JP2008197847A - Random number inspection device and inspection method therefor - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide random number inspection technology to easily inspect and check a required section of or the quality of random numbers necessary for a computer application by use of statistical technology, in a short time. <P>SOLUTION: This random number inspection device 10 has: a random number storage means 12 storing the random number (a) generated by a random number generation means 11; a statistic calculation means 13 provided as the need arises so as to calculate a statistic of the random number output from the random number storage means 12; a statistic decision means 14 deciding the calculated statistic, and having a decision vale storage function therefor; and an output control means 15 outputting the random number according to a decision result from the statistic decision means 14. The statistic decision means 14 generates the decision result required by the application 16. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a random number inspection technique applied to a wide range of fields from general-purpose computers to consumer levels such as personal computers and game machines, and in particular, inspects and confirms the nature and interval of random numbers required for applications in a short time. The present invention relates to a random number inspection apparatus capable of performing the same and an inspection method thereof.

The random number sequence in the column of numbers arranged in random, sequence X _1, X 2, _..., is that the X _n of the following numbers X _{n + 1} can not be predicted sequence. Numeric values constituting such a random number sequence are called random numbers. A device or computer algorithm that generates a random number sequence is called a random number generator.

  Random numbers are roughly classified into physical random numbers and pseudo-random numbers according to the generation method. A physical random number is a random number generated using a physical phenomenon, and a pseudo-random number is a random number generated using a computer algorithm. Although physical random numbers are sometimes referred to as hardware random numbers, random numbers obtained by implementing computer algorithms in hardware without using physical phenomena are also referred to as hardware random numbers. The terms use physical random numbers and pseudo-random numbers.

  Other random number names include true random numbers, uniform random numbers, normal random numbers, and binary random numbers. Intrinsic random numbers, uniform random numbers, normal random numbers, binary random numbers, and the like are names indicating characteristics of random numbers. True random numbers are ideal random numbers according to the definition of random numbers, uniform random numbers are random numbers with the same probability of occurrence in a certain interval, normal random numbers are random numbers whose distribution of occurrence probability is normal distribution, binary random numbers are random numbers with two types of values It is a designation.

  A random number incorporated as a function in a computer is generally a uniform random number. If a non-uniform probability distribution is required, it can be converted from a uniform random number into another probability distribution.

  When using random numbers, it is important to check the quality of the random numbers. A high quality random number means that it is close to a true random number. Checking the quality of random numbers based on statistical theory is called random number testing, and high-dimensional uniformity can be tested to confirm that it is a true random number. However, a low-dimensional test is relatively easy, but a high-dimensional test is not practical because it takes a long time to confirm.

  Therefore, in general, the properties of true random numbers are confirmed using multiple test methods with different purposes. For example, there is uniformity (no bias), no periodicity, and reproducibility. Evaluate that there is no.

  Since pseudo-random numbers are generated using a computer algorithm, if the initial values are the same, the same random number sequence is generated (reproducibility), and the setting value (seed) when generating the next random number is the same as the previously generated seed. If they are the same, there is a property that the same random number sequence is repeatedly generated (periodicity) from the generation of the seed.

  Due to the periodic nature of this same random number sequence, in principle, pseudo-random numbers cannot be said to be true random numbers. However, if the period is long, it can be used as a random number until the period is reached, so it is used as a random number incorporated as a function in the computer.

  Physical random numbers generate physical numbers by quantifying physical phenomena, and in principle do not have reproducibility or periodicity. In the case of physical random numbers, a different random number is generated each time a random number is generated. Therefore, as with pseudo-random numbers, once the quality is confirmed, it is not guaranteed that the quality is always maintained. Confirmation is required.

  Patent Document 1 (Japanese Patent Laid-Open No. 2000-259395) and Patent Document 2 (Japanese Patent Laid-Open No. Hei 11) are techniques for generating physical random numbers and applied to a wide range of fields from general-purpose computers to consumer levels such as personal computers and game machines. -85472).

  On the other hand, depending on the application using random numbers, even if the quality of the random numbers is good, the generated random numbers may have to be discarded. For example, when simulating a playing card, a joker is added and 53 different values are required. The random number generated by the random number generator used in the computer is often in units of bits, and generates a random number in the interval [0, 2 to the power-1].

  In the case of an 8-bit random number generator, random numbers in the interval [0 to 255] are generated. 53 different values are extracted from the 256 different values. For example, there is a method of using any 53 types and discarding the remaining 203 pieces. However, in the method of throwing away the rest from 53 types, the number to be thrown away is wasteful, and therefore the remainder obtained by dividing the generated random number value by 53 is usually used. However, even with this processing method, 44 random numbers must be discarded.

