JP5268741B2 - Pseudorandom number generator, pseudorandom number generation method, and pseudorandom number generation program - Google Patents

Description

  The present invention relates to a pseudo-random number generator that performs pseudo-random number generation using a modified tent function, a pseudo-random number generation method thereof, and a pseudo-random number generation program.

  In the generation of random numbers using a conventional tent type map, the trajectory is diffused by changing the internal parameters every time the map calculation is performed (see Patent Document 1). However, according to this method, the internal parameter variation process occurs every time the mapping calculation is performed, which complicates the process and requires time. Further, there is a problem that the portion that can be used as a random number is limited to the lower-order bits of the mapping value.

  Also known is an encryption and decryption method in which plaintext is an initial value X0 and X0 is mapped using a modified tent mapping to generate ciphertext Y, while decryption is reverse mapped and ciphertext Y is returned to plaintext X0. . In this encryption and decryption, a plurality of sub-keys AN are generated from the key A and a different sub-key AN is input for each mapping (N) to provide an encryption method that is resistant to slide attacks (Patent Document 2). reference). This technique performs encryption and decryption, and is not a technique for generating a pseudo-random number itself, and does not perform encryption using the generated pseudo-random number.

  Furthermore, there is also known a method of extracting a random value from a chaos system obtained by a fixed operation using a modified tent function. In this method, a period detection mechanism is provided, and a sub key is used after period detection (see Patent Document 3). In this case, any system of chaos can be used, but an example of continuous chaos (differential equation system) is shown. In general, the differential equation system takes time to generate random numbers. There is. Also, when extracting a long random number value, it is expected that a plurality of subkeys will be required, and there is a problem that key management becomes complicated.

  The present invention has been made in view of the above-described problems in pseudo-random number generation, and the object thereof is to obtain a long-period pseudo-random number without a frequent change in internal parameters while having a simple configuration. It is to provide a pseudo-random number generator that can be generated in a short time. Another object of the present invention is to provide a pseudo-random number generation method and a pseudo-random number generation program for generating such pseudo-random numbers.

  The pseudorandom number generator according to the present invention comprises initial value preparation means for preparing initial parameters and mapping initial values, and first time applies the initial parameters and the mapping initial values to the modified tent function to perform mapping calculation, and subsequent times Applies the initial parameter or other parameters and the previously obtained mapping value to the modified tent function to perform mapping calculation, and extracts a predetermined bit from the mapping value obtained by the mapping calculation means to simulate A bit extraction means for making a random number, a parameter creation updating means for creating and updating other parameters used by the mapping calculation means based on a comparison result between the mapping value obtained by the mapping calculation means and the mapping initial value, and a pseudo-random number Based on the generation end condition information, a determination is made at the end, the progress to the next calculation by the mapping calculation means, the bit extraction means and the parameter Characterized by comprising a control means for controlling the progression to the next process by the data creation updating means.

  In the pseudorandom number generator according to the present invention, the mapping calculation means performs mapping calculation by a plurality of tent functions, and the initial value preparation means prepares seed information, and mapping calculation is performed based on the seed information. It is characterized by comprising switching instruction means for instructing switching of a tent function used by the means.

  In the pseudo random number generator according to the present invention, the bit extraction unit determines a range for extracting a predetermined bit from the mapping value based on the seed information, and the parameter creation update unit performs parameter creation update based on the seed information. Features.

  The pseudorandom number generation method according to the present invention includes an initial value preparation step of preparing an initial parameter and a mapping initial value, and a mapping calculation is performed by applying the initial parameter and the mapping initial value to a modified tent function for the first time and subsequent times. Applies the initial parameter or other parameters and the previously obtained mapping value to the modified tent function to perform a mapping calculation, extracts a predetermined bit from the mapping value obtained by the mapping calculation step, and simulates A random number bit extraction step, a parameter creation update step for creating and updating other parameters used in the mapping calculation step based on a comparison result between the mapping value obtained by the mapping calculation step and the mapping initial value, Based on the end condition information of random number generation, the end time is determined, and the following calculation is performed by the mapping calculation step. And progression to, characterized by comprising a control step of controlling the progression to the next process by the parameter generation updating step and said bit extraction step.

