JP2007287079A - Pseudo random number generation device, pseudo random number generation method, pseudo random number generation program, ciphering device and deciphering device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a pseudo random number generation device capable of outputting the random number sequence of a long cycle by a relatively small device scale. <P>SOLUTION: The pseudo random number generation device comprises: a pseudo random number generator 11 for generating a primary random number R1; a register 12 comprising storage elements for the same number as the number of kinds of the random number patterns of a secondary random number R2, where the different random number patterns are stored in the respective storage elements; and a control part 13 for agitating the register 12 with the two or more storage elements specified by selected first address and second address as objects and outputting a numerical value stored in the storage element specified by a selected third address as the secondary random number. At least one of the first address, the second address and the third address is supplied as the primary random number R1 or an operational value based on the primary random number R1. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a pseudo-random number generation device, a pseudo-random number generation method, a pseudo-random number generation program, an encryption device, and a decryption device, and more particularly, an array configured of a plurality of storage elements and storing all types of random number patterns. Pseudorandom number generation device, pseudorandom number generation method, pseudorandom number generation program, pseudorandom number generation program capable of generating long-term secondary random number from primary random number with short cycle, and encryption device and decryption including the pseudorandom number generation device The present invention relates to a conversion device.

  Here, terms used in this specification are defined as follows. The random number pattern means a random number bit pattern generated with a bit string having a predetermined number of bits as a unit. A random value means a random number represented by a decimal number. An array refers to a continuous or intermittent collection of a plurality of storage elements each having a unique address. Specifically, the array is given as a predetermined storage area on a register or RAM.

  Stirring an array means replacing the numerical values stored in the storage elements without changing the combination of the numerical values stored in the array. For example, it is assumed that numerical values a, b, and c are stored in the storage elements A, B, and C, respectively. When the array is agitated for the storage element A and the storage element B, the numerical value b is stored in the storage element A, and the numerical value a is stored in the storage element B. When the array is agitated for the storage elements A, B, and C, the numerical value c is stored in the storage element A, the numerical value a is stored in the storage element B, and the numerical value b is stored in the storage element C.

  An arithmetic value means a numerical value obtained as a result of an arbitrary arithmetic process executed based on one or more given numerical values. Examples of the arithmetic processing include arithmetic processing for calculating a function value by substituting a numerical value given to a variable constituting the function, and dividing one or a plurality of bit strings representing a numerical value given based on a predetermined rule Processing for generating numerical values, arithmetic processing for generating numerical values by combining bit strings each representing a plurality of numerical values given based on a predetermined rule, and inputting numerical values given to a buffer such as a FIFO Examples include arithmetic processing for outputting numerical values, arithmetic processing for outputting numerical values corresponding to numerical values given by referring to a table such as an address correspondence table, and arithmetic processing realized by arbitrarily combining these arithmetic processing.

  In the present invention, the array has the same number of storage elements as the number of random number patterns of random numbers output from the pseudo-random number generator. The storage element has a storage capacity equal to or greater than the number of bits that is a unit for generating random numbers. The agitation of the array is performed on at least two storage elements. Two addresses for specifying two storage elements to be an object of stirring the array are set as a first address and a second address, respectively. Also, an address for specifying a storage element from which the secondary random number is extracted is assumed to be a third address.

  Currently used encryption methods are roughly classified into a public key encryption method and a common key encryption method. In the public key cryptosystem, one of a public key and a secret key is used for encryption, and the other key is used for decryption. In the common key cryptosystem, the same key (common key) is used for encryption and decryption. The common key cryptosystem is roughly classified into a block cryptosystem and a stream cryptosystem. In the block encryption method, plaintext is divided into blocks of a predetermined size, and encryption is executed in units of blocks. Also for the ciphertext, the ciphertext is decrypted in units of blocks by using the same key as that used to encrypt the block for each block. In the stream encryption method, on the encryption device side, for example, a pseudo random number (key stream) sequentially generated from a predetermined initial state given by a common key is used as a key in a bit unit or a predetermined number of bit strings. Performs a logical operation (preferably exclusive OR) on the unit to encrypt the plaintext. Also on the decryption device side, the ciphertext is decrypted by performing a logical operation in bit units or a predetermined number of bit string units with the ciphertext using the same key stream.

  In the common key cryptosystem, pseudo random numbers are often used as a session key changed for each session or as a key stream. In particular, in the stream encryption method, since plain text is encrypted as it is into cipher text using a key stream given as a pseudo random number, the randomness of the pseudo random number has a strong influence on the encryption strength. As a pseudo random number generator for generating a pseudo random number, a linear congruence generator, a linear feedback shift register (LFSR), and the like are known.

The linear congruence generator generates pseudo-random numbers based on the following mathematical formula.
_Xn = (aXn _-1 + b) mod m (1)
X ₀ given as an initial value, for example given by the common key shared by the transmission side and the receiving side. Since the total number of states is m, the maximum period (longest period) is m. It is known that this pseudo-random number generation method has a simple generation algorithm, can generate random numbers at high speed, and exhibits a good statistical behavior.

FIG. 7 is a diagram illustrating an example of the configuration of the linear feedback shift register. The values of C _{1 to} C _{n in} the figure are set to 0 or 1 in advance. For each stage of the n-stage shift register, the exclusive OR of the numerical values S _i−k stored in the storage elements of the stage where C _k = 1 is the output S _i . In the shift operation, this output S _i is fed back. The initial state of the linear feedback shift register is given by, for example, a common key shared between the transmission side and the reception side. If 0 is stored in all stages, it is only output permanently 0, so this cannot be used as a random number. Therefore, the maximum period of the linear feedback shift register is 2 ⁿ −1. The random number sequence having the maximum period is called an M sequence. The pseudo-random number generator such as the linear congruence generator and the linear feedback shift register as described above is described in, for example, “Introduction to Cryptography” (Kyoritsu Publishing Co., Ltd., Eiji Okamoto, published in 1993).