As described above, when using a random number, quality confirmation is required, but a part of the generated random number may be discarded.
JP 2000-259395 A JP-A-11-85472

  It is theoretically possible to perform a high-dimensional uniformity test to check whether the generated random number is a true random number. It is not realistic because the memory capacity and processing time of a computer required for high-dimensional uniformity inspection are enormous.

  For this reason, a method of confirming each property of the true random number using a plurality of test methods is used, but it takes a processing time to try all the test methods and is not practical. Furthermore, the quality of random numbers cannot be confirmed with a small number of test methods. Thus, in order to confirm and use the quality of the random numbers to be used, it is a problem that it takes a huge amount of processing time.

  The present invention has been made in consideration of the above-described circumstances, and an object of the present invention is to provide a random number inspection apparatus and an inspection method thereof that can confirm the quality of random numbers required for an application easily and in a short time.

  In order to solve the above-described problem, a random number inspection device according to the present invention stores a random number storing unit that stores a random number generated by a random number generating unit, and a statistic that calculates a statistical amount of a random number output from the random number storing unit. A quantity calculating means; a statistic judging means for judging a calculated statistic; and an output control means for outputting a random number stored in the random number storing means to an application in accordance with a judgment result from the statistic judging means. The output control means outputs a random number required by the application.

  In order to solve the above-described problem, the random number inspection method according to the present invention stores a generated physical random number or a pseudo-random number, determines a calculated random number statistic, and determines an application from the random statistic. Is a method to output the random numbers required by.

  In the random number inspection apparatus and the inspection method according to the present invention, the quality of random numbers required for an application can be confirmed easily and in a short time.

  Embodiments of a random number inspection apparatus and an inspection method thereof according to the present invention will be described with reference to the accompanying drawings.

  FIG. 1 is a block diagram showing a first embodiment of a random number inspection apparatus according to the present invention.

  This random number inspection device 10 is applied to random number inspection technology applied to a wide range of fields from general-purpose computers to consumer levels such as personal computers and game machines. The random number inspection device 10 includes a generator 11, a random number storage unit 12, a statistic calculation unit 13, a total metric determination unit 14, an output control unit 15, and a computer application 16.

  The random number generator 11 functions as a random number generating means for generating a physical random number or a pseudo random number that is a random number for various applications. The random number a generated by the random number generator 11 is sent to and stored in the random number storage unit 12. The distribution shape of the generated random number a may be various probability distributions. This probability distribution is a random number that can be inspected based on a statistical theory.

  The random number storage unit 12 is a storage device such as a memory or a hard disk. The random number storage means 12 may be a memory built in the physical random number generator or a storage medium such as FD, MO, CD, DVD. Further, the random number storage means 12 may be temporarily stored in a large-capacity storage device such as a hard disk and used as many random numbers as the computer application 16 requires.

  Furthermore, the calculation target of the statistic calculation means 13 differs depending on the test method. The test methods include chi-square test, KS (Kolmogorov-Smirnov) test, uniform distribution test (frequency test), series test (serial test), interval test (gap test), poker test (poker test), split test ( partition test, bill collection test, permutation test, run test, maximum number of t-number test (maximum-of-t test), collision test There are several types, such as a serial correlation test.

  The selection of the verification method is determined and checked according to what random number the computer application 16 requires and what random number is unnecessary.

  For example, when it is necessary to extract an unnecessary random number from uniform random numbers as in the example of the playing card described in the background art, the ratio of the random number used to the generated random number is 4 × 53 / The function of extracting necessary random numbers or the function of discarding unnecessary random numbers by statistically testing whether it is 256 or the ratio of discarded random numbers is (256-4 × 53) / 256 It can be used, and quality confirmation and inspection required by the application 16 can be performed simultaneously.

  The statistic determination means 14 determines a significance level and tests whether or not the random number a generated by the random number generator 11 occurs. The determination level is determined by a request from the computer application 16, and the determination condition is held in the determination value holding function of the statistic determination means 14. The determination value holding function may be held in a storage device or a storage medium, or may be stored in the determination value holding function from the computer application 16 before each determination.

  The output control unit 15 outputs the random number b stored in the random number storage unit 12 to the computer application 16 if the result determined by the statistic determination unit 14 is a random number requested by the computer application 16. At this time, whether to output the entire random number b stored in the random number storage means 12, whether to output the entire random number for which the statistic calculation means 13 is to be calculated, or whether to output a part of each, is a target test method And it is necessary to use an optimum method.

