Xi into at least two and correspond to each of the divided digits An integer described in the following equation, which generates an expanded form of the Xi consisting of a sum of monomials consisting of a product of an integer and a power of M with the number of digits as a power, and uses the stored number E as a power In the E power multiplication operation of Xi , the integer Xi is raised to the E power and the modulus is modulo N by the remainder calculation expanded by replacing the calculation between the integers corresponding to the respective digits using the expansion form of the integer Xi A cryptographic generation unit that calculates an integer Yi, generates an integer Yi obtained by encrypting the integer Xi , and stores it in a storage unit ;

a decoding preparation unit that generates F that satisfies the following expression with m as an arbitrary integer, and stores the generated F in the storage unit ;

The stored number F is an exponent, and the encrypted integer Yi described in the following equation is raised to the F power to generate an integer Xn modulo N and stored in the storage means, whereby the encrypted Yi is Xn, that is, an integer encryption and decryption device including a decryption unit decrypting to Xi .

(10) The decoding preparation unit generates m that satisfies [Equation 17], where m is an arbitrary integer, and the power of the integer Yi causes overflow in the integer calculation of the computing means of the computer device A means for repeating the generation of the number F and the determination until the determination result is true, and a means for storing in the storage means F for which the determination result is true. The unit converts the encrypted integer Yi into M-decimal notation based on the integer M, divides the number of digits of the Yi M-decimal notation into at least two, and corresponds to each of the divided digits Means for generating the expanded form of Yi consisting of a monomial sum consisting of the product of an integer to be raised and a power of M with the exponent being the exponent, and F of integer Yi having the generated number F as the exponent In the multiplication operation, the expansion form of the integer Yi is used to (9) including means for calculating an integer Xn modulo N by multiplying the integer Yi by F to the power of the integer calculation corresponding to each digit and expanding the calculation between integers corresponding to each digit. An integer encryption and decryption device as described.

In the integer encryption and decryption device according to the present invention, it is only necessary to be able to detect overflow of an integer operation in the CPU or detection of overflow of an integer operation during program execution. You may select the integer E contained in the power calculation represented by Numerical formula (VI).
Furthermore, in the integer encryption and decryption apparatus according to the present invention, after selecting E in the above formula (VI) under the condition that overflow occurs, Xi is expanded using, for example, the above formula (IV). Thus, Yi which is an encrypted integer can be obtained accurately by avoiding overflow.
Therefore, the integer encryption and decryption apparatus according to the present invention can accurately obtain the integer Yi even in a situation where a digit overflow occurs in a computer apparatus or the like that does not include the implementation means of the method according to the present invention. . That is, the integer encryption and decryption apparatus according to the present invention can accurately perform both encryption and decryption.

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をＦ乗してＮを法とする整数Ｘｎを計算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に復号する手段と、を含む、整数を暗号化及び復号するシステム。

（１２） 前記Ｆを生成し記憶手段に記憶する手段は、ｍを任意の整数として前記［数２０］を成立する数Ｆを生成して、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を含み、前記復号する手段は、暗号化した整数Ｙｉを整数Ｍを基数とするＭ進表記に変換し、前記ＹｉのＭ進表記の桁数を、少なくとも２つ以上に分割し、前記分割したそれぞれの桁に対応する整数と当該桁数をべき指数とするＭのべき乗との積からなる単項式の和からなる前記Ｙｉの展開形を生成する手段と、前記生成した数Ｆをべき指数とする、整数ＹｉのＦ乗冪演算において、整数Ｙｉの前記展開形を用いて、前記それぞれの桁に対応する整数間の計算に置き換えて展開した剰余計算により、整数ＹｉをＦ乗してＮを法とする整数Ｘｎを計算する手段とを含むことを特徴とする、（１１）に記載の整数を暗号化及び復号するシステム。 (11) A system for encrypting and decrypting an input integer Xi excluding 0 and 1, wherein two prime numbers A and B having a product N exceeding the integer Xi are generated, and the generated N, A, B Is stored in the storage means, and a product D of (A-1) and (B-1) and a least common multiple K of (A-1) and (B-1) are generated, and the D and K are stored in the storage means. means for storing in said generates a D or K and prime a number E, multiply E term Xi is determined whether or not to generate an overflow in integer arithmetic calculation means of the computer device, the determination result Means for repeating the generation of the number E that is prime with D or K and the determination until the value becomes true, means for storing E for which the determination result is true in the storage means, and the integer Xi for the integer M Convert to the base M notation and divide the number of digits of the integer Xi in M notation into at least two Means for generating an expanded form of the integer Xi consisting of a monomial sum consisting of a product of an integer corresponding to each of the divided digits and a power of M with the number of digits as a power exponent; and the stored number In the E power operation of the integer Xi described in the following equation, where E is a power exponent, by using the expansion form of the integer Xi, the calculation is performed by replacing the calculation between integers corresponding to the respective digits, Means for calculating integer Yi modulo N with integer Xi raised to E, means for storing integer Yi obtained by encrypting integer Xi in storage means,

means for generating F that holds the following expression with m as an arbitrary integer and storing it in the storage means;

The stored number F is an exponent, and the encrypted integer Yi described in the following equation is raised to the F power to calculate an integer Xn modulo N and stored in the storage means. A system for encrypting and decrypting integers, including Xn, ie, means for decrypting to Xi .

(12) The means for generating F and storing it in the storage means generates a number F that satisfies the above [Expression 20], where m is an arbitrary integer, and the power of the integer Yi is an integer of the computing means of the computer device Means for determining whether or not overflow occurs in the operation, repeating the generation of the number F and the determination until the determination result is true, and means for storing F in which the determination result is true in the storage means And the means for decrypting converts the encrypted integer Yi into M-decimal notation based on the integer M, divides the number of digits in Y-M notation into at least two, and each of the divided Means for generating the expanded form of Yi consisting of the sum of monomials consisting of the product of an integer corresponding to the number of digits and a power of M with the number of digits as the exponent, and the generated number F as the exponent In the F-power operation of integer Yi, the above-mentioned expansion of integer Yi And a means for calculating an integer Xn modulo N by multiplying the integer Yi by the power of the remainder by replacing the calculation with an integer corresponding to each digit and expanding it using a shape. A system for encrypting and decrypting the integer according to (11).