"Introduction to cryptography" (Kyoritsu Publishing Co., Ltd., written by Eiji Okamoto, published in 1993)

  The pseudo-random number generator as described above has a relatively simple random number generation algorithm and outputs a random number sequence with a relatively short period. There was a problem that there was. Further, a method of combining outputs of a plurality of linear feedback shift registers with a non-linear combiner has been devised, but there is a problem that the apparatus scale becomes large in order to obtain a sufficient period.

  In order to solve the above problems, the present invention provides a pseudo-random number generation device, a pseudo-random number generation method, a pseudo-random number generation program, and a pseudo-random number generation device capable of generating a long-period random number sequence with a relatively small device scale. It is an object of the present invention to provide an encryption device and a decryption device that are provided.

  The random number is given as a bit string composed of a set of binary bits having a value of “0” or “1”. As a random number generation unit, for example, 2 bits are considered. There are four types of random number patterns obtained as 2 bits: “00”, “01”, “10”, and “11”. The permutation obtained from four random values is 4! Gives 24 patterns. On the other hand, in random number generation using a linear congruence generator or a linear feedback shift register, a random number value x is output next to a random number value y, and then a random number value x is output and then a random number value y other than the random number value y. Will not be output. That is, the random number sequence output from the linear congruence generator or the linear feedback shift register has a cyclic characteristic. In such a case, a random number sequence having a maximum period composed of random numbers generated in units of 2 bits is 8 bits (2 bits * 4 patterns).

Next, 1 byte (8 bits) that can be easily handled by a computer is considered as a random number generation unit. There are 2 ⁸ = 256 random number patterns of random numbers obtained as 8 bits. The permutation obtained from 256 random values is 256! Is approximately 8.6 * 10 ⁵⁰⁶ , and an almost infinite pattern can be obtained. On the other hand, in random number generation using a linear congruence generator or a linear feedback shift register, since a generated random number sequence has a cyclic characteristic, a random number sequence having a maximum period consisting of random numbers generated in units of 8 bits is 2048. This is a bit (8 bits * 256 patterns).

  As described above, the maximum period of the random number sequence output from the linear congruence generator or the linear feedback shift register and having the cyclic characteristic is not large. In the present invention, for a random number generated with a predetermined number of bits as a unit, a numerical sequence given by a permutation based on a set of different random values corresponding to each random number pattern has a very large number of patterns. Pay attention to. Therefore, an array having the same number of storage elements as the number of types of random number patterns is prepared. By storing different random number patterns in the respective storage elements in the array, it is possible to express numerical sequences of all patterns as permutations in the array.

  In the present invention, in principle, the arrangement is agitated for two storage elements specified by the first address and the second address selected based on a predetermined rule. Further, the numerical value stored in the storage element specified by the third address selected based on a predetermined rule is output as a random number from the pseudo random number generation device. As described above, since a numerical sequence given by a permutation based on a set of different random values has an almost infinite pattern, it is highly possible to obtain a random sequence having a long period from the array. The present invention provides at least one of the first address, the second address, and the third address as a first random number having a short period or an operation value based on the first random number, It is intended to generate a long second random number.

  In order to solve the above technical problem, a pseudo-random number generation device according to the present invention comprises a pseudo-random number generation means for generating a first random number, and the same number of storage elements as the number of types of second random number patterns. And an array in which different random number patterns are stored in each storage element, and at least two storage elements specified by the first address and the second address selected are agitated. And a control means for outputting a numerical value stored in the storage element specified by the selected third address as a second random number, and comprising the first address, the second address, and the third At least one of the addresses is given as a first random number or an operation value based on the first random number.

  In the pseudo random number generation device according to the present invention, the control means calculates a remainder obtained by dividing the number of generations of the first random number by the number of types of the random number pattern of the second random number, and the first address or the second At least one of the addresses is given as the remainder or an operation value based on the remainder.

  In the pseudo random number generation device according to the present invention, the first address and the third address are given as the first random number or an operation value based on the first random number, and the second address is the remainder or the remainder. It is made to be given as a calculation value based on.

  In the pseudo random number generation device according to the present invention, the first address and the third address are given as the remainder or a calculated value based on the remainder, and the second address is the first random number or the first random number. It is made to be given as a calculation value based on.

  In the pseudorandom number generation device according to the present invention, the pseudorandom number generation means is provided as a linear congruence generator or a linear feedback shift register.

  The pseudo-random number generation device according to the present invention includes a first pseudo-random number generation unit that generates a first random number, a second pseudo-random number generation unit that generates a third random number, and a random number of a second random number. It is composed of the same number of storage elements as the number of types of patterns, and each storage element stores an array in which different random number patterns are stored, and at least two or more specified by the selected first address and second address Control means for agitating the array for the storage element and outputting a numerical value stored in the storage element specified by the selected third address as a second random number, At least one of the address, the second address, and the third address is provided as a first random number or an operation value based on the first random number, and the first address or the second address is provided. At least one of the address-less, is obtained as given as an operation value based on the third random number and the third random number.

  In the pseudo random number generation device according to the present invention, the control means calculates a remainder obtained by dividing the number of generations of the first random number by the number of types of random number patterns of the second random number, and the first address is the third number. Given as a computation value based on a random number or a third random number, a second address is given as a computation value based on the remainder or the remainder, and a third address is a computation value based on the first random number or the first random number Is to be given as

  The encryption device according to the present invention is configured to include the pseudo-random number generation device according to the present invention, and the bit sequence for the random number sequence output from the pseudo-random number generation device and the data sequence constituting the plaintext A predetermined logical operation is executed every time or every predetermined number of bit strings to generate a data series constituting the ciphertext.

  The pseudo-random number generation method according to the present invention includes a step of generating a first random number, a step of calculating a remainder obtained by dividing the number of generations of the first random number by the number of types of random number patterns of the second random number, In an array comprising a step of selecting the first address and the second address, and the same number of storage elements as the number of types of the random number pattern of the second random number, each storage element storing a different random number pattern Exchanging the numerical value stored in the storage element specified by the first address with the numerical value stored in the storage element specified by the second address, selecting the third address, and array And outputting a numerical value stored in the storage element specified by the third address as a second random number, and the number of the first address, the second address, and the third address is small. One address is given as the first random number or the calculated value of the first random number, and at least one address of the first address or the second address is given as the calculated value of the remainder or the remainder It is a thing.