  For example, the statistic calculation means 13 determines whether or not to output all the random numbers (statistics v) to be calculated to the computer application 16 in the test method using the average value or variance (frequency or correlation test). Will do.

  In addition, if the computer application 16 does not need data having a long run length, for example, 0 continues several times, as in the case of a run test in the statistic calculation means 13, when a long run is detected, Control without outputting only the ream is also possible. In this case, for example, the random number storage unit 12 has a capacity of about the length of the series to be discarded, and can be processed in real time.

  In the random number inspection apparatus 10 shown in FIG. 1, the random number a generated by the random number generator 11 is temporarily stored in the random number storage unit 12, and the statistic calculation unit 13 stores the random number b stored in the random number storage unit 12. The statistic is calculated, and the statistic determination unit 14 determines the statistic v calculated by the statistic calculation unit 13. The output control unit 15 outputs the random number b stored in the random number storage unit 12 to the computer application 16 according to the determination result of the statistic determination unit 14.

  Conventionally, the computer application 16 directly uses the random number a generated by the random number generator 11 using a random number generation function. At that time, a necessary random number a section was selected. Further, in order to confirm the quality of the random number a, it is necessary to periodically perform a test in the case of a physical random number, and it is necessary to test a random number sequence to be used in the case of a pseudo random number.

  In the random number inspection device 10 shown in the present embodiment, it is possible to perform only tests and tests focusing on the properties of random numbers required by the computer application 16 and the sections to be used. Since the statistic of the random number b to be calculated is calculated by the means 14 and the calculated statistic is determined, the random number can be used while efficiently checking the quality in real time.

  In addition, since the random number inspection apparatus 10 can select a random number section required by the computer application 16, the computer application 16 does not need to select a random number.

  FIG. 2 shows an example of the configuration of exponent conversion means provided in, for example, the statistic calculation means 13 of the random number inspection apparatus 10.

  The statistic calculation means 13 (or statistic determination means 14) of the random number inspection device 10 is provided with an exponent conversion means 19 and an interval conversion means 20 for converting random numbers into exponents, as shown in FIG. The exponent conversion means 19 includes a sign setting means 22 for setting a sign in the sign section 21, an exponent setting means 24 for setting an (exponential) value in the exponent section 23, and a mantissa setting means 26 for setting a random number bit string in the mantissa section 25. It consists of.

  The exponent conversion means 19 converts binary random numbers and integer random numbers into floating point types and performs calculations. The exponent conversion means 19 has a fixed-point type storage format 27 in which random numbers are converted and stored. The floating-point type storage format 27 includes a sign part 21, an exponent part 22, and a mantissa part 25.

  The floating-point type storage format 27 is standardized by IEEE, and is actually converted into a type conforming to the IEEE standard. Here, for convenience of explanation, the floating-point storage format 27 is generalized and described.

The exponent conversion unit 19 includes a sign setting unit 22, an exponent setting unit 23, and a mantissa setting unit 24, and sets a code in the sign setting unit 22. The sign part 21 is usually 1 bit, for example, 0 indicates positive and 1 indicates negative. If a random number is input to the encoding unit 21, it is possible to generate positive / negative at random. The exponent part 23 represents a power of 2, and if the power value is e, it represents 2 ^e .

  Normally, a bias is used so that the exponent part 23 can be handled by unsigned integer arithmetic. However, the random number inspection device 10 of the present embodiment will be described as having no bias. The mantissa part 25 represents a value of 1.0 or more and less than 2.0.

For example, by setting a binary random number mantissa 25, it is possible to convert the binary random number to any floating point random number of 2.0 × less than 2 ^e at 1.0 × 2 ^e or more. The precision that can be expressed in floating point depends on the number of bits of the mantissa part 25.

  Since the most significant bit of the mantissa part 25 is always 1, normally, the most significant bit is not included in the floating-point storage format 27, and the number of significant digits of the mantissa part 25 is improved by one bit. This bit is called an implicit bit. For example, when the mantissa part 25 is 2 bits, the mantissa part 25 can express four types of values of 100, 101, 110, and 111.

In this example, when b0 × 2 ⁰ + b0 × 2 ⁻¹ + b0 × 2 ⁻² is calculated by setting 3 implicit bits as b0, b1, and b2, respectively, as a specific numerical value expressed in the mantissa part 25, 1; 1 Four values of .25; 1.5; 1.75 are obtained. In this way, binary random numbers can be converted into arbitrary floating-point random numbers. However, since the computer application 16 usually uses random numbers of 0.0 or more and less than 1.0, it is necessary to change the interval. .