In the system for encrypting and decrypting information 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. The integer E included in the power calculation represented by the formula (IX) may be selected.
Further, in the system for encrypting and decrypting integers according to the present invention, after selecting E in the above formula (IX) under the condition that overflow occurs, Xi is expanded using, for example, the above formula (VI). Thus, Yi which is an encrypted integer can be accurately obtained while avoiding overflow.
Therefore, the system for encrypting and decrypting information according to the present invention can accurately obtain the integer Yi even in a situation where overflow occurs in a computer system or the like that does not include the means for implementing the method according to the present invention. Become. That is, the integer encryption and decryption apparatus according to the present invention can accurately perform both encryption and decryption.

  The method, apparatus, system, and the like for encrypting and decrypting integers according to the present invention can be combined with existing information transmission technologies, such as computer network technologies, and the combined technologies are also the technologies of the present invention. Included in the range. 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. Furthermore, the technique of the present invention provides the steps of encryption and decryption in FPGA (field programmable gate array), ASIC (application specific integrated circuit), equivalent hardware logic elements, programmable integration. It may be provided as a program form that can be stored in the circuit or a combination thereof, 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., and such an integrated circuit The form of the program product stored in is also included in the technical scope of the present invention.

  According to the present invention, an identification number for identifying an individual is generated by encrypting an identification number or the like under a condition in which the computer overflows, so that the third party can estimate the identification number from the integer. Therefore, the identification number can be concealed. In addition, according to the present invention, it is extremely difficult to estimate a plurality of other personal information associated with the same identification number from a third party even in a situation where specific personal information associated with the identification number is leaked. There is an effect that can be made. Further, according to the present invention, by encrypting an integer with an increased number of digits using an integer representing a character string including the same personal information such as date of birth and an arbitrarily selected integer, the same A plurality of different encrypted integers can be generated from 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.

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

[Flow diagram of encryption and decryption]
FIG. 1 shows a flow diagram of a method for encrypting and decrypting an integer according to one embodiment of the present invention. FIG. 1A is an example of a method flow diagram for encrypting an integer according to the present invention, and FIG. 1B is an example of a flowchart of a method for decrypting the encrypted integer.
First, the encryption steps will be described. In the method for encrypting an integer according to the present invention, a variable area is secured 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, the word lengths of integers Xi, Yi, and Xn in a computer device or the like used for calculation are within the maximum bit width of a register that can be used to represent one integer in an internal instruction of a CPU included in the computer device or the like. It can be. For example, in a computer device having a CPU that can execute integer operations included in internal instructions using a 16-bit register, the word lengths of integers Xi, Yi, and Xn are 16 bits or less, and these integer variables are 10 It can be 0 or more and 65535 or less in the decimal notation.

桁あふれの検出は、計算手段が備えるＣＰＵの内部動作の状況を記憶するための、ＣＰＵの特定のレジスタに含まれるフラグ（例えばステータスレジスタ又はコンディションレジスタ等に含まれるオーバーフローフラグ等）の値を参照してもよく、コンパイラ言語等により予めオペレーティングシステムに例外処理等を登録して当該例外処理の動作を参照してもよく、スクリプト言語又はコンパイラ言語等に付属するライブラリ等が備えるオーバーフローエラー処理を参照してもよく、適宜設計しうる。 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.
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 an integer E that is prime with 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 formula (XII) (Xi raised to the E power) generates 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.

For detection of overflow, refer to the value of a flag included in a specific register of the CPU (for example, an overflow flag included in the status register or condition register) for storing the internal operation status of the CPU provided in the calculation means You may register exception handling etc. in the operating system in advance using the compiler language, etc., and refer to the operation of the exception handling, or refer to the overflow error handling provided by the library attached to the script language or compiler language etc. They may be designed as appropriate.

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。すなわり、このようにして置き換えたＸｕ又はＸｄを用いて、数式（ＸＩＩ）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する方法においては、桁あふれを発生する条件で前述の数式（ＸＩＩ）のＥを選択した後に、数式（ＸＩＩＩ）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。
一実施形態において、記数法の底であるＭを１０とし、Ｘｉの桁数を１０桁、下位の桁数Ｃｔを５桁とする場合、数式（ＸＩＩＩ）は次式のように表される。