  The pseudorandom number generation method according to the present invention performs mapping calculation using a plurality of tent functions in the mapping calculation step, prepares seed information in the initial value preparation step, and uses the tent function used by the mapping calculation step based on the seed information. A switching instruction step for instructing switching is provided.

  In the pseudorandom number generation method according to the present invention, in the bit extraction step, a range for extracting a predetermined bit from the mapping value is determined based on the seed information, and in the parameter creation update step, the parameter creation / update is performed based on the seed information. Features.

  The pseudorandom number generation program according to the present invention is a computer for generating pseudorandom numbers by calculation, initial value preparing means for preparing initial parameters and mapping initial values, and applying the initial parameters and the mapping initial values to the modified tent function for the first time. A mapping calculation means for performing a mapping calculation, and for the second and subsequent times, a mapping calculation means for performing a mapping calculation by applying the initial parameter or other parameters and a previously determined mapping value to the modified tent function, and a mapping value obtained by the mapping calculation means A bit extracting means for extracting a predetermined bit from a pseudo random number, a parameter for creating and updating other parameters used by the mapping calculation means based on a comparison result between the mapping value obtained by the mapping calculation means and the mapping initial value Based on the creation update means and the end condition information of pseudo-random number generation, determination at the end is performed, and the mapping calculation means And progression to calculate, characterized to function as control means for controlling the progression to the next process by the parameter generation updating means and said bit extraction means.

  In the pseudorandom number generation program according to the present invention, the computer functions as a mapping calculation means to perform mapping calculation by a plurality of tent functions, and the computer functions as an initial value preparation means to prepare seed information. Are operated as switching instruction means for instructing switching of the tent function used by the mapping calculation means based on the seed information.

  In the pseudo-random number generation program according to the present invention, the computer functions as a bit extraction unit to determine a range for extracting a predetermined bit from the mapping value based on the seed information, and the computer functions as a parameter creation update unit based on the seed information. It is characterized by functioning to create and update parameters.

  According to the present invention, since the modified tent function is used, it is not necessary to change the internal parameter for each mapping calculation, so that the random number generation can be speeded up, and the bit signal is uniformly randomized. In addition, a pseudo random number can be obtained by extracting predetermined bits. In addition, since other parameters used by the mapping calculation means are created and updated based on the comparison result between the mapping value and the mapping initial value, pseudorandom numbers generated by changing the parameters can be continued.

  Further, according to the present invention, since the tent function used by the mapping calculation means is switched based on the seed information, it is possible to randomize the pseudo random number generated by switching the tent function. Furthermore, according to the present invention, since a range for extracting a predetermined bit from the mapping value is determined based on the seed information, the bit signal is uniformly randomized by mapping calculation, and further randomization is achieved by extracting the mapping value. There are advantages that can be made.

The block diagram which shows the structure of the 1st Example of the pseudorandom number generator which concerns on this invention. The figure which shows the deformation | transformation tent function employ | adopted in 1st Example of the pseudorandom number generator which concerns on this invention. The block diagram which shows an example of the computer which implement | achieves the pseudorandom number generator which concerns on this invention. The flowchart for demonstrating operation | movement of the 1st Example of the pseudorandom number generator which concerns on this invention. The figure which shows the program of an example of the initial value preparation process by 1st Example of the pseudorandom number generator which concerns on this invention. The figure which shows the flowchart of an example of the function switching process by 1st Example of the pseudorandom number generator which concerns on this invention. The figure which shows the program of an example of the function switching process by 1st Example of the pseudorandom number generator which concerns on this invention. The figure which shows the program of an example of the bit extraction process by 1st Example of the pseudorandom number generator which concerns on this invention. The figure which shows the operation example of the bit extraction process by 1st Example of the pseudorandom number generator which concerns on this invention. The figure which shows the program of an example of the bit extraction process by 1st Example of the pseudorandom number generator which concerns on this invention. The figure which shows the operation example of the bit extraction process by 1st Example of the pseudorandom number generator which concerns on this invention. The figure which shows the program of an example of the bit extraction process by 1st Example of the pseudorandom number generator which concerns on this invention. The figure which shows an example of the bit extraction process by 1st Example of the pseudorandom number generator which concerns on this invention. The figure which shows an example of the bit extraction process by 1st Example of the pseudorandom number generator which concerns on this invention. The figure which shows an example of the bit string memory | storage process by 1st Example of the pseudorandom number generator which concerns on this invention. The flowchart for demonstrating the parameter creation change operation | movement of 1st Example of the pseudorandom number generator which concerns on this invention. The block diagram which shows the structure of the 2nd Example of the pseudorandom number generator which concerns on this invention. The flowchart for demonstrating operation | movement of the 2nd Example of the pseudorandom number generator which concerns on this invention. The flowchart for demonstrating the parameter creation change operation | movement of 2nd Example of the pseudorandom number generator which concerns on this invention.