  Next, an example in which the mantissa part 25 is 2 bits is represented in the method of converting the value of 1.0 or more and less than 2.0 expressed in the mantissa part 25 of the exponent conversion means 19 to a value of 0.0 or more and less than 1.0 I will explain it.

  First, the sign part 21 of the exponent conversion means 19 is set to 0 (positive), the exponent part 23 is set to 0, and a binary random number is set to 2 bits of the mantissa part 25. Since the value of the set binary random number is 1 or more and less than 2, conversion can be easily made by subtracting 1 so that a random number of 0 or more and less than 1 can be generated. However, specific arithmetic processing is not as simple as integer arithmetic.

  Specifically, subtracting 1 in the 3 bits of the mantissa part 25 including the implicit bits considers the upper bits to be 0. That is, the mantissa part 25 is considered to be four types of values of 000, 001, 010, and 011. In the floating-point type storage format 27, since the most significant is 1, correction is made so that the most significant becomes 1 by the left shift operation of the mantissa part 25 and the countdown (decrement) of the exponent part 23.

  Here, a shift operation and subtraction of the exponent part 23 are used for explaining the exponent conversion means 19, but there is also a method of obtaining the shift amount in advance and setting the exponent part 23 for speeding up. When the mantissa part 25 is 000, the exponent part 23 is set to the minimum value.

When the mantissa part 25 constituting the floating point type storage format 27 of the exponent conversion means 19 is 001, the mantissa part 25 is shifted left twice, and the exponent part 23 is counted down twice. When the mantissa part 25 is 010, it shifts left once and counts down the exponent part once. When the mantissa part 25 is 011, the exponent part 23 is counted down once by shifting once to the left. As a result, 0.0; 1.0 × 2 ⁻² ; 1.0 × 2 ⁻¹ ; 1.5 × 2 ⁻¹ respectively, values of 0.0; 0.25; 0.5; 0.75 Is obtained.

  The effect of using the interval conversion unit 20 after converting a binary random number or an integer type random number into a floating point type by the exponent conversion unit 19 provided in the random number inspection device 10 will be described next.

In order for the mantissa part 25 of the floating-point type storage format 27 to convert an n-bit integer to a floating-point type having a value not less than 0.0 and less than 1.0, assuming that the value to be converted is v, the normal operation is performed. v / 2 ⁿ is executed. For example, there is no problem in converting a 32-bit integer into a floating-point storage format 27 having a mantissa of 32 bits or more. However, there is a problem when converting the number of bits of an integer into a mantissa part 25 smaller than the number of bits, and an example of converting from a 3-bit integer to a 2-bit mantissa part will be described.

  There are eight types of values that the 3-bit integer can take in the mantissa part 25: 000, 001, 010, 011, 100, 101, 110, and 111. Correct answers obtained by dividing the integer value by 8 are 0.000, 0.125, 0.250, 0.375, 0.500, 0.625, 0.750, and 0.875. However, because of the 2-bit precision, the mantissa part 25 of the floating-point type storage format 27 has 0.0, 0.0, 0.25, 0.25, 0.5, 0.5, 0.75, Stored as a value of 0.75.

In the mantissa part 25 of the floating point type storage format 27, the generation ratio of each value is ¼ when the value is 0.0 or more and less than 1.0. When the value divided by 8 is expressed in binary, it becomes 0.000, 0.001, 0.010, 0.011, 0.100, 0.101, 0.110, 0.111, but the mantissa with 2-bit precision Rounding is performed to the nearest value for inclusion in part 25. By this rounding when shown a right shoulder value higher bit changes become operational results as follows 0.000,0.01 ^1, 0.01,0.10 ^1, 0.10,0.11 ¹ , 0.11, 1.00 ¹ .

  When the calculation result put into the mantissa part 25 is expressed in decimal, it becomes 0.0, 0.25, 0.25, 0.5, 0.5, 0.75, 0.75, 1.00. This does not satisfy 0.0 or more and less than 1.0, and the generation ratio of each value is 0.0, 1.0 is 1/8, and other (0.25, 0.5, 0.75) is 1. / 4. Although rounding to the nearest value is defined in the standard and is not an error or a bug, there is a problem in the computer application 16 that is created expecting a random number of 0.0 or more and less than 1.0.