別の実施形態において、記数法の底であるＭを２とし、Ｘｉの桁数を１６桁、下位の桁数Ｃｔを８桁とする場合、数式（ＸＩＩＩ）は次式のように表される。

例えば、本発明に係る整数を暗号化し復号する方法の実施手段等が１６ビット幅のレジスタを有するＣＰＵを備えるコンピュータ装置等である場合に、元の整数Ｘｉの値が１０進数の６５５３２等であると、Ｘｉのべき乗の計算において、最も小さい整数のべき数でありうる２を用いた時点で、当該ＣＰＵが備える１６ビット幅のレジスタを用いて表しうる整数の上限値６５５３５を超えてしまう。すなわち、単に元の整数をそのままべき乗する通常の計算方法に従って数式（ＸＩＩ）の右辺に含まれるＸｉのＥ乗の計算を実施すると、正確なべき乗の値が得られない場合がある。
本発明に係る方法においては、数式（ＸＩＩＩ）又はその具体例である数式（ＸＩＶ）又は数式（ＸＶ）等を用いて上位の桁と下位の桁を分離しうる。例えば前述の元の整数Ｘｉの値である６５５３２を、２進数の１１１１１１１１１１１１１１００（２）として表し、上位８桁と下位８桁等に分割し、上位８桁に含まれる整数１１１１１１１１（２）（１０進数の２５５）及び下位８桁に含まれる整数１１１１１１００（２）（１０進数の２５２）を用い、２５５の２乗、２５５と２５２の積、２５２の２乗をそれぞれ計算すると、これらの整数の積はいずれも当該ＣＰＵが備える１６ビット幅のレジスタを用いて表しうる整数の範囲内にあることは明白である。３２ビット幅のレジスタ、６４ビット幅のレジスタ等についても同様である。
従って、前述の数式（ＸＩＩ）として表されるＸｉのべき乗の計算において、最も少ない回数であるＸｉの２乗の場合に、数式（ＸＶ）の右辺の２乗からは、Ｘｕの２乗、Ｘｕ・Ｘｄ、及びＸｄの２乗が生成され、これらはいずれも元のＸｉの桁数以下の整数でありうるため、桁あふれを避けられる。すなわち、Ｘｉの任意のべき乗において、数式（ＸＶ）の手順を繰り返すことにより、べき乗の計算過程での桁あふれを避けることが可能になる。
分割する桁数は、計算手段等が備えるＣＰＵの整数演算のためのレジスタのビット幅等に基づいて適宜設定しうる。好適には、符号なし整数演算のためのレジスタのビット幅を等分した上位の桁数及び下位の桁数を、分割した桁数として用いうる。 Next, in step S150, the method for encrypting an integer according to the present invention may generate an integer Yi obtained by encrypting the integer Xi using the expanded form of the mathematical formula (XII). For example, the following expression can be used as the expanded form of the expression (XII).

Where M is the base of the numeration system, Cd is the number of the lower digits, and Cd can be at least 1. In other words, the remainder calculation of Formula (XII) can be performed using Xu or Xd thus replaced.
In this way, in the method of encrypting and decrypting an integer according to the present invention, after selecting E in the above formula (XII) under the condition that overflow occurs, Xi is calculated using the formula (XIII). Yi that is an encrypted integer can be obtained accurately by expanding and avoiding overflow.
In one embodiment, when M, which is the base of the numeration system, is 10, the number of digits of Xi is 10 digits, and the number of lower digits Ct is 5 digits, the formula (XIII) is expressed as: .

In another embodiment, when M, which is the base of the numeration system, is 2, the number of digits of Xi is 16 digits, and the number of lower digits Ct is 8 digits, Formula (XIII) is expressed as: The

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 decimal 65532 In the calculation of the power of Xi, when 2 which can be the smallest integer power is used, the integer upper limit value 65535 that can be expressed using the 16-bit register provided in the CPU is exceeded. That is, if the calculation of the Ei power of Xi included in the right side of the mathematical formula (XII) 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, the upper digit and the lower digit can be separated using Equation (XIII) or a specific example of Equation (XIV) or Equation (XV). For example, the above-mentioned original integer Xi value 65532 is expressed as a binary number 1111111111111100 (2), divided into upper 8 digits and lower 8 digits, etc., and an integer 11111111 (2) (decimal number) included in the upper 8 digits. 255) and the integer 11111100 (2) (decimal number 252) included in the lower 8 digits, and calculating the square of 255, the product of 255 and 252 and the square of 252 respectively, the product of these integers is It is clear that both are in the range of integers that can be expressed using a 16-bit register provided in the CPU. The same applies to 32-bit wide registers, 64-bit wide registers, and the like.
Therefore, in the calculation of the power of Xi expressed as the above-described mathematical formula (XII), in the case of the square of Xi which is the smallest number of times, the square of the right side of the mathematical formula (XV) is calculated from the square of Xu, Xu Xd and the square of Xd are generated, and both of these can be integers less than or equal to the number of digits in the original Xi, thus avoiding overflow. That is, it is possible to avoid overflow in the power calculation process by repeating the procedure of the mathematical formula (XV) at an arbitrary power of Xi.
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, 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 the divided digits.

  Through the above steps, Yi which is an encrypted integer can be 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.

数式（ＸＶＩ）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する方法は、ステップＳ２２０において、次の数式（ＸＶＩＩ）を用いて前記暗号化したＹｉをＸｎに復号する。

Next, steps of decoding will be described. In the method for encrypting an integer according to the present invention, a variable area is secured 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, and the encryption and decryption stages are built in one computer device or the like, and the common variable area is both encrypted and decrypted. It may be used in these stages.
Next, the method for decrypting an encrypted integer according to the present invention generates F that satisfies the following mathematical formula (XVI) where m is an arbitrary integer in step S210.

In the formula (XVI), the integer F may be any factor as long as it is a factor of the right-side formula (m × K + 1) 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 (XVII).

In this way, in the method of encrypting and decrypting integers according to the present invention, since E in Formula (XII) is selected under the condition that overflow occurs, in a computer apparatus or the like that does not use the method of the present invention Cannot accurately obtain the encrypted integer Yi, and it is possible to implement encryption with high information confidentiality.
Furthermore, in the method for encrypting and decrypting an integer according to the present invention, the integer F included in the formula (XVI) and the formula (XVII) that are not included in the formula (XII) that is the process of decryption is included in the formula (XII) that is the process of decryption. High security can be secured based on the fact that it is difficult to be known or estimated by the three parties.

  In the method for encrypting and decrypting an integer according to the present invention shown in FIG. 1, an identifier for identifying an individual or the like can be received and encrypted as an integer type identifier. 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 and decryption. For example, an image converted into an integer is encrypted and decrypted using the method of the present invention, thereby enabling transmission of a concealed image to a third party. Further, for example, a storage medium or the like concealed from a third party can be provided by encrypting and decrypting a file allocation table or the like for referring to a specific storage area of the storage medium using the method of the present invention. . These storage media that can be provided using the method for encrypting and decrypting integers according to the present invention do not need to go through a computer network or the like in various stages of encryption or decryption, and are in an offline state separated from the network or the like However, encryption and decryption 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.