  Embodiments of a pseudo random number generator, a pseudo random number generation method, and a pseudo random number generation program according to the present invention will be described below with reference to the accompanying drawings. In each figure, the same components are denoted by the same reference numerals, and redundant description is omitted. As shown in FIG. 1, the pseudo-random number generator according to the first embodiment includes an initial value preparation unit 10, a mapping calculation unit 20, a bit extraction unit 30, a bit string storage unit 40, a parameter creation / updating unit 50, a switching instruction. Means 60 and control means 70 are provided.

The initial value preparation means 10 prepares seed information Seed, a random bit length n, mapping function selection information k _{0 to} km ₋₁ , an initial parameter P, and a mapping initial value X ₀ . The seed information Seed is m-bit information, and is input by the user with a random bit length n, for example. The mapping function selection information k _{0 to} km ₋₁ is information used by the switching instruction means 60, and each bit k _j is a result value obtained by numerical processing such as an arbitrary calculation using the seed information Seed. Represents the jth bit from the beginning, which is a bit in the numerical sequence further changed to m bits.

The mapping initial value X ₀ is a value obtained by adaptively selecting a result value obtained by numerical processing such as an arbitrary calculation using an m-bit seed Seed within a specifiable range (1 ≦ X ₀ ≦ 2 ^L −1). It is. For example, a value after calculation of mod (2 ^L −1) +1 can be adopted. The initial parameter P is a value obtained by adaptively selecting a result value obtained by numerical processing such as an arbitrary calculation using an m-bit seed Seed within a specifiable range (1 ≦ X ₀ ≦ 2 ^L −1). It is. For example, a value after calculation of mod (2 ^L −1) +1 can be adopted. The above L is a numerical value resulting from the fact that the calculation accuracy in the mapping calculation means 20 is L bits and the coefficient M of the modified tent function described later is M = 2 ^L. Then, (2 ^L -1) is the 0 to 2 ^L from an integer value (including 0) (2 ^L +1) number exists, except 0 and the 2 ^L is a value at the end of this This means that it is (2 ^L −1). The meaning of excluding the numerical values at both ends is to exclude the case where the slope of one of the left and right mapping functions is infinite in the mapping function described later.

  The mapping calculation means 20 applies the initial parameter prepared by the initial value preparation means 10 and the mapping initial value to the modified tent function for the first time to perform mapping calculation, and for the second and subsequent times, the initial parameter or other parameters were previously obtained. The mapping value is applied to the modified tent function to perform mapping calculation.

  The mapping calculation means 20 of this embodiment performs mapping calculation using a plurality of tent functions. Here, mapping calculation is performed using the two modified tent functions F1 and F2 shown in FIGS. 2A and 2B, and an integer of the modified tent mapping by the modified tent function F1 in FIG. 2A. The arithmetic expression is as shown in the following expression (1), and the integer arithmetic expression of the modified tent mapping by the modified tent function F2 in FIG. 2B is as shown in the following expression (2).