  In addition, the computer application 16 using random numbers is often created in expectation of uniformity in a section of 0.0 or more and less than 1.0, and does not satisfy the uniformity. On the other hand, once the random number is set in the mantissa part of the floating-point type, rounding from the lower bits is avoided, and the uniformity in the interval of 0.0 or more and less than 1.0 is obtained. It is what

  FIG. 3 shows a specific example of the exponent conversion means 19 provided in the random number inspection device 10.

  The floating point type storage format 27 constituting the exponent conversion means 19 is a single precision floating point type standardized by IEEE. Since the configuration of the specific example is not different from that shown in FIG. 2, the same components will be described with the same reference numerals.

  A selector circuit that changes the sign setting means 22 to positive, negative, binary random numbers, a selector circuit that converts the exponent setting means 24 to another section, and a shift register circuit (when the random number of the mantissa setting means 20 is a binary random number ( It is also possible to add (not shown).

  The sign portion 21 of the floating point type storage format 27 constituting the exponent conversion means 19 is 1 bit, and an L level signal line is connected as the sign setting means 22. The exponent part 23 has 8 bits, and as the exponent setting means 24, an L level signal line is connected to the most significant bit and an H level signal line is connected to the other bits. The mantissa part 25 is 23 bits, and the mantissa setting means 26 connects 23 bits of a 32-bit integer random number.

  The conversion from the integer type to the floating-point type using the exponent conversion means 19 can be realized simply by connecting a signal line, and since signal processing is not performed, the conversion is completed at the moment when a random number is generated. A subtractor or a shift register may be used as the section conversion means 20, but at present, it is cheaper to read a random number into the CPU and use a coprocessor built in the CPU than using hardware logic. This is preferable because it can satisfy the high speed. It is also possible to use a coprocessor obtained separately or provided on a board.

  The random number inspection device 10 provided in the present embodiment is provided with exponent conversion means 19, and in the fixed-point type format 27 constituting the exponent conversion means 19, since data once converted into a floating-point type is used, Even if the coprocessor performs rounding according to the IEEE standard, the section and uniformity are not affected.

  FIG. 4 shows a configuration example of the statistic determination means 14 provided in the random number inspection device 10.

  The statistic determination unit 14 directly compares the measurement value and the determination value with M measurement units 30, a degree-of-freedom conversion unit 31 that converts the degree of freedom into 1, and a statistic calculation unit 32 that is provided as necessary. And a measured value determining means 33.

M measuring means 30 obtain M measured values s (s ₁ , s ₂ ,... S _m ). Assume that M expected values k (k ₁ , k,... K _M ) are statistically obtained corresponding to _M measured values s (s ₁ , s ₂ ,... S _M ), respectively. The degree-of-freedom conversion means 31 converts the M measurement means 30 into measurement values s (s ₁ , s ₂ ,... S _M ) with _one degree of freedom. The statistic calculation means 32 calculates the statistic v from the two measured values s with one degree of freedom and the two expected values k. However, the statistic calculating means 32 becomes unnecessary by converting it into the measured value s with one degree of freedom. do not need.

  FIG. 4 shows a processing procedure of the statistic determination means 14. The measurement value determination means 33 compares the measurement value s with a preset determination value to make a determination.

  Next, the principle of the processing example of the statistic determination means 14 will be described using mathematical formulas in the case of the Kini power test.

The M determination means 30 of the statistic determination means 14 perform N trials and measure the measurement values s (s ₁ , s ₂ ,...) For M types of measurement objects x (x ₁ , x ₂ ,... X). s _M ) is obtained. When the occurrence probability of each measurement object x is ρ (ρ ₁ , ρ ₂ ,... Ρ _M ), and the statistic v shown in the following equation follows a chi-square distribution, the validity of the measurement value s is determined by chi-square test. Can do.

Validity determines whether or not the measured value s (s ₁ , s ₂ ,... S _M ) rarely occurs. If it is likely to occur, the measured value s is determined to be valid. . However, in the following equation, for the sake of explanation, the product of the occurrence probability ρ _i for each measurement object and the number of trials N is shown to be an expected value, but it may differ depending on the statistic v to be tested.

Here, M measurement values s are s ₁ , s ₂ ,... S _M , and M expected values k (k ₁ , k ₂ ,... K _M ) are e (ρ ₁ N, ρ ₂ N, ρ _3. N, ..., corresponding to ρ _M N). If each element of the measurement value s (s ₁ , s ₂ ,... S _M ) is independent, the degree of freedom is M. For example, when the remaining values are known from M−1 measurement values s, the degree of freedom is obtained. Decreases by one to M-1.