  Further, the pseudo random number generation program according to the present invention includes a step of generating a first random number, a step of calculating a remainder obtained by dividing the number of generations of the first random number by the number of types of random number patterns of the second random number, A step of giving the first address and the second address as a first random number or a calculated value based on the first random number, or the remainder or a calculated value based on the remainder, respectively, and the number of types of random number patterns of the second random number In the array in which different random number patterns are stored in each storage element, specified by the numerical value stored in the storage element specified by the first address and the second address Exchanging the numerical value stored in the storage element, and the third address, the first random number, the calculated value based on the first random number or the remainder or And providing a calculated value based on the serial remainder is obtained by the numerical values stored in the storage element specified by a third address in the sequence to a step of outputting the second random number.

  According to the present invention, it is composed of pseudo-random number generating means for generating a first random number and the same number of storage elements as the number of types of random number patterns of the second random number, and different random number patterns are stored in the respective storage elements. The array is agitated for at least two or more storage elements specified by the selected first address and second address, and the storage element specified by the selected third address Control means for outputting a stored numerical value as a second random number, wherein at least one of the first address, the second address, and the third address is the first random number or the first random number. Since it is configured to be given as a calculation value based on a random number, it is possible to express a numerical series with a huge number of patterns as a permutation by stirring. By retrieving the second random number from 憶 element, an effect that can be obtained a long random sequence of cycles.

  According to the present invention, a remainder obtained by dividing the number of generations of the first random number by the number of types of random number patterns of the second random number is calculated, and at least one of the first address and the second address is the remainder. Alternatively, since it is configured to be given as an operation value based on the remainder, it is guaranteed that the addresses of all the storage elements in the array are evenly selected, and the array can be uniformly stirred over the entire range. Therefore, there is an effect that the possibility of obtaining a random number sequence having a long cycle can be increased. In addition, since the remainder can be calculated by a simple calculation using a simple calculation circuit such as a counter, the circuit configuration of the pseudo random number generation device can be simplified.

  According to the present invention, since the pseudo-random number generation means is configured to be provided as a linear congruence generator or a linear feedback shift register, it is possible to generate the first random number using a relatively simple arithmetic circuit. Therefore, the circuit configuration of the pseudorandom number generator can be simplified.

  According to the present invention, the third pseudo random number generating means provided separately from the first pseudo random number generating means for generating the first random number is used to generate the third random number, and the third random number is used. Since the arrangement is agitated, the influence of the first random number period can be reduced and the stored contents of the arrangement can be changed. An array that can represent a sequence can be used more effectively, and a random number sequence having a long period can be obtained.

  First, the operation principle of the pseudorandom number generator according to the present invention will be described using a simple model. FIG. 1 is a diagram showing the configuration of a model for explaining the operating principle of the pseudorandom number generator according to the present invention. In FIG. 1, 1 is a pseudo-random number generator that generates a primary random number R1 having a short cycle, 2 is a register composed of 10 storage elements having addresses 0 to 9, and 3 is a register that agitates register 2 and registers 2 is a control unit that outputs a numerical value stored in one of the storage elements 2 as a secondary random number R2.

  The pseudo random number generator 1 outputs a numerical value in a numerical range of 0 to 9 as a random number. The ten storage elements of the register 2 store numerical values of 0 to 9 one by one. That is, the same numerical value is not stored in different storage elements of the register 2. Thereby, if a numerical value stored in an arbitrary storage element in the register 2 is taken out as a secondary random number, the secondary random number takes any numerical value in a numerical range of 0-9.

The control unit 3 counts the number of generations of the primary random number R1 and sets a sequence number I indicating the generation order of the secondary random numbers. The control unit 3 calculates the circulation sequence number Im based on the formula (2).
Im = I mod 10 (2)
That is, the circulation sequence number Im is given as a remainder obtained by dividing the sequence number I by 10 and circulates in the cycle 10. A numerical value 10 excluding the sequence number I is the same as the number of storage elements constituting the register 2. As a result, it is possible to select the addresses of all the storage elements constituting the register 2 based on the primary random number R1 and the cyclic sequence number Im output from the pseudo-random number generator 1.

  Table 1 is a table showing a process of generating pseudo random numbers. Here, it is assumed that the pseudorandom number generator 1 sequentially outputs a random number sequence “0-1-4-3” having a period of 4. It is assumed that the sequence number I starts from 0 corresponding to the address of the register 2 starting from 0. As for the address that specifies the two storage elements to be targeted when the register 2 is stirred, the first address is given as the primary random number R1, and the second address is given as the circulation sequence number Im. In Table 1, these numerical values given as addresses are hatched. Further, the third address for specifying the storage element from which the secondary random number R2 is extracted is given as the primary random number R1. The control unit 3 exchanges a numerical value stored in the storage element having the primary random number R1 as an address and a numerical value stored in the storage element having the circulation sequence number Im as an address. Thereafter, the control unit 3 outputs the numerical value stored in the storage element having the primary random number R1 as an address as the secondary random number R2.

  As an example, after the random number sequence of “0-1-4-3” is generated as the primary random number R1 for three periods, the secondary random number R2 is generated when “0” is output as the next primary random number R1. Will be described. When “0” is output as the primary random number R1, the sequence number I is incremented by 1, so that 12 is set as I. Since mod (12, 10) is 2, 2 is set as the circulation sequence number Im. Due to the agitation of the register up to the previous time, the numerical value 6 is stored in the storage element of the address “0” given as the primary random number R1 in the register 2, and the storage element of the address “2” given as the circulation sequence number Im is stored in the register 2 The numerical value 4 is stored. The control unit 3 exchanges these numerical values. That is, the numerical value 4 is stored in the storage element at the address “0”, and the numerical value 6 is stored in the storage element at the address “2”. When the exchange of numerical values is completed, the control unit 3 outputs the numerical value 4 stored in the storage element of the address “0” given as the primary random number R1 as the secondary random number R2.