The switching instruction means 60 instructs the switching of the tent function used by the mapping calculation means 20 based on the seed information Seed. As described above, the initial value preparation unit 10 obtains the mapping function selection information k _{0 to} km ₋₁ from the seed information Seed, and the mapping function selection information k _{0 to} km ₋₁ is “1” or “0”. ", An instruction to select one of the formula (1) and the formula (2) is given.

  The bit extraction unit 30 extracts a predetermined bit from the mapping value obtained by the mapping calculation unit 20 to obtain a pseudo random number. The bit extraction unit 30 determines a range for extracting a predetermined bit from the mapping value based on the seed information Seed, and performs extraction. That is, when the mapping value obtained by the mapping calculation means 20 has an L bit length, the number q of bits to be extracted from the L bit length is determined based on the seed information Seed, and which bits in the L bits are extracted. Decide whether to use q bits. The extracted bits are stored in the bit string storage unit 40 having a buffer. The storage is performed from the head side of the bit string storage unit 40, for example.

  The bit string storage unit 40 has a function of outputting a bit string from the buffer, and performs output processing at a predetermined timing. As a specific example, output is performed when the buffer is full. In this case, the buffer is cleared after output, the remaining bits that cannot be stored when the buffer is full are stored from the beginning of the bit string storage unit 40, and the same processing is repeated thereafter.

The parameter creation / updating means 50 creates and updates other parameters used by the mapping calculation means 20 based on the comparison result between the mapping value X _i obtained by the mapping calculation means 20 and the mapping initial value X ₀ . Since the mapping initial value X ₀ is sent by the initial value preparation means 10, it is stored in the register mem, and the mapping calculation means 20 determines the m-th mapping value X _i that is the same as the bit length m of the seed information Seed. When it is calculated, it is detected whether or not the calculated m-th mapping value X _i matches the mapping initial value X _0, and if they match, other parameters are created and updated.

Specifically, other parameters are created and updated by the following function h (P, Seed).
h (P, Seed) = (P + r (Seed)) mod (2 ^L −1) +1
In the above, r (Seed) indicates a result value obtained by numerical processing such as an arbitrary calculation using the seed information Seed.

  The control means 70 makes a determination at the end based on the end condition information of the pseudo-random number generation, proceeds to the next calculation by the mapping calculation means 20, and the next processing by the bit extraction means 30 and the parameter creation update means 50 To control the progress to. Specifically, it is detected whether the total number of bits extracted by the bit extraction means 30 has reached the random bit length n of a desired pseudorandom number set in advance. On the other hand, if the random bit length is n, the processing by each means is terminated.

  The pseudo-random number generator configured as described above is realized by, for example, a computer system as shown in FIG. The computer system has a configuration in which a CPU 1 is connected to a main memory 3, an input device 4, an output device 5, and an external storage device 6 via a bus 2. The main memory 3 stores a pseudo random number generation program PRG. Yes.

  The above-described CPU 1 executes the pseudo-random number generation program PRG corresponding to the flowchart shown in FIG. 4 to realize each unit in FIG. 1, and the processing of the pseudo-random number generation method will be described with reference to this flowchart. . Here, the seed information Seed and the random bit length n are given by, for example, the outside of the input device 4 or the like, but may be included in the pseudorandom number generation program PRG.

The CPU 1 starts an operation by the pseudo random number generation program PRG and performs initial value preparation processing (S11). In the initial value preparation process S11, mapping function selection information k _{0 to} km _-1 , an initial parameter P, and a mapping initial value X ₀ are prepared using seed information Seed. Here, as in the processing program shown in FIG. 5, the seed information Seed is held as it is as the mapping function selection information k _{0 to} km ₋₁ , the initial parameter P and the mapping initial value X ₀ , and the random bit length n is also set. Hold. Further, the mapping initial value X ₀ is held in the register mem, while the mapping count i is reset to zero.