Next, assuming that the measurement value s is divided into two groups A and B by the degree-of-freedom conversion means 32 and a statistic v ₂ with one degree of freedom is obtained, equation (1) becomes equation (2).

Since the total of all measured values s is N, and the total probability of each measurement object is 1,

The statistic determination means 14 determines the statistic v ₂ by the measurement value determination means 34 obtained from the equation (4). If statistics v ₂ is large indicates that the large difference from the expected value k, is smaller indicates that close to the expected value k.

が自由度１のカイ二乗分布の下限値Ｘ_Ｌと上限値Ｘ_Ｈの間に入っているか否かを用いて行う。

Normally, an event that is far from the expected value k or an event that is too close to the expected value k is unlikely to occur, and the determination is based on a statistical quantity as shown in equation (5).

It is performed using whether enters between the lower limit value X _L and the upper limit value X _H of the chi-square distribution with one degree of freedom.

  An example in which a dice is used as the statistic determination means 14 in the random number inspection device 10 will be described.

  The act of observing the number of eyes that have passed through the dice corresponds to the generation of 6-value random numbers and the measurement of their frequencies by the M measuring means 30 of the statistic determining means 34. The value generated as a random number is a numerical value from 1 to 6, and six measuring means for measuring the number of times of each numerical value are required. For example, it is assumed that the random number computer application 16 is set to output a shift when the 1st or 6th eye comes out, and outputs a deviation when the 2nd, 3rd, 4th, or 5th eye comes out, and determines the winning. .

  The computer application 16 needs to have a function of selecting 1 or 6 from 1 to 6 obtained by rolling the dice. Usually, the dice is rolled in the hope that the act of rolling the dice will be correct. If there is anxiety, roll the dice many times in advance and statistically confirm that the dice are correct using multiple test methods.

  However, when actually operating a device that determines winning, a question may arise whether there are many wins or not. It is not practical to temporarily stop the act of dice and perform multiple time-consuming tests. In such a case, it is judgment condition J that can judge whether or not the hit is statistically correct from two data of the number of trials and the number of hits, and the determination of the statistic is an integer. Therefore, the circuit configuration when realized by hardware is simplified.

When classifying M types of measurement objects into two, whether or not the computer application 16 requires them, or when classifying them into a plurality of, for example, two groups within the computer application 16, one of the classification results is used. Can be converted to a chi-square test with one degree of freedom. It can be understood that it is not necessary to calculate the statistic v ₂ by this conversion. As a result, the chi-square test can be performed by an integer comparison circuit in hardware, and the chi-square test can be executed in a short time in software.

  FIG. 5 shows an example of random number conversion means provided in the statistic determination means 14 of the random number inspection device 10.

The statistic determination unit 14 of the random number inspection device 10 includes a random number conversion unit 35 that converts an integer random number into a random number having one degree of freedom. In this random number conversion means 35, an N-bit integer random number A and an i-th bit B or an N-bit integer random number A are constituted by shift registers. The random number conversion means 35 in the statistic determination means 14 of the random number inspection device 10 requires a determination means (not shown) that directly compares the measurement values s (s ₁ , s ₂ ,..., S _M ) with the determination value J _v. . As this determination means, the statistic determination means 14 described in FIG. 4 is used.

The random number conversion means 35 is a means for converting an integer random number into a random number (information) having one degree of freedom. In the statistic determination means 14 shown in FIG. 4, a specific method for converting M types of measurement values s (s ₁ , s ₂ ,..., S _M ) into measurement values s with one degree of freedom will be described. For example, the types of measurement objects can be classified into two groups A and B.

When M types of measurement values s (s ₁ , s ₂ ,..., S _M ) are powers of 2, each bit representing M is a binary random number. Further, the sequence of bits constituting M is also a binary random number. Inside the computer is a binary number, integers are stored in required units such as 8 bits, 16 bits, 32 bits, 64 bits, etc., and M is a power of 2.

  In the random number conversion means 35, when the generation range of the random number is an integer number of bits, the i-th 1-bit B of the N-bit integer random number A is a binary random number. However, since only 1 bit out of N bits is used as a random number, there is a lot of waste. In this case, if the storage function of the N-bit integer random number A is a shift register, N-bit binary random numbers can be generated. FIG. 5 shows a shifted binary random number B obtained by shifting to the LSB (Least Significant Bit) side. Although not shown, it is also possible to obtain a binary random number by shifting to the MSB (Most Significant Bit) side. In this case, all the generated random numbers can be converted into binary random numbers.