[Example of personal information hiding procedure]
FIG. 2 shows an example of a personal information hiding procedure using a method for encrypting an integer 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. Specifically, the individual 20 is one of the members belonging to the business entity, and the integer type identifier 30 is an integer of a plurality of digits that is appropriately used to identify a plurality of members in the business entity. May be a member identifier or the like. For example, the form of the member identifier is assigned to each of a plurality of members including a two-digit number representing the year in which the business entity or the like has belonged and other members who have started belonging at the same time. The number is composed of 6-digit numbers and the like, and is an 8-digit number as a whole, and can be set as appropriate. 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 integers according to the present invention, the thus converted hexadecimal integer is encrypted, and a set of original computer-processable character codes is obtained from the encrypted hexadecimal integer. Can be decrypted. Even when the member identifier or the like is image data, encryption and decryption can be performed in the same manner by treating the original image data as a collection of hexadecimal integers.

  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 the use of a computer network inside the business entity including transmission / reception or the like, the use of online banking business or insurance service associated with the business entity, or the recording action related to the 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 mathematical formula (XII).

  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 by using the expansion form of the mathematical formula (XII) 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 performs encryption instead of the integer identifier 30 for identifying a specific individual 20. The integer A (42) can be provided to the computer network 132 of the business entity via 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-insured 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.
As shown in FIG. 1, using the identification application A (122), the unique information (62) of the identification application A, the encryption calculation A (72), and the encrypted integer A (42), as described above, according to the present invention. The encryption means 100 can conceal specific personal information for specific identification applications. Here, since the integer type identifier 30 accepted by the encryption unit 100 is 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 next line having different integer type identifiers 30, etc. Can obtain different encrypted integers A (72).
For example, the network administrator or the like of the business entity selects the specific information (62) of the identification usage A according to specific conditions such as the date and time of network maintenance, so that each of the network account information of the members of the business entity is selected. 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, 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.

  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 for 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 special computer or the like. Furthermore, in the present invention, if the method for encrypting and decrypting integers according to the present invention is not used, overflow in any stage of encryption or decryption occurs, and accurate encryption and / or decryption cannot be performed. Therefore, it becomes possible to conceal personal information such as member identifiers from third parties who do not implement the method of the present invention.

[Another example of the procedure for hiding personal information]
FIG. 3 shows another example of the personal information hiding procedure using the method of encrypting an integer according to an embodiment of the present invention. A description of portions common to those in FIG. 2 is omitted.

In FIG. 3, 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 a predetermined procedure from the integer identifier 30. May be generated. 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、Ｘ_３８は桁増しした識別子３８の値、Ｘ_３０は整数型の識別子３０の値、Ｘ_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、Ｘ_３８の値はＸ_３０を１００倍してＸ_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２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 an 8-digit integer and the additional digit 37 is a 2-digit integer, the identifier 38 with an additional digit is an integer with 10 digits, and the value of the identifier 38 with an additional digit is It is expressed by a formula.

Where X ₃₈ is the value of identifier 38 incremented by digits, X ₃₀ is the value of integer type identifier 30, X ₃₇ is the value of additional digits 37, and M is the base of numeration. For example, these integers is at an integer _decimal, the value of _{X 38} may be a value obtained by adding _{X 37} and the _{X 30} 100 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 two digits and can be set as appropriate.

  The steps of encryption for an extended identifier 38 including additional digits 37 may be performed depending on the flow diagram of one embodiment shown in FIG. 1 or the identification application of one embodiment shown in FIG. This is the same as the encryption procedure. That is, the encrypted integer generated by the various stages of encryption shown in FIG. 3 may be generated as computer-processable data using the computer network 132 or the work management storage device 134, etc. You may produce | generate in 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 the date of birth of a member as an identifier includes the date of birth of the member using the method of encrypting and decrypting an integer according to the present invention. Arbitrary two-digit numbers can be combined as additional digits 37 in addition to numbers. Thus, even if there are multiple members with the same date of birth, if any two-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 digit 37 having a predetermined number of digits, the integer input to the various stages of encryption of the encryption device 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.

[Example of decryption procedure]
FIG. 4 shows an example of an encrypted integer decryption procedure according to an embodiment of the present invention. In FIG. 4, 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 apparatus 100 shown in FIG. 44), the same applies to the decryption of an encrypted integer that can be transmitted in the form of a call or a document. Descriptions of portions common to FIG. 2 or FIG. 3 are omitted.

FIG. 4 shows that the decryption device 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 40. . Here, the encrypted integer A ′ (52) is obtained by using the encrypted integer A (42) generated by the encryption apparatus 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 device 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 decrypting apparatus 110 according to the present invention performs the steps from Step S200 to Step S220 shown in FIG. 1 on the encrypted integer A ′ (52) and the encrypted integer B ′ (54). A decrypted identifier 40 of the type 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 apparatus 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 mathematical formula (XII), 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) for the decryption 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 device 110, or may be generated by one or both of the encryption device 100 and the decryption device 110 according to a predetermined procedure. Can be set as appropriate.

FIG. 4 illustrates a network or the like that can transmit numerical values that can be processed by a computer 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 apparatus 100 to the decryption apparatus 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 via these transmission paths or means are encrypted, and the identification used for encryption under the condition that overflow occurs The original integer cannot be decoded unless the method of the present invention for decoding with the numerical value of is used. Therefore, in the present invention, the personal information is concealed from a third party who may access the transmission path or the transmission means, and the predetermined unique information and the predetermined encryption and decryption method are used. Only the implementation means of the invention can correctly decrypt the personal information.

  In FIG. 4, each of the encryption device 100 and the decryption device 110 is shown separately. However, the present invention is not limited to this, and the encryption device 100 and the decryption device 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 each transmission path or transmission means, an encrypted integer may be generated separately and independently from one integer type identifier 30, and the additional digits 37 shown in FIG. The integer identifier 30 may be encrypted after being processed. In this way, in the method for encrypting and decrypting an integer according to the present invention, an integer that conceals personal information is used as an identifier for each of various information transmission means using the identifier from one identifier such as a member identifier. Can be provided instead. Since the various stages 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 does not pay special attention to these procedures, and can automatically set an integer that conceals his / her personal information. It can be used instead of the identifier.