Next, the CPU 1 counts up (S12). This count-up is a count-up of the number of mappings i, and is a process of “i ← i + 1”. Next, the CPU 1 performs function switching / mapping calculation processing (S13). This function switching / mapping calculation process is a process by the switching instruction unit 60 and the mapping calculation unit 20, and in detail, referring to the mapping function selection information k _j as shown in the flowchart of FIG. Depending on whether the mapping function selection information k _j is 0 or 1 (S21), either one of the above-mentioned formulas (1) and (2) is selected as an integer arithmetic formula (S22, S23). If this is shown as a processing program, it can be represented as shown in FIG. Subsequent to the above processing, the mapped value X _i is calculated by the selected integer arithmetic expression.

Next, the CPU 1 performs a bit extraction process (S14). In the bit extraction process, specifically, the following three examples can be given. The function of the first example is
b _{s to} b _{s + q} = g1 (X _i , X _{i + 1} , Seed),
q indicates the number of extracted bits at one time (arbitrary), s indicates the total number of extracted bits, and “s = s + q” after processing. The specific contents of g1 (X _i , X _{i + 1} , Seed) can be expressed by a program in C language shown in FIG. The contents of the symbols are shown on the right side of FIG.

To explain the specific examples, indicating a mapping value X _i to the third binary number from the first calculated as shown in FIG. 9, is like the right side of X _1, X _2, X _3, If the mapping function selection information k _j corresponding to the corresponding seed information is (k ₁ , k ₂ , k ₃ ) = ( ₁ , ₁ , 0), the mapping value X ₃ where k _j is 0 is bit-inverted. / get the X _3. For each of X ₁ , X ₂ , and / X ₃ , corresponding to the bit position where the bit in the mapping value X _{i + 1} (or / X _{i + 1} ) obtained later is 1, The bit value of the mapping value X _i (or / X _i ) obtained in the above is extracted.

  As a result, the bit value circled in FIG. 9 is extracted, and {1,0,1,0,0,1,1,0,0,...} Is stored in the buffer like BUF. Retained.

The function of the second example is
b _i = g2 (X _i , X _{i + 1} , Seed)
The specific contents of g2 (X _i , X _{i + 1} , Seed) can be expressed by a program in C language shown in FIG. The contents of the symbols are shown on the right side of FIG.

To explain with a specific example, it is the same as that in FIG. 9, and the mapping values X _i calculated from the first time to the third time as shown in FIG. 11 are expressed in binary numbers as X ₁ , X ₂ , X _If the mapping function selection information k _j corresponding to the corresponding seed information is (k ₁ , k ₂ , k ₃ ) = ( ₁ , ₁ , 0), the mapping is such that k _j is 0. The value X ₃ is bit-inverted to obtain / X ₃ . For each of X ₁ , X ₂ , and / X ₃ , corresponding to the bit position where the bit in the mapping value X _{i + 1} (or / X _{i + 1} ) obtained later is 1, The bit value of the mapping value X _i (or / X _i ) obtained in the above is extracted.

As a result of the above, the bit values circled in FIG. 11 are extracted as in FIG. 9, but after this, an exclusive OR operation is performed for each mapping value unit, and X _{1 is} calculated. Extract 1 and extract 0 for X ₂ .

The function of the third example is
b _i = g3 (X _i , Seed)
The specific contents of g3 (X _i , Seed) can be expressed by a program in C language shown in FIG. The contents of the symbols are shown on the right side of FIG.

More specifically, assuming that mapping function selection information k _j corresponding to seed information is {1, 1, 0, 0, 1, 1,...} As shown in FIG. The amount is increased by 2, and the shift amount is calculated as {2, 4, 4, 4, 6, 0 (8),. When the i-th mapping value X _i is represented by a binary number, if X ₁ = { _1, 0, _1, 0, 0, ₁ , _1, 0, 0}, a right shift of the calculated shift amount. Is done. If the shift amount of k _j is 6, the shift X ₁ becomes {0, 0, 0, 0, 0, 0, 1, 0, 1}.