  As shown in Table 1, in the random number generation process of 15 times, all numerical values of 0 to 9 are output as the secondary random number R2, and no period appears. The stored contents of the register 2 are all different from the initial values. As described above, it is possible to generate a secondary random number having a long cycle based on the primary random number “0-1-4-3” having a cycle 4 output from the pseudo-random number generator 1. In the above random number generation process, the secondary random number is extracted after the register is stirred. However, the register may be stirred after the secondary random number is extracted.

  Embodiments according to the present invention will be described below with reference to the accompanying drawings. In the following description, in order to clarify the correspondence between each constituent element of the embodiment and each constituent element of the invention described in the claims, each constituent element of the embodiment is described. Each component of the invention described in the corresponding claims will be appropriately indicated in parentheses in the following description.

Embodiment 1 FIG.
FIG. 2 is a diagram showing an example of the configuration of the pseudorandom number generator according to Embodiment 1 of the present invention. Here, a pseudo-random number generator that outputs a 1-byte (8-bit) random number that is easy to handle by a computer will be described. A random number given by 8 bits has 256 different random number patterns. In FIG. 2, 11 is a pseudorandom number generator (pseudorandom number generating means) that generates a primary random number (first random number) R1 having a relatively short cycle, which is given as, for example, a linear congruence generator or a linear feedback shift register. Is a register (array) configured with the same number of storage elements as the random number pattern of the secondary random number (second random number) R2, each storing a different random number pattern. The register 12 is agitated for two storage elements in the register 12 specified by the first address and the second address, and stored in the storage element in the register 12 specified by the selected third address. It is a control part (control means) which outputs a numerical value as secondary random number R2.

In this embodiment, as the pseudo-random number generator 11, a linear congruence generator that generates an 8-bit random number pattern in a numerical range of 0 to 255 based on the following equation (3) is adopted.
R _{i + 1} = (3 * R _i +1) mod 256 (3)
A remainder obtained by multiplying the generated random number R _i by 3 and adding 1 to the result is divided by 256 to be a newly generated random number R _{i + 1} . The linear congruence generator that generates random numbers based on Equation (3) generates a random number sequence with a period of 128 when generating random numbers with an initial value R ₀ = 0. That is, this linear congruence generator outputs 128 types of random number patterns which are half of 256 types of random number patterns represented by 8 bits.

  The register 12 is composed of 256 storage elements having addresses in the numerical range of 0 to 255, and each storage element employs a register having a storage capacity of 8 bits. For the control unit 13, in order to exchange numerical values stored in any two storage elements in the register 12, a storage unit that stores one or both numerical values, a counter that counts the number of random numbers generated, and the like It is good also as a structure which incorporates. Further, these components can be provided independently in the control unit 13.

FIG. 3 is a flowchart showing an example of the pseudo-random number generation method according to Embodiment 1 of the present invention. The pseudo random number generator 11 generates and outputs a primary random number R1 consisting of 8 bits (step 1). The control unit 13 increments the sequence number I by 1 each time the primary random number R1 is output from the pseudo random number generator 11 (step S2). For example, the processing value can be realized by associating the count value of the counter built in the control unit 13 with the sequence number I and incrementing the count value of the counter by 1 each time the primary random number R1 is output. it can. If the sequence number I is set, the control unit 13 calculates the circulation sequence number Im based on the following equation (4) (step S3).
Im = I mod 256 (4)
256 represents the number of types of secondary random number patterns. As a result, Im gives a numerical value in the range of 0 to 255 in order, so that the addresses of the storage elements in the register 12 are evenly selected based on the cyclic sequence number Im or the calculated value based on the cyclic sequence number Im. Is possible.

  If the circulation sequence number Im is set, the control unit 13 exchanges the numerical value stored in the storage element having the primary random number R1 as an address and the numerical value stored in the storage element having the circulation sequence number Im as an address. (Step S4). For example, the process can be realized by executing a numerical value exchange between a storage unit built in the control unit 13 and a storage element in the register 12. If the stirring of the register is completed, the control unit 13 outputs the numerical value stored in the storage element having the primary random number R1 as an address as the secondary random number R2 (step S5). If the secondary random number R2 is output, it is determined whether or not the output of a predetermined number of random number sequences has been completed (step S6). If the output of the predetermined number of random number sequences has not been completed, the process returns to step S1, and the process of generating a new secondary random number R2 is continued. If the output of the predetermined number of random number sequences has been completed, the processing relating to random number generation is terminated.

  Table 2 is a table showing the appearance tendency of the random number pattern appearing in the random number sequence obtained by using the pseudo random number generation device according to the first embodiment. As shown in Table 2, the number of types of random number patterns in the random number sequence appearing as the secondary random number reaches the upper limit of 256 by generating the secondary random number over the number of times that the primary random number circulates seven times. . When actually verified, it was found that the secondary random number has a period of 32,768. Since the period of the primary random number is 128, the secondary random number has a period 256 times that of the primary random number (32,768 / 128 = 256).

  Table 3 is a table showing the distribution status of each random number pattern appearing in the random number sequence obtained by using the pseudo-random number generator according to the first embodiment. In Table 3, the random pattern appearance average number represents the average value of the number of appearances for each random number pattern of the secondary random number. The minimum number of appearances of the random number pattern indicates the minimum number of appearances among the appearance numbers of all the random number patterns of the secondary random numbers. The maximum number of appearances of the random number pattern indicates the maximum number of appearances among the appearance numbers of all random number patterns of the secondary random number. For the maximum deviation of the number of appearances, the absolute value of the difference between the average number of appearances of the random number pattern and the minimum number of appearances of the random number pattern and the absolute value of the difference between the average number of appearances of the random number pattern and the maximum number of appearances of the random number pattern Indicates the number divided by the average number of times. The average deviation of the number of appearances is the type of random number pattern obtained by accumulating the numerical value obtained by dividing the absolute value of the difference between the number of appearances and the random number pattern appearance average number by the random number pattern appearance average number for each random number pattern of the secondary random number. A numerical value divided by a number (ie 256) is shown. The deviation rate is a percentage of the average appearance frequency deviation. As shown in Table 3, it can be seen that as the number of random number generations increases, the deviation rate decreases and the number of appearances of each random number pattern is averaged. The deviation rate of 0.01% means that each random number pattern appears on average from 9999 to 10001 times in 256 * 10000 random number generation.