(Method to encrypt and decrypt integer using internal function of worksheet)
FIG. 5 shows an example of implementing the steps of the encryption and decryption method according to an embodiment of the present invention using a spreadsheet-type calculation application package. As a spreadsheet format calculation application package, Microsoft Excel 2007 or the like can be used. However, the present invention is not limited thereto, and package software capable of performing integer power and remainder calculation can be arbitrarily used.
The integer encryption and decryption calculation worksheet 200 shown in FIG. 5 may be spreadsheet application data including cells arranged in a plurality of rows and columns. Individual cells included in the encryption and decryption calculation worksheet 200 may be identified using a set of row numbers and column numbers. For example, a cell with 1 row and 1 column can be used to store an input Xi for encryption. Similarly, an encrypted integer Yi can be stored in a cell of 11 rows and 5 columns, and a decrypted integer Xn can be stored in a cell of 19 rows and 5 columns. The value that can be stored in one cell or the type and number of calculation formulas can be set as appropriate. It is also 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.

The rectangular area having the 1st row and 1st column cell and the 11th row and 5th column cell included in the integer encryption and decryption calculation worksheet 200 is encrypted in steps S100 to S150 shown in FIG. It can be used for calculations related to the various stages.
Specifically, a cell in one row and one column can be used to store the input Xi.
The 2 × 1 cell and the 2 × 2 cell can be used to store two prime numbers A and B. A cell with 2 rows and 3 columns can be used to determine that the product of A and B exceeds the input Xi. The product of A and B is N in the above formula (XII), and N may be the base of the remainder calculation included in the integer encryption according to the present invention.
A cell of 3 rows and 1 column can be used to store a D value that is the product of (A-1) and (B-1).
A cell of 4 rows and 1 column can be used to store a K value which is the least common multiple of (A-1) and (B-1).
A 5 × 1 cell can be used to store an integer E that is prime with D or K.
A cell in 6 rows and 1 column can be used to store the value of Xi raised to the E power. The cell of 6 rows and 2 columns can be used to determine whether or not this Xi raised to the E power has caused an overflow in the integer operation incorporated in the worksheet. For example, the occurrence of the overflow is represented by a character such as “error” indicating that the value of 6 rows and 1 column exceeds the range that can be handled in the spreadsheet-type calculation application package. In the cell of the column, a numerical value representing false of the logical value can be stored corresponding to the error.
The cell of 7 rows and 1 column can be used for the expanded form of the input Xi, but is not limited thereto, and may be a flag or a character such as a memo indicating that the input Xi is expanded. The cells in the 7th row and the 2nd column and the 8th row and the 2nd column are obtained by dividing the numeration digits described using the step S150 shown in FIG. 1 or the formula (XIII), the formula (XVI), or the formula (XVII). Can be used to store an integer generated from input Xi. For example, 7 rows and 2 columns may be integers generated from upper digits, and 8 rows and 2 columns may be integers generated from lower digits.
The cell in the 9th row and 1st column can be used for calculating the power to use the integer generated from the upper digit and the lower digit, but is not limited to this and may be a character such as a memo. A cell of integers generated from the upper digits in the cell of 9 rows and 2 columns, a product of integers generated from the lower digits in 11 rows and 2 columns, and the upper and lower digits of these in 10 rows and 2 columns. Each product can be stored.
The cell of 11 rows and 3 columns can store the sum of the products stored in the above-mentioned 9 rows and 2 columns to 11 rows and 2 columns. That is, the sum of the products can include a remainder of a remainder calculation with N as the product of A and B.
11 rows and 4 columns can store N remainders for the values of 11 rows and 3 columns.
The 11th row and the 5th column can store Yi that is an output of encryption. Substantially Yi may be the same as the value of 11 rows and 3 columns.

The rectangular region including the 12th row and 1st column cell and the 19th row and 5th column cell included in the integer encryption and decryption calculation worksheet 200 is decrypted in steps S200 to S220 shown in FIG. It can be used for calculations according to the steps.
The cell of 12 rows and 1 column can be used to store an arbitrary integer m included in the above formula (XVI).
The cell of 13 rows and 1 column can be used to store the integer F that satisfies the above-described equation (XVI).
The cell of 14 rows and 1 column can be used to store the value of Yi raised to the F power included in the above formula (XVII). The cell of 14 rows and 2 columns can be used to determine whether this Yi raised to the E power has overflowed in the integer operation incorporated in the worksheet. For example, the occurrence of the overflow is represented by a character such as “error” indicating that the value of 14 rows and 1 column exceeds the range that can be handled in the spreadsheet format calculation application package. In the cell of the column, a numerical value representing false of the logical value can be stored corresponding to the error.
The cell of 15 rows and 1 column can be used for the expansion form of Yi, but is not limited thereto, and may be a flag or a character such as a memo indicating expansion of Yi. The 15 × 2 and 16 × 2 cells can be used to store integers generated from Yi by dividing the numeration digits. For example, 15 rows and 2 columns may be integers generated from upper digits, and 16 rows and 2 columns may be integers generated from lower digits.
The cell of 17 rows and 1 column can be used for the calculation of the power which should use the integer generated from the upper and lower digits. The cell of the integers generated from the upper digits in the cell of 17 rows and 2 columns, the product of the integers generated from the lower digits in 19 rows and 2 columns, and the upper and lower digits of these in 18 rows and 2 columns. Each product can be stored.
In the cell of 19 rows and 3 columns, the sum of the products stored from the 17 rows and 2 columns to the 19 rows and 2 columns can be stored. That is, the sum of the products can include a remainder of a remainder calculation with N as the product of A and B.
19 rows and 4 columns may store N remainders for the values of 19 rows and 3 columns.
19 rows and 5 columns can store Xn which is an output of decoding. Substantially, Xn can be the same as the input Xi of 1 row and 1 column.

  Thus, the steps of the method for encrypting and decrypting integers according to the present invention can be implemented in a spreadsheet-type calculation application package capable of performing power and remainder calculations. Therefore, the method for encrypting and decrypting the integer according to the present invention can be implemented using a personal computer or the like in which the mounting means such as the spreadsheet is installed, and the integer according to the present invention is encrypted and decrypted as spreadsheet format data. It is possible to provide means for performing the method.