FIG. 14 (a) shows a case where the shift amount is increased 2 when the mapping function selection information k _j is 1, FIG. 14 (b), the mapping function selection information k _j in 2 bits (e.g., k _j And k _{j + 1} ), the shift amount is increased by 0 when they are 00, the shift amount is increased by 3 when they are 01, and the shift amount is increased by 9 when they are 10. This shows a case where the shift amount is increased by 0 when.

  Here, since cyclic shift (rotate) is used by shifting, even if a shift amount of 7 or more is allowed, all bits in the cyclic shift result value do not become zero. For example, in the processing corresponding to FIG. 14A, when the shift amount is 3, a shift result value is obtained as shown in FIG. 14C by cyclic shift, and the lowest (rightmost) result value is obtained. By extracting one bit, the bit extraction process in step S14 can be completed.

  In the present invention, since all the digits of the mapping value can be used as random numbers by using the modified tent mapping, the extraction position of the mapping value bit digit can be arbitrarily selected, and the degree of freedom can be widely utilized. As a technique that makes use of these features, this embodiment is configured to provide a mechanism that allows the user to freely change the random bit generation pattern by referring to the mapping function selection information corresponding to the seed information in the bit extraction process. ing.

  Furthermore, by using the seed information Seed used for initial value setting and the separate seed information for the bit extraction process, the user can make the pattern of the random bit sequence rich. Further, the random bit string generation pattern can be changed by using seed information and other seed information given to the mapping function as in this embodiment, and the variation of the random bit string pattern can be further increased.

  Following the bit extraction process in step S14, the CPU 1 performs a bit string recording output process (S15). In the bit string recording output process, the bits extracted in the bit extraction process are stored in the buffer in order from the head side to create a bit string, and output at a predetermined timing. As a specific example, output is performed when the buffer is full.

  For example, as shown in FIG. 15, the size of the buffer BUF is 1 byte, {1,0,1} is obtained by the first bit extraction, and {0,0,1,1 is obtained by the second bit extraction. , 0, 0} are extracted. In this case, the first extraction bit {1, 0, 1} is stored in the buffer BUF, and then {0, 0, 1, 1 up to the fifth bit in the second extraction bit. , 0} is stored, the buffer BUF becomes full. Here, the output bit string {1, 0, 1, 0, 0, 1, 1, 0} is output. After the output, the buffer BUF is cleared and the remaining 1 bit {0} in the second extracted bit is stored in the buffer BUF. Thereafter, the processing proceeds in the same manner as described above.

  Instead of the output bit string output processing as described above, a request is generated from a system using pseudo-random numbers, and the CPU 1 may output the output bit string when requested by this system. good. Alternatively, the user may be configured to generate an output request, and the output bit string may be output when the user requests. Further, the output bit string may be output when the pseudo random number generation is completed. Any output timing may be adopted, but in each case, the capacity of the buffer BUF is set to a necessary capacity.

Following the bit string record output process, the CPU 1 performs a parameter creation update process (S16). In the parameter creation / updating process, the mapping value X _i obtained by performing the function switching / mapping calculation process in step S13 and the mapping initial value X ₀ prepared in the initial value preparation process in step S11 and stored in the register mem. Based on the comparison result, the parameter P is created and updated.

Specifically, as shown in FIG. 16, when it is detected that the number of mapping calculations is the same as the bit length m of the seed information Seed, the mapping initial value X ₀ stored in the register mem and the current time The calculated map value X _i is compared (S31), and it is detected whether it is the same value (S32).

If it is detected in step 32 that they are not the same value, it passes as it is, and if it is detected in step 32 that it is the same value, other parameters are created and updated by the next function h (P, Seed) (S33).
h (P, Seed) = (P + r (Seed)) mod (2 ^L −1) +1
In the above, r (Seed) indicates a result value obtained by numerical processing such as an arbitrary calculation using the seed information Seed.

When the parameter creation / updating process in step S16 is completed, the CPU 1 performs an end determination process S17 (S17). That is, it is detected whether the total number of bits extracted by the bit extraction process has reached a random bit length n of a desired pseudo-random number set in advance. In order to perform the process, the process returns to the count-up process (S12) to continue the process. On the other hand, if the random bit length is n, the process is terminated. In this way, the output bit string output by the bit string recording output process (S15) becomes {b ₁ , b ₂ , b ₃ ,..., B _n }, and a pseudo-random number having a required bit length can be obtained.