  If the computer application 16 uses a binary random number of either the i-th 1-bit B or a binary random number C obtained by shifting, a 1-bit random number of 1 degree of freedom can be obtained directly without converting the degrees of freedom. Thereby, there can exist an effect similar to the structure of the statistic determination means 14 demonstrated in FIG.

Further, the statistic determination unit 14 (or the statistic calculation unit 13) of the random number inspection device 10 includes a frequency distribution measurement unit that measures (calculates) a partial frequency distribution in the N-dimensional space as a statistic. As shown in FIG. 4, the frequency distribution measuring unit constitutes, for example, a statistic calculating unit 32 and calculates an Nth-order frequency distribution as a statistic. When the frequency distribution measuring means 36A and 36B generate M random numbers N times to determine an N-dimensional frequency distribution, the frequency distribution measuring means 36A and 36B calculate ^MN types of frequencies. When obtaining a high-dimensional frequency distribution, if M and N are large, it takes a huge amount of processing time and it is actually difficult to test all frequencies. Therefore, the frequency distribution measuring means 36A and 36B perform monitoring (inspection) and determination that are subject to verification only for a region where the degree of freedom is 1 in a part of the N-dimensional space.

  The frequency distribution measuring means 36A and 36B can obtain the frequency even if the dimension for performing the uniformity test is increased by obtaining the frequency in the main memory of the computer.

  On the other hand, the random number inspection device 10 includes frequency distribution measuring means 36A and 36B for measuring the continuous frequency distribution, as shown in FIGS.

  As shown in FIGS. 6 (A) and 6 (B), the frequency distribution measuring means 36A and 36B are either a binary random number measuring means or a counter 38 that counts the length of a series from binary random numbers measured by a counter 37. The shift register 39 includes a counter 40 that counts the frequencies 40a and 40b for each length of the run.

  The frequency distribution measuring means 36A and 36B have several types in addition to handling binary random numbers for continuous inspection for measuring the length of the series. As the length of a series, there is a method of obtaining a length of a series of 0, a length of a series of 1, a length of another series regardless of 0 or 1. Here, a method for obtaining the length of bit 1 will be described.

  In the frequency distribution measuring means 36A shown in FIG. 6A, the frequency 40a for each length of the counter 38 and the counter 40 is first cleared to zero. A binary random number 37 is sequentially input to the counter 38. The counter 38 continues counting while 1 continues, and when 0 is input, the counter 38 records the length of a series of 1s. The frequency 40 for each run length is constituted by a counter 40 and counts the number of run lengths corresponding to the count result of the counter 38.

  Thereafter, the counter 38 clears the count value and stops counting until the binary random number 37 becomes 1 next. By repeating this operation until N binary random numbers 37 are input, the frequency 40a for each run length records the number of occurrences for each run length for the N random numbers.

  Next, FIG. 6B will be described. The frequency distribution measuring means 36 </ b> B in FIG. 6B is obtained by replacing the counter 38 with a shift register 39.

  In the frequency distribution measuring means 36B, the shift register 39 and the frequency 40b for each run length are cleared to zero. When the value of the binary random number 37 is 1, the value 1 is shifted. When the binary random number 37 becomes 0, the shift is stopped. As a result, the bit in the position corresponding to the number of runs is 1 in the shift register 39. The frequency 40b for each run length is constituted by a counter 40, and the counter 40 whose bit of the shift register 39 is 1 is selected and counted.

  After the count of the frequency 40b is performed for each run length, the shift register 39 is cleared and the count is stopped until the binary random number 37 becomes 1 next. By repeating this operation until N binary random numbers 37 are input, the frequency 40b for each run length records the number of occurrences for each run length for the N random numbers.

  In the method shown in FIG. 6B using the shift register 39, it is possible to select the counter 40 constituting the frequency 40b for each run length directly at the bit position corresponding to the run length frequency 40b. However, since the R-bit shift register 39 is necessary to measure the frequency R of the series having the length R, it is preferable to use the counter 38 when handling the frequency 40b of the long series.

The frequency distribution (distribution for each run length) measuring means 36A and 36B shown in FIGS. 6 (A) and 6 (B) is used to calculate the chirp using the formula (1) from the number of occurrences for each run length. A square statistic v can be calculated. However, the expected value E _v does not take the form of ρ _i N as in the case of obtaining a uniform distribution statistic, and depends on the number N of random numbers generated, the number of runs of 0, and the number of runs of 1 Will be.