(Encryption and decryption calculation by worksheet)
FIG. 6 shows an example in which the steps of the encryption and decryption method according to an embodiment of the present invention are implemented in a spreadsheet-type calculation application package. In the example calculation, Excel 2003 made by Microsoft Corporation was used as a calculation application package in a spreadsheet format. This application software can handle numerical values in the range of −1 × 10 ³⁰⁷ to 1 × 10 ³⁰⁷ , but if the calculation result of an internal function or the like generates a numerical value not in this range, “#num!” Etc. is displayed. Therefore, it is possible to know from the error message that an overflowing numerical value that cannot be handled by this application software has occurred.
Each cell of the spreadsheet shown in FIG. 6 is a calculation formula corresponding to each cell of the worksheet described with reference to FIG. 5 for performing the steps for integer encryption and decryption according to the present invention. Respectively.

In the worksheet calculation example 210 shown in FIG. 6, the rectangular region diagonally having the 1-row and 1-column cell and the 11-row and 5-column cell is used for the calculation related to the steps for encrypting the input integer. Used for.
The 1-by-1 cell is used to store an input integer (Xi). In this example, the input integer is assumed to be “99999912345” in decimal.
As two prime numbers stored in the cell of 2 rows and 1 column and the cell of 2 rows and 2 columns, for example, “13” can be selected as the prime A and “7692309769” can be selected as the prime B. The cell of 2 rows and 3 columns displays “9999999997” which is the product (N) of these two prime numbers. Since the value of this product is larger than the input integer, the condition necessary for the integer encryption method according to the present invention is satisfied. In other words, the prime number A and the prime number B may be arbitrarily selected as long as their product is larger than the input integer.
In the cell of 3 rows and 1 column, “9230769216” is displayed as the D value which is the product of (A-1) and (B-1).
In the cell of 4 rows and 1 column, "769276868" is displayed as the K value which is the least common multiple of (A-1) and (B-1) using the LCM function which is an internal function for calculating the least common multiple. Is done.
In the cell of 5 rows and 1 column, “11114323” is displayed as an example of the integer E that is prime with the D value or K value. In this selection, an arbitrary number of candidates that can be used in advance as an integer E are appropriately prepared, and whether or not each of the D value and the K value calculated as described above has a common divisor other than 1 is determined as follows. It is determined using a GCM function that is an internal function for calculating a common divisor, and can be implemented based on this determination. However, the present invention is not limited to this, and the integer E is a condition that is prime with a D value or a K value. It can be set as appropriate.
In the cell of 6 rows and 1 column, the value of Xi raised to the E power is displayed, but in the example shown in FIG. 6, an error “#num!” Occurs due to an overflowing numerical value that cannot be handled by the application software. A message is displayed. Accordingly, the prime number A, prime number B, D value, K value, and integer E set by the above-described procedure are the conditions for encrypting the input integer Xi using the integer encryption method according to the present invention. Satisfies.
The cell of 6 rows and 2 columns indicates that an overflow has occurred in the cell of 6 rows and 1 column. For example, a cell of 6 rows and 2 columns displays a predetermined character string such as “overflow” on condition that the calculation result of the cell of 6 rows and 1 column exceeds the range of a positive integer that can be calculated. Can be set. For example, the display of the predetermined character string may notify the user of the calculation method that the condition for the integer encryption method according to the present invention is satisfied.
The cell of 7 rows and 1 column represents the input Xi in FIG. The cells in the 7th row and the 2nd column and the 8th row and the 2nd column respectively represent the upper 5 digits and the lower 5 digits of the input Xi in FIG.
The cell of the 9th row and the 2nd column has the square of the upper digit of the input Xi, the 10th row and the 2nd column has twice the product of the upper and lower digits, the 11th row and the 2nd column have the lower digit squared, Represent. That is, the three cells from 9 rows 2 columns to 11 rows 2 columns have the values of the expressions included in the expanded form shown in the above formula (XIII), etc., for the square which is the smallest number of powers of the input Xi. May be included.
In the cell of 11 rows and 3 columns, the value of the expression included in this expanded form can be expressed as one integer having decimal digits. Specifically, in the example of FIG. 6, “99998246690768399025”, which is the result of 9999800001 × 10 ¹⁰ + 24689755310 × 10 ⁵ +1523999025, is displayed.
In the 10th row and the 4th column, the quotient “9999824493” obtained by dividing the value in the 11th row and the 3rd column by the value (N) of the cell in the 2nd row and the 3rd column is displayed. Is displayed. Since the quotient of 10 rows and 4 columns is not used in the subsequent calculation in the encryption process according to the present invention, the display may be omitted. In the encryption and decryption calculation worksheet 200 shown in FIG. 5 described above, a mode in which the display of the quotient is omitted is shown.
Returning to FIG. 6 again, the value of the remainder for the cube of Xi is the product of the value of 11 rows and 4 columns and the value of 1 row and 1 column (input Xi) as the cell value (N) of 2 rows and 3 columns. Can be obtained. The same applies to the fourth power or higher, and this process is repeated until the number of times the input Xi is multiplied reaches the integer E, whereby an encrypted integer Yi is finally obtained in the cell of 11 rows and 5 columns. The example of FIG. 6 indicates that the integer “2655731903” has been obtained.