Needless to say, the pseudo-random number generator 11 is not limited to a linear congruence generator that executes random number generation based on Equation (3). For example, you may employ | adopt the linear congruence generator which produces | generates the 8-bit random number pattern of the numerical value range of 0-255 based on the following formula | equation (5).
R _{i + 1} = 3 * R _i mod 256 (5)
A random number generation test was also performed using this linear congruence generator. A linear congruence generator that generates primary random numbers based on equation (5) outputs a random number sequence with a period of 64. It was found that the secondary random number output from the pseudo random number generator adopting this linear congruence generator as the pseudo random number generator 11 has a period of 65,536. Since the period of the primary random number is 64, the secondary random number has a period of 1,024 times (65,536 / 64) of the primary random number.

In the first embodiment, the register 12 given as an array has 256 storage elements, and each storage element has a storage capacity of 8 bits. However, the present invention has such a configuration. It is not limited. For example, when the computer operates in units of 2 bytes, a register including 65536 storage elements each having a storage capacity of 2 bytes is prepared. When the storage element has a storage capacity of n bits and the numerical value stored in the storage element is output as a secondary random number, the number of types of the random number pattern of the secondary random number is ²ⁿ . Therefore, by preparing a register composed of 2 ⁿ storage elements, it is possible to generate an n-bit secondary random number having a long cycle as in the case of 8 bits.

  In the first embodiment, the register 12 is agitated for the storage element whose address is the primary random number R1 and the storage element whose address is the circulation sequence number Im, and the storage element whose address is the primary random number R1. However, the present invention is not limited to such a configuration. In the pseudo random number generation device according to the present invention, the addresses of the two storage elements to be agitated (first address and second address) and the address of the storage element from which secondary random numbers are extracted (third address) are obtained. It is necessary to select. In view of the gist of the present invention to generate a secondary random number having a long period from a primary random number having a short period using an agitated arrangement, at least one address among the first address, the second address, and the third address Is a primary random number or an arithmetic value based on the primary random number is an essential requirement. The number of addresses given as a primary random number or an operation value based on the primary random number may be 1, 2 or 3. Further, any of the first address, the second address, and the third address is given as a primary random number or a calculated value based on the primary random number. For example, the first address and the third address may be given as primary random numbers, and the second address may be given as an operation value based on the primary random numbers.

  For the cyclic sequence number Im, it is not an essential requirement that at least one of the first address, the second address, and the third address is given as an operation value based on the cyclic sequence number or the cyclic sequence number. However, by using the circulation sequence number Im, the addresses of all the storage elements in the register 12 can be selected equally. That is, by using the circulation sequence number Im, it is possible to stir the register 12 without deviation. In view of such characteristics of the cyclic sequence number, it is preferable that at least one of the first address and the second address is given as an operation value based on the cyclic sequence number or the cyclic sequence number. Note that the third address may be given as a cyclic sequence number or an operation value based on the cyclic sequence number.

  Among the first address, the second address, and the third address, an address that is not given as a first random number, an operation value based on the first random number, or a circulation sequence number or an operation value based on the circulation sequence number It is necessary to select using another calculation method based on a predetermined rule.

Below, some arithmetic processing based on the primary random number R1 will be described. For example, the operation value based on the primary random number R1 is calculated by calculating the function value by substituting the primary random number R1 into the variable constituting the function. Here, in the first embodiment, consider an apparatus configuration in which the pseudo random number generator 11 generates the primary random number R1 in units of 9 bits. Since the primary random number R1 takes a numerical value in the range of 0 to 511, the number of types of random number patterns of the primary random number R1 is 512. In this case, the primary random number R1 is converted using, for example, Equation (6).
R1 ′ = {R1-mod (R1,2)} / 2 (6)
Since the random number R1 ′ obtained by this conversion takes a numerical value in the numerical range of 0 to 255, the address of the storage element in the register 12 is selected using this random number R1 ′.

  One or a plurality of calculation values based on the primary random number R1 may be generated by dividing the bit string representing the primary random number R1 based on a predetermined rule. For example, when a 4-byte (32-bit) random number pattern is generated as the primary random number R1, the primary random number R1 is divided into four, and an operation value is generated every 8 bits. Using this calculated value, the address of the storage element in the register 12 is selected. When a 16-bit random number pattern is generated as the primary random number R1, the random number pattern is divided and the first half 8 bits or the second half 8 bits are used as the operation value. Using this calculated value, the address of the storage element in the register 12 is selected.

  An arithmetic value based on the primary random number R1 may be generated by combining bit strings representing the primary random number R1 based on a predetermined rule. For example, when a 4-bit random number pattern is generated as the primary random number R1, an 8-bit bit pattern obtained by combining two consecutive primary random number R1 bit patterns is used as an operation value. Using this calculated value, the address of the storage element in the register 12 is selected.

  A primary random number R1 may be input to the buffer, and a numerical value obtained as an output may be used as an operation value. For example, a FIFO is arranged between the pseudorandom number generator 11 and the control unit 13. The FIFO receives the primary random number R1 from the pseudo-random number generator 11 and outputs the numerical value input first to the FIFO in accordance with the input of the primary random number R1 to the control unit 13 as an arithmetic value. Using this calculated value, the address of the storage element in the register 12 is selected.