  The frequency distribution measuring means 36A, 36B is a chi-square test when testing a frequency with continuous 0 or 1, so that the effect equivalent to the effect obtained by the statistic determination means 14 after conversion to the degree of freedom 1 is obtained. Is obtained.

  Next, a specific example of the frequency distribution measuring means 36A, 36B provided in, for example, the statistic determination state 14 of the random number inspection device 10 will be described with reference to FIG. 1 and FIG.

  The computer application 16 may not require a random number in which 1 or 0 continues. For example, it is inconvenient when modulation is performed using random numbers for communication. In addition, when used for encryption, there is a possibility that the original plaintext may be seen at a portion where 0 or 1 continues, resulting in inconvenience. Such a computer application 16 discards, for example, without using a series having a required length r or more.

In this case, the frequency 40a or 40b for each run length shown in FIGS. 6A and 6B is a means for counting the number of times a run having a length smaller than the length r (an arbitrary integer) is generated. It is sufficient if there is a means for counting the number of times that a series having a length of r or more occurs. As a result, the frequency distribution measuring means 36A and 36B have two types of measurement objects, the statistic v ₂ having one degree of freedom, and the determination means (not shown) in the form of the determination condition J can be used. The effect similar to the effect shown by 14 is acquired.

  An example in which the statistic determination means 14 constituting the random number inspection apparatus 10 is provided with an integer type digital comparison circuit 44 will be described with reference to FIG.

  The integer type digital comparison circuit 44 includes an n-bit integer type determination value holding circuit 45, an n-bit integer type measurement value counter 46, and an n-bit digital comparison circuit 47.

The integer type determination value holding circuit 45, the determination value J _v based on the determination condition J is maintained.

The determination value _Jv setting method performed by the integer type digital comparison circuit 44 provided in the statistic determination means 14 is performed as follows.

  In the determination value holding circuit 45 of the integer type digital comparison circuit 44, when the determination value is fixed, each bit is connected to GND or a power source so that the output signal line of the determination value holding circuit 45 becomes the determination value. When the determination value is semi-fixed, the setting is changed using a switch, a pull-up resistor, or the like for each bit. When the determination value is frequently changed, a storage unit such as a register, a latch, or a D-type flip-flop is used as the determination value holding circuit 45 and communication means with the computer application 16 (see FIG. 1) is provided and set.

In this integer type digital comparison circuit 44, the determination result can be realized by an integer. The measured value 46 (s _i ) at the counter 46 is an integer obtained by calculating the frequency of the measurement object. In the chi-square test shown in the equation (1), each expected value k _i needs to be 5 or more in consideration of the accuracy of the test. For this reason, it is necessary to set a measurement condition for the measured value s _i to be 5 or more. Specific measurement condition setting methods include a method of increasing the number of trials N and a method of reducing the degree of freedom.

The integer type digital comparison circuit 44 specifically describes a method of comparing the measured value s _i and the judgment value J _v , and includes the statistic judgment means 14, the random number conversion means 35, and the frequency distribution of the random number inspection device 10. The same effects as those shown in the measuring means 36A and 36B can be obtained.

  Next, determination conditions in the integer type digital comparison circuit 44 provided in the statistic determination state 14 will be described with reference to FIG.

The statistic determination means 14 is provided with a comparison determination means 49 for performing one to four types of comparison as a constituent element. Four conditions are shown as the judgment conditions of the comparison judgment means 49. In FIG. 8, the horizontal axis x represents the measured value s _i and the vertical axis y represents the expected value.

The determination condition J in the statistic determination means 14 of the random number inspection device 10 includes individual determination conditions J _{1 to} J ₄ . In FIG. 8, the expressions (7) corresponding to the respective determination conditions J _{1 to} J ₄ exist individually as represented by the expressions (7-1) to (7-4), respectively, and are represented by the following expressions. It is.

(7-1) equation, corresponding to the lower limit determination value _{A v} shown in FIG. 8, (7-2) where the upper threshold value _{B v} 8, (7-3) equation 8 the lower limit determination value _{C v,} (7-4) equation is the lowest upper threshold value _{D v} of Figure 8, the corresponding. Furthermore, (7-5) equation is the determination value _{J v} expected value _{E v} shown in FIG.

In comparison determination unit 49 of the statistic determining means 14, for example, the lower limit value of the chi-square distribution X _L and the upper limit value X _H of the 1% significance level, respectively, and the determination value at 5%. Expected value _{E v} in the x axis direction of the comparing and determining means 49, a plurality, for example, is divided into six regions to F.

In comparison determination unit 49 of the statistic determining means 14, the regions