In the worksheet calculation example 210 shown in FIG. 6, a rectangular area whose diagonal is a cell of 12 rows and 1 column and a cell of 19 rows and 5 columns is used for calculations related to various stages of decoding.
In the cell of 12 rows and 1 column and the cell of 13 rows and 1 column, an arbitrary integer m included in the above formula (XVI) and an integer F that holds the above formula (XVI) are displayed. These m and F should just satisfy | fill numerical formula (XVI). In the example of FIG. 6, “1219862” is displayed as the integer m, and “844275579” is displayed as the integer F. For example, an arbitrary number of candidates that can be used as the integer F are prepared in advance, and the integer m and the integer F are selected so as to satisfy the formula (XVI) based on the E value and the K value used in the encryption stage. May be.
In the cell of 14 rows and 1 column, the value of the power of Yi included in the above formula (XVII) is displayed, but in the example shown in FIG. 6, it is the same as the calculation of the power to be included in the encryption process. In addition, an error message “#num!” Is displayed when a numerical value overflowing digits occurs. Therefore, the integer F set by the above-described procedure satisfies the condition for decrypting the encrypted integer Yi using the method for decrypting the encrypted integer according to the present invention.
The 14th row and 2nd column cell indicates that an overflow has occurred in the 14th row and 1st column cell. This is the same as the cell of 6 rows and 2 columns in the encryption process, and the details are omitted.
The cell of 15 rows and 1 column represents the encrypted integer Yi in FIG. 6, and the cell of 15 rows and 2 columns and 16 rows and 2 columns in FIG. 6 represents the upper 5 digits and the lower 5 digits of the encrypted integer Yi. Represents each of
The cell of the 17th row and the 2nd column is the square of the upper digit of the encrypted integer Yi, the 18th row and the 2nd column is twice the product of the upper and lower digits, and the 19th row and 2nd column is the square of the lower digit. Respectively. That is, the three cells from the 17th row and the second column to the 19th row and the second column express the value of the expression included in the expanded form of the above formula (XVII) for the square that is the smallest number of times of the power of the encrypted integer Yi. May be included.
In the cell of 19 rows and 3 columns, the value of the expression included in the expanded form of the expression (XVII) can be expressed as one integer having decimal digits. Specifically, in the example of FIG. 6, “7052911944061140409”, which is the result of 7052747449 × 10 ¹⁰ + 1694995942 × 10 ⁵ +101801409, is displayed.
In the 18th row and the 4th column, the quotient “705291194” obtained by dividing the value in the 19th row and the 3rd column by the value (N) of the cell in the 2nd and 3rd column is displayed. In the 19th row and the 4th column, the remainder “2727287991” at this time is displayed. Is displayed. Note that the quotient of 18 rows and 4 columns is not used in subsequent calculations in the encryption process according to the present invention, and may be omitted. In the encryption and decryption calculation worksheet 200 shown in FIG. 5 described above, a mode in which the display of the quotient is omitted is shown.
Returning to FIG. 6 again, the value of the remainder for the cube of Yi is obtained by dividing the product of the value of 19 rows and 4 columns and the value of 17 rows and 2 columns (Yi) by the cell value (N) of 2 rows and 3 columns. Can be obtained. The same applies to the fourth power or higher, and by repeating this process until the number of times of multiplying the encrypted integer Yi reaches the integer F, the decrypted integer Xn is finally obtained in a cell of 19 rows and 5 columns. . In the example of FIG. 6, it is shown that the integer “999912345” has been obtained, which matches the input Xi.
Therefore, by using the steps of the integer encryption and decryption method according to the present invention, the input integer is input under the condition that overflow occurs in the calculation process in both the encryption step and the decryption step. An encrypted integer Yi is obtained by encrypting Xi, and an integer Xn decrypted from the encrypted integer Yi is obtained. By generating overflow in the calculation process, correct encryption and decryption cannot be performed in a calculation means that does not use the method of the present invention. Thus, 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.

  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.

FIG. 3 is a flow diagram of a method for encrypting and decrypting an integer according to an embodiment of 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 the example of the decoding procedure of the encrypted integer based on one Embodiment of this invention. FIG. 3 is a diagram illustrating an example of implementing steps of an encryption and decryption method according to an embodiment of the present invention using a spreadsheet-type calculation application package. FIG. 5 is a diagram illustrating an example of calculating and implementing the steps of the encryption and decryption method in a spreadsheet-type calculation application package according to an embodiment of the present invention.

Explanation of symbols

20 Specific individuals 30 Integer type identifiers 37 Additional digits 40 Integer type decoded identifiers 42, 44, 46, 52, 54 Encrypted integers 62, 64, 66, 92, 94 Unique information 72, 74, 76 Encryption Calculation calculation 82, 84, 102, 104 Information transmission path 100 Encryption device 110 Decryption device 112, 114 Decryption calculation 122, 124, 126 Identification application

Claims (12)

A method in which a computer device encrypts and decrypts an integer Xi excluding 0 and 1 ,
A computer device generating two prime numbers A and B , the product N of which is greater than the input integer Xi , and storing the N, A, and B in a storage means ;
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 the number of digits in the M-ary notation of the integer Xi into at least two, and corresponds to each of the divided digits Generating an expanded form of the integer Xi consisting of a monomial sum consisting of an integer and a power of M with the number of digits as a power exponent;
In the E-power multiplication operation of the integer Xi described in the following equation, in which the computer apparatus uses the stored number E as a power exponent, the expansion between the integers Xi is used to calculate the interval between the integers corresponding to the respective digits. Calculating an integer Yi modulo N by raising the integer Xi to the E power by a remainder calculation expanded by replacing with the calculation of
A computer device storing the integer Yi obtained by encrypting the integer Xi in a storage means ;

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 ;

The computer device calculates the integer Xn modulo N by multiplying the encrypted integer Yi described in the following equation with the stored number F as a power exponent;
A computer device storing the integer Xn in a storage means, and decrypting the encrypted integer Yi into Xn, that is, Xi.