  By referring to a table such as an address conversion table, a numerical value corresponding to the primary random number R1 may be used as the operation value. The arrangement according to the present invention is given as a register used in the above embodiment, a predetermined storage area on the RAM, or the like. A numerical value in the numerical range of 0 to 255 is not necessarily assigned to an address of a storage element existing in such a storage area. Also, numerical values assigned as addresses are not necessarily given as consecutive numerical values. In such a case, even if the primary random number R1 is given as a continuous numerical value in the numerical range of 0 to 255, the primary random number is associated with different addresses of the storage elements in the register for each primary random number. There is a need. By using the address conversion table, it is possible to associate the primary random number R1 and the address of the storage element in the register on a one-to-one basis. Therefore, a numerical value obtained by referring to the address conversion table is used as a calculation value. Using this calculated value, the address of the storage element in the register 12 is selected.

  Furthermore, it is good also as a structure which calculates the calculated value based on the primary random number R1 using the calculation process which combined said calculation process concerning the primary random number R1. For example, a buffer is arranged between the pseudorandom number generator 11 and the control unit 13. A numerical value stored in a storage element in the buffer specified by using a function value having the primary random number R1 output from the pseudo random number generator 11 as a variable is output. The primary random number R1 is stored in this storage element.

  As for the circulation sequence number Im, the calculation value can be obtained by appropriately applying the above calculation processing. Furthermore, it is good also as a structure which calculates | requires a calculated value based on both the primary random number R1 and the circulation order number Im. For example, a function f (R1, Im) having both the primary random number R1 and the circulation sequence number Im as variables may be defined, and the address of the storage element may be selected using this function value as an operation value.

  In the first embodiment, the register 12 is agitated by exchanging the numerical value stored in the storage element having the primary random number R1 as the address and the numerical value stored in the storage element having the circulation sequence number Im as the address. Later, the numerical value stored in the storage element having the primary random number R1 as an address is output as the secondary random number R2, but the present invention is not limited to such a configuration. In the pseudo random number generation method (pseudo random number generation program) according to the present invention, the numerical value stored in the storage element specified by the selected third address is output as the secondary random number R2, and then the first selected The register 12 may be agitated for the numerical values stored in the two storage elements specified by the address and the second address.

  Further, every time the register 12 is stirred, the secondary random number R2 is output. However, the present invention is not limited to such a configuration. In the pseudorandom number generation method (pseudorandom number generation program) in the present invention, a configuration may be adopted in which a plurality of secondary random numbers R2 are output each time the register 12 is stirred once. Alternatively, the register 12 may be stirred a plurality of times each time the secondary random number R2 is output once. The steps (steps) constituting the invention according to the pseudorandom number generation method and the pseudorandom number generation program described in the claims of the present application are not necessarily executed in time series in the order described, and the order is reversed. In some cases, another process (step) may be executed a plurality of times while a certain process (step) is executed once. It should be noted that the technical scope of the invention relating to the pseudo-random number generation method and the pseudo-random number generation program described in the claims of the present application is given as encompassing all the various embodiments described above.

  As described above, according to the pseudo random number generation device according to the first embodiment, the pseudo random number generator 11 that generates the primary random number R1 and the number of storage elements equal to the number of types of the random number pattern of the secondary random number R2 are configured. In addition, the register 12 in which different random number patterns are stored in each storage element, and the register 12 are agitated for the two storage elements specified by the selected first address and second address, And a control unit 13 that outputs a numerical value stored in the storage element specified by the selected third address as a secondary random number R2, and includes the first address, the second address, and the third address. Since at least one address is given as a primary random number R1 or a calculated value based on the primary random number R1, the expansion is performed as a permutation by stirring. By taking out the secondary random number R2 from any storage element in the register 12 is possible to express a pattern number of the numerical sequence, it is possible to obtain a long random sequence of cycles.

  Further, a circulation sequence number Im given as a remainder obtained by dividing the number of generations of the primary random number R1 by the number of types of random number patterns of the secondary random number R2 is calculated, and at least one address of the first address or the second address is calculated. Since it is configured to be given as a cyclic sequence number Im or an operation value based on the cyclic sequence number Im, it is guaranteed that the addresses of all the storage elements in the register 12 are equally selected by using the cyclic sequence number Im. As a result, the register 12 can be agitated without bias over the entire range, so that the possibility of obtaining a random number sequence having a long period is increased. Furthermore, since the circulation sequence number Im can be calculated by a simple calculation using a simple calculation circuit such as a counter, the circuit configuration of the pseudo-random number generation device can be simplified.

  In addition, since the pseudo random number generator 11 that generates the primary random number R1 is provided as a linear congruence generator or a linear feedback shift register, the primary random number R1 can be generated using a relatively simple arithmetic circuit. Therefore, the circuit configuration of the pseudorandom number generator can be simplified.

Embodiment 2. FIG.
FIG. 4 is a diagram showing an example of the configuration of a pseudorandom number generator according to Embodiment 2 of the present invention. In FIG. 4, reference numeral 21 denotes a pseudo random number generator (first pseudo random number generating means) which is given as, for example, a linear congruence generator or a linear feedback shift register and generates a primary random number R1 (first random number) having a relatively short period. ), 22 is given as, for example, a linear congruence generator, a linear feedback shift register or the like, and generates a random number for stirring RS (third random number) with a relatively short cycle (second pseudo random number control means), 23 is a register (array) configured with the same number of storage elements as the number of types of random number patterns of the secondary random number R2 (second random number), and each storage element stores a different random number pattern, and 24 is selected. The register 23 is agitated and selected for the two storage elements in the register 23 specified by the first address and the second address. Controller for outputting a numerical value stored in the storage element in the register 23, identified as secondary random number R2 by less is (control means).

In the second embodiment, as the pseudo-random number generator 21, a linear congruential generation that generates an 8-bit random number pattern in the numerical range of 0 to 255 based on the equation (5) (R _{i + 1} = 3 * R _i mod 256). A vessel shall be adopted. Further, as the pseudo-random number generator 22, a linear congruence generator that generates an 8-bit random number pattern in a numerical range of 0 to 255 based on the following equation (7) is adopted.
R _{i + 1} = (5 * R _i +1) mod 256 (7)
Further, as the register 23, a register which is composed of 256 storage elements having an address in a numerical range of 0 to 255, and each storage element has a storage capacity of 8 bits is adopted.