  Next, a second embodiment will be described. In the pseudo random number generator according to the second embodiment, as shown in FIG. 17, the switching instruction means 60 provided in the pseudo random number generator of FIG. 1 is not provided, and the map calculation means 20A and A parameter creation / updating means 50A is provided. Except this, it has the same configuration as the pseudo-random number generator of FIG.

  The mapping calculation means 20A performs mapping calculation by one modified tent function, and uses, for example, the modified tent function F1 shown in FIG. Therefore, the switching instruction means 60 for instructing switching of the tent function is not necessary.

The parameter creating / updating means 50A detects whether the calculated mapping value X _i matches the mapping initial value X ₀ every time mapping calculation by the mapping calculation means 20A is performed. Create and update parameters. In this process, when the m-th mapping value X _i that is the same as the bit length m of the seed information Seed is calculated by the mapping calculation means 20, the calculated m-th mapping value X _i is the mapping initial value X _0. Is different from the parameter creating / updating means 50 that creates and updates other parameters when they match.

  The pseudo-random number generator according to the second embodiment configured as described above is realized by, for example, a computer system as shown in FIG. 3 in the same manner as the pseudo-random number generator according to the first embodiment. The CPU 1 shown in FIG. 3 executes the pseudo-random number generation program PRG corresponding to the flowchart shown in FIG. 18 to implement the means shown in FIG. The process will be described.

  As apparent from the comparison of the flowchart shown in FIG. 18 with the flowchart shown in FIG. 4, instead of step S <b> 13 in FIG. 4, mapping calculation processing is performed as step S <b> 13 </ b> A in FIG. 18. Also, instead of step S16 in FIG. 4, in FIG. 18, parameter creation / update processing is performed as step S16A. Since the other processes are the same as those in the first and second embodiments, only step S13A and step S16A will be described.

In the mapping calculation process of step S13A, mapping calculation is performed by the following equation using the modified tent function F1.
_{X i = F1 (X i-} 1, P)
F1 has already been shown as equation (1). In this way, when the mapping calculation process in step S13A is performed and the mapping value X _i is obtained, the CPU 1 performs the bit extraction process (S14) and the bit string recording output process (S15) as described above. Then, the parameter creation / updating process of step S16A is performed.

In the parameter creation / updating process in step S16A, as shown in FIG. 19, when it is detected that the mapping calculation has been performed, the mapping initial value X ₀ stored in the register mem and the mapping value calculated this time are calculated. comparing the X _i (S31A), to detect whether the same value (S32).

If it is detected in step 32 that they are not the same value, it passes as it is, and if it is detected in step 32 that it is the same value, other parameters are created and updated by the next function h (P, Seed) (S33).
h (P, Seed) = (P + r (Seed)) mod (2 ^L −1) +1
In the above, r (Seed) indicates a result value obtained by numerical processing such as an arbitrary calculation using the seed information Seed.

When the parameter creation / updating process in step S16A is completed, the CPU 1 performs an end determination process S17 (S17). That is, it is detected whether the total number of bits extracted by the bit extraction process has reached a random bit length n of a desired pseudo-random number set in advance. In order to perform the process, the process returns to the count-up process (S12) to continue the process. On the other hand, if the random bit length is n, the process is terminated. In this way, the output bit string output by the bit string recording output process (S15) becomes {b ₁ , b ₂ , b ₃ ,..., B _n }, and a pseudo-random number having a required bit length can be obtained.