In the expanded form, the computer device divides the Xi digit into two, generates an integer Xu represented by the upper digit of the divided digit, and an integer Xd represented by the divided lower digit. Expand by replacing Xi using the formula,

Where M is the base of the numeration system, Cd is the number of the lower digits, Cd is at least 1, and the computing device performs a remainder calculation using the replaced Xu or Xd. A method for encrypting and decrypting an integer according to claim 1. The method according to claim 1, wherein the integer Xi is an integer reversibly converted by a computer device from a part or the whole of a character or a number included in an identifier. The integer Xi, the computer device, the part or whole of reversibly transformed one-dimensional image from a one-dimensional image or a two-dimensional image, which is reversibly converted integer, integer of claim 1 How to encrypt and decrypt. 5. The computer device of claim 1, further comprising the step of replacing the integer Xi with an integer Wi with increased digits by adding at least one digit to the integer Xi prior to encryption. A method of encrypting and decrypting an integer described in any one of the above. 6. The method of encrypting and decrypting an integer according to claim 5, further comprising the step of the computer device further removing the added at least one digit from the decrypted integer Wi after decryption. The step of generating F and storing it in the storage means includes:
Whether the computer apparatus generates a number F that satisfies the mathematical expression [Equation 2], where m is an arbitrary integer, and whether 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;
A computer device storing F in the storage means for which the determination result is true,
The step of calculating the integer Xn includes:
The computer apparatus converts the integer Yi into M-ary notation based on the integer M, divides the number of digits in the M-ary notation of the integer Yi into at least two, and corresponds to each of the divided digits Generating an unfolded form of the integer Yi consisting of a monomial sum consisting of an integer and a power of M with the number of digits as a power exponent;
In the F power multiplication operation of the integer Yi using the stored number F as a power exponent, the computer apparatus replaces the calculation between the integers corresponding to the respective digits using the expansion form of the integer Yi And an integer Xn modulo N by calculating the integer Yi to the Fth power by a residue calculation expanded in an encrypted manner. How to decrypt . A computer program for causing a computer device to execute the steps of the method according to claim 1. A device for encrypting and decrypting an input integer Xi different from 0 and 1 ,
A prime number generating unit that generates two prime numbers A and B having a product N exceeding the integer Xi , and stores the N, A, and B in a storage unit ;
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, the number of digits in the M notation of the Xi is divided into at least two, and the integer corresponding to each of the divided digits and the number of digits are Generating an expanded form of the Xi consisting of a sum of monomials consisting of a product of a power of M as a power exponent;
In the E power operation of the integer Xi described in the following equation using the stored number E as a power exponent, the expansion of the integer Xi is used to replace the calculation between integers corresponding to the respective digits. An integer Yi modulo N by calculating the integer Xi to the power E , generating an integer Yi obtained by encrypting the integer Xi , and storing it in the storage means ;

a decoding preparation unit that generates F that satisfies the following expression with m as an arbitrary integer, and stores the generated F in the storage unit ;

The stored number F is an exponent, and the encrypted integer Yi described in the following equation is raised to the F power to generate an integer Xn modulo N and stored in the storage means, whereby the encrypted Yi is Xn, that is, an integer encryption and decryption device including a decryption unit decrypting to Xi .

The decryption preparation unit
The above F that holds the above [Formula 6] is generated, where m is an arbitrary integer, and it is determined whether or not the integer Yi raised to the F power will cause an overflow in the integer operation of the computing means of the computer device. Means for repeating the generation of the number F and the determination until the result is true;
Means for storing in the storage means F for which the determination result is true,
The decoding unit
The encrypted integer Yi is converted into M-ary notation based on the integer M, the number of digits of the Yi in M-ary notation is divided into at least two, and an integer corresponding to each of the divided digits Means for generating the expanded form of Yi consisting of a monomial sum consisting of a product of a power of M with the number of digits as a power exponent;
In the power multiplication operation of the integer Yi using the generated number F as a power exponent, by using the expansion form of the integer Yi and replacing the calculation between integers corresponding to the respective digits, 10. The integer encryption and decryption device according to claim 9, further comprising means for calculating an integer Xn modulo N by raising the integer Yi to the power of F. A system for encrypting and decrypting an input integer Xi excluding 0 and 1 ,
Means for generating two prime numbers A and B having a product N exceeding the integer Xi , and storing the generated N, A and B in a storage means ;
Means for generating a product D of (A-1) and (B-1) and a least common multiple K of (A-1) and (B-1) and storing said D and K in a storage means ;
Wherein to generate the D or K and prime a number E, multiply E term Xi is determined whether or not to generate an overflow in integer arithmetic calculation means of the computer device, until the determination result is true, Means for repeating generation of the number E that is prime with D or K and the determination;
Means for storing in the storage means E for which the determination result is true ;
The integer Xi is converted into an M-ary notation based on the integer M, the number of digits in the M-ary notation of the integer Xi is divided into at least two, and the integer corresponding to each of the divided digits and the digit Means for generating an expanded form of the integer Xi consisting of a monomial sum consisting of a product of a power of M with a number as a power exponent ;
In the E power operation of the integer Xi described in the following equation using the stored number E as a power exponent, the expansion of the integer Xi is used to replace the calculation between integers corresponding to the respective digits. by the remainder calculated, means for calculating an integer Yi modulo N and multiplication E integers Xi,
It means for storing the integer Yi obtained by encrypting the integer Xi in the storage means,

means for generating F that holds the following expression with m as an arbitrary integer and storing it in the storage means;

The stored number F is an exponent, and the encrypted integer Yi described in the following equation is raised to the F power to calculate an integer Xn modulo N and stored in the storage means. A system for encrypting and decrypting integers , including Xn, ie, means for decrypting to Xi .

The means for generating F and storing it in the storage means,
A number F that satisfies the above [Equation 9] is generated by using m as an arbitrary integer, and it is determined whether or not the integer Yi raised to the F power causes an 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 is true;
Means for storing in the storage means F for which the determination result is true ;
The means for decoding is
The encrypted integer Yi is converted into an M-ary notation based on the integer M, the number of digits in the Y-M notation is divided into at least two, and the integer corresponding to each of the divided digits and the corresponding Means for generating the expanded form of Yi consisting of a monomial sum consisting of a product of a power of M with the number of digits as a power exponent;
In the power multiplication operation of the integer Yi using the generated number F as a power exponent, by using the expansion form of the integer Yi and replacing the calculation between integers corresponding to the respective digits, 12. The system for encrypting and decrypting integers according to claim 11, comprising means for calculating an integer Xn modulo N by raising the integer Yi to the power of F.

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