  FIG. 5 is a flowchart showing an example of a pseudo-random number generation method according to Embodiment 2 of the present invention. The pseudorandom number generator 21 generates and outputs an 8-bit primary random number R1 (step S11). The pseudo random number generator 22 generates and outputs an 8-bit stirring random number RS (step S12).

  If the primary random number R1 and the stirring random number RS are output, the control unit 24 stores the numerical value stored in the storage element having the primary random number R1 as an address and the storage element having the stirring random number RS as an address. The numerical value is exchanged (step S13). That is, the register 23 is stirred using the primary random number R1 as the first address and the stirring random number RS as the second address. When the stirring of the register 23 is completed, the control unit 24 outputs the numerical value stored in the storage element having the primary random number R1 as an address as the secondary random number R2 (step S14).

  If the secondary random number R2 is output, it is determined whether or not the output of a predetermined number of random number sequences has been completed (step S15). If the output of the predetermined number of random number sequences has not been completed, the process returns to step S11 and the random number generation process is continued. If the output of the predetermined number of random number sequences has been completed, the processing relating to random number generation is terminated.

  The linear congruence generator that generates random numbers based on Equation (5) outputs a random number sequence with a period of 64. The linear congruence generator that generates random numbers based on Equation (7) outputs a random number sequence with a period of 64. Two storage elements specified by the first address given by the primary random number R1 output from the pseudorandom number generator 21 and the second address given by the random number RS for stirring output from the pseudorandom number generator 22 Embodiment in which register 23 is agitated as a target, and a numerical value stored in a storage element specified by a third address given by primary random number R1 output from pseudorandom number generator 21 is output as secondary random number R2 It has been found that the pseudorandom number generator according to 2 has a period of 4,194,048. Since the period of the primary random number R1 is 64, the secondary random number R2 has a period 65,532 times (4,194,048 / 64) times that of the primary random number R1.

  Similar to the description of the pseudo-random number generator according to the first embodiment, a primary random number or an arithmetic value based on the primary random number, an arithmetic value based on the stirring random number or the random number for stirring, or the circulation used in the first embodiment An operation value based on the sequence number or the cyclic sequence number can be given as any one of the first address, the second address, and the third address. The stirring random number RS is given as a random number for stirring the register 23. In consideration of this role, it is preferable to provide a stirring random number or a calculated value based on the stirring random number as at least one of the first address and the second address.

  Further, every time the primary random number R1 is generated, the agitation random number RS is generated and the register 23 is agitated. However, the present invention is not limited to such a configuration. The generation of the random number for stirring RS may be executed before the generation of the primary random number R1. Further, the primary random number R1 may be generated a plurality of times while the stirring random number RS is generated once, and the stirring of the register 23 and the output of the secondary random number R2 may be executed.

  The pseudo random number generation device according to the second embodiment has the same effects as the pseudo random number generation device according to the first embodiment. Furthermore, since the random number for stirring RS is generated separately from the primary random number R1 using the pseudo random number generator 22, and the register 23 is stirred using the random number for stirring RS, the primary random number R1 Since the memory contents of the register 23 can be changed by reducing the influence of the period, the register 23 that can represent a numerical sequence having a huge number of patterns as a permutation by stirring can be used more effectively. A long random number sequence can be obtained.

  A pseudo-random number generation program comprising program codes for executing the steps described in the flowcharts shown in FIGS. 3 and 5 is an information storage medium such as a CD-ROM or DVD-ROM in which the pseudo-random number generation program is stored. It can be used by obtaining it or by downloading it from an external server storing the pseudo random number generation program. The pseudo-random number generation program read from the information storage medium or downloaded from an external server is installed in a storage unit in a terminal device provided as a personal computer, for example. By executing the pseudo random number generation program installed in the storage means by the CPU in the terminal device, the pseudo random number generation method described in the first and second embodiments can be realized.

Application Example 1
FIG. 6 is a diagram showing an example of the configuration of an encryption system to which the pseudo random number generation device according to the present invention is applied. In FIG. 6, reference numerals 31 and 32 denote pseudo-random number generators according to the present invention, reference numerals 33 and 34 denote logical operation processors, and reference numeral 35 denotes a communication path. The pseudo random number generation device 31 and the pseudo random number generation device 32 are configured to be the same or have the same logical structure. The logical operation processing device 33 and the logical operation processing device 34 are configured to be the same or have the same logical structure. The logical operation processing devices 33 and 34 are generally provided as arithmetic circuits that execute exclusive OR operations. In this cryptographic system, the random number sequence output from the pseudo-random number generators 31 and 32 is used as a key stream for generating a stream cipher.

  In the encryption device configured to include the pseudo random number generation device 31 and the logical operation processing device 33, the pseudo random number generation device 31 is set to an initial state using a common key shared between the transmission side and the reception side. To do. Specifically, an initial value of a pseudo random number generator that generates a primary random number (and a random number for stirring) is set, and initial storage contents are set in a register. The logical operation processing device 33 inputs a data sequence constituting a plaintext and a random number sequence output from the pseudo random number generation device 31, executes a predetermined logical operation in units of bits or a predetermined number of bit strings, and performs encryption. A data series constituting the sentence is generated and output to the communication path 35.

  In a decryption device configured to include the pseudo random number generation device 32 and the logical operation processing device 34, the pseudo random number generation device 32 is set to an initial state using a common key. The logical operation processing device 34 inputs the data sequence constituting the ciphertext and the random number sequence output from the pseudo-random number generation device 32, executes a predetermined logical operation in units of bits or a predetermined number of bit strings, Generate data series that make up plaintext.