1 CPU
2 Bus 3 Main memory 4 Input device 5 Output device 6 External storage device 10 Initial value preparation means 20, 20A Mapping calculation means 30 Bit extraction means 40 Bit string storage section 50, 50A Parameter creation update means 60 Switching instruction means 70 Control means

JP 2001-285277 A JP 2002-2105018 A JP 2005-529364A

Claims (9)

Initial value preparation means for preparing initial parameters and mapping initial values;
In the first time, the initial parameter and the initial value of the mapping are applied to the modified tent function to perform the mapping calculation. In the second and subsequent times, the initial parameter or other parameters and the previously determined mapping value are applied to the modified tent function. Mapping calculation means for performing
A bit extraction unit that extracts a predetermined bit from the mapping value obtained by the mapping calculation unit to obtain a pseudo-random number;
Based on a comparison result between the mapping value obtained by the mapping calculation means and the mapping initial value, parameter creation updating means for creating and updating other parameters used by the mapping calculation means;
Control for determining the end time based on the end condition information of the pseudo-random number generation and controlling the progress to the next calculation by the mapping calculation means and the progress to the next processing by the bit extraction means and the parameter creation / update means And a pseudo-random number generator. The mapping calculation means performs mapping calculation by a plurality of tent functions.
The initial value preparation means prepares seed information,
2. The pseudorandom number generator according to claim 1, further comprising switching instruction means for instructing switching of a tent function used by the mapping calculation means based on the seed information. The bit extraction means determines a range for extracting a predetermined bit from the mapping value based on the seed information,
3. The pseudorandom number generator according to claim 2, wherein the parameter creation / update means performs parameter creation / update based on the seed information. An initial value preparation step for preparing initial parameters and initial mapping values;
In the first time, the initial parameter and the initial value of the mapping are applied to the modified tent function to perform the mapping calculation. In the second and subsequent times, the initial parameter or other parameters and the previously determined mapping value are applied to the modified tent function. A map calculation step for performing
A bit extraction step of extracting a predetermined bit from the mapping value obtained by the mapping calculation step and making it a pseudo-random number;
Based on the comparison result between the mapping value obtained by the mapping calculation step and the mapping initial value, a parameter creation update step for creating and updating other parameters used in the mapping calculation step;
Control for determining the end time based on the end condition information of the pseudo random number generation and controlling the progress to the next calculation by the mapping calculation step and the progress to the next processing by the bit extraction step and the parameter creation and update step A pseudo-random number generation method comprising the steps of: In the map calculation step, the map calculation is performed using a plurality of tent functions.
In the initial value preparation step, seed information is prepared,
5. The pseudorandom number generation method according to claim 4, further comprising a switching instruction step for instructing switching of a tent function used by the mapping calculation step based on the seed information. In the bit extraction step, a range for extracting a predetermined bit from the mapping value based on the seed information is determined,
6. The pseudo-random number generation method according to claim 5, wherein the parameter creation / update step performs parameter creation / update based on seed information. A computer that generates pseudo-random numbers through computation,
Initial value preparation means for preparing initial parameters and initial mapping values;
In the first time, the initial parameter and the initial value of the mapping are applied to the modified tent function to perform the mapping calculation. In the second and subsequent times, the initial parameter or other parameters and the previously determined mapping value are applied to the modified tent function. Mapping calculation means for performing
Bit extraction means for extracting a predetermined bit from the map value obtained by the map calculation means and making it a pseudo-random number;
Based on a comparison result between the mapping value obtained by the mapping calculation means and the mapping initial value, parameter creation updating means for creating and updating other parameters used by the mapping calculation means;
Control for determining the end time based on the end condition information of the pseudo-random number generation and controlling the progress to the next calculation by the mapping calculation means and the progress to the next processing by the bit extraction means and the parameter creation / update means A pseudo-random number generation program characterized by functioning as a means. Using a computer as a mapping calculation means, functioning to perform mapping calculation with a plurality of tent functions,
Let the computer function as an initial value preparation means to prepare seed information,
8. The pseudo-random number generation program according to claim 7, wherein the computer is caused to function as switching instruction means for instructing switching of a tent function used by the mapping calculation means based on the seed information. The computer functions as a bit extraction means to determine a range for extracting a predetermined bit from the mapping value based on the seed information,
8. The pseudo-random number generation program according to claim 7, wherein the computer functions as parameter creation / update means so as to create / update parameters based on seed information.

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