  Note that the pseudo-random number generation device and the like described in the first embodiment and the second embodiment are not intended to limit the present invention but are disclosed for the purpose of illustration. The technical scope of the present invention is defined by the description of the scope of claims, and various design changes can be made within the technical scope of the invention described in the scope of claims. For example, in the above embodiment, the register is stirred for two storage elements specified by the first address and the second address, but the register is stirred for three or more storage elements. It is good also as a structure. Also in this case, at least one address among the three or more addresses that specify the storage element to be agitated and the address that specifies the storage element from which the secondary random number is extracted is an operation based on the primary random number or the primary random number. Given by value. Furthermore, it is preferable that at least one of these addresses is given by a cyclic sequence number or an operation value based on the cyclic sequence number.

  Moreover, the pseudo random number generation device according to the present invention is not only applicable to a stream cipher system. For example, by using a random number sequence output from the pseudorandom number generator as a session key, the pseudorandom number generator according to the present invention can be applied to a block cipher system. Furthermore, by using the random number sequence output from the pseudo-random number generator as a random number for Monte Carlo simulation, the pseudo-random number generator according to the present invention can be applied to a computer simulation system.

  The present invention can be widely applied to pseudo-random number generators used in various systems such as stream cipher systems, block cipher systems, and computer simulation systems.

It is a figure which shows the structure of the model for demonstrating the operating principle of the pseudorandom number generation apparatus which concerns on this invention. It is a figure which shows an example of a structure of the pseudorandom number generation apparatus by Embodiment 1 of this invention. 5 is a flowchart illustrating an example of a pseudo random number generation method according to the first embodiment. It is a figure which shows an example of a structure of the pseudorandom number generation apparatus by Embodiment 2 of this invention. 6 is a flowchart illustrating an example of a pseudo-random number generation method according to a second embodiment. It is a figure which shows an example of a structure of the encryption system to which the pseudorandom number generator which concerns on this invention is applied. It is a figure which shows an example of a structure of a linear feedback shift register.

Explanation of symbols

1 pseudo random number generator, 2 registers, 3 control unit, 11 pseudo random number generator (pseudo random number generation means), 12 register (array), 13 control unit (control means), 21 pseudo random number generator (first pseudo random number generator) Generating means), 22 pseudo random number generator (second pseudo random number generating means), 23 register (array), 24 control unit (control means), 31, 32 pseudo random number generating device, 33, 34 logical operation processing device, 35 Communication path

Claims (10)

Pseudo-random number generation means for generating a first random number;
An array composed of the same number of storage elements as the number of types of random number patterns of the second random number, each storage element storing a different random number pattern;
The array is agitated for at least two or more storage elements specified by the selected first address and the second address, and a numerical value stored in the storage element specified by the selected third address is Control means for outputting as a second random number,
A pseudo-random number generation device, wherein at least one of the first address, the second address, and the third address is given as a first random number or an operation value based on the first random number. The control means calculates a remainder obtained by dividing the number of generations of the first random number by the number of types of random number patterns of the second random number,
The pseudorandom number generation device according to claim 1, wherein at least one of the first address and the second address is given as the remainder or an operation value based on the remainder. The first address and the third address are given as a first random number or an operation value based on the first random number,
The pseudo-random number generation device according to claim 2, wherein the second address is given as the remainder or an operation value based on the remainder. A first address and a third address are given as the remainder or an operation value based on the remainder;
3. The pseudo-random number generation device according to claim 2, wherein the second address is given as a first random number or an operation value based on the first random number. 2. The pseudo-random number generation device according to claim 1, wherein the pseudo-random number generation means is provided as a linear congruence generator or a linear feedback shift register. First pseudo random number generating means for generating a first random number;
Second pseudo-random number generation means for generating a third random number;
An array composed of the same number of storage elements as the number of types of random number patterns of the second random number, each storage element storing a different random number pattern;
The array is agitated for at least two or more storage elements specified by the selected first address and the second address, and a numerical value stored in the storage element specified by the selected third address is Control means for outputting as a second random number,
At least one of the first address, the second address, and the third address is provided as a first random number or an operation value based on the first random number;
A pseudo-random number generation device, wherein at least one of the first address and the second address is given as an operation value based on a third random number or a third random number. The control means calculates a remainder obtained by dividing the number of generations of the first random number by the number of types of random number patterns of the second random number,
The first address is given as a third random number or an arithmetic value based on the third random number,
A second address is given as the remainder or an arithmetic value based on the remainder;
The pseudo-random number generation device according to claim 6, wherein the third address is given as a first random number or an operation value based on the first random number. The pseudorandom number generator according to claim 1 is provided.
A data sequence constituting the ciphertext is obtained by executing a predetermined logical operation for each bit or a predetermined number of bit strings on the random number sequence output from the pseudorandom number generator and the data sequence constituting the plaintext. An encryption device characterized by generating. Generating a first random number;
Calculating a remainder obtained by dividing the number of generations of the first random number by the number of types of random number patterns of the second random number;
Selecting a first address and a second address;
It is composed of the same number of storage elements as the number of types of random number patterns of the second random number, and is stored in the storage element specified by the first address in an array in which different random number patterns are stored in each storage element. Exchanging the numerical value and the numerical value stored in the storage element specified by the second address;
Selecting a third address;
Outputting a numerical value stored in a storage element specified by a third address in the array as a second random number,
At least one of the first address, the second address, and the third address is given as a first random number or an operation value of the first random number;
A pseudo-random number generation method, wherein at least one of the first address and the second address is given as the remainder or the operation value of the remainder. Generating a first random number;
Calculating a remainder obtained by dividing the number of generations of the first random number by the number of types of random number patterns of the second random number;
Providing the first address and the second address as a first random number or a calculated value based on the first random number, or the remainder or a calculated value based on the remainder, respectively;
It is composed of the same number of storage elements as the number of types of random number patterns of the second random number, and is stored in the storage element specified by the first address in an array in which different random number patterns are stored in each storage element. Exchanging the numerical value and the numerical value stored in the storage element specified by the second address;
Providing a third address as a first random number, a calculated value based on the first random number, or the remainder or a calculated value based on the remainder;
And a step of outputting a numerical value stored in a storage element specified by a third address in the array as a second random number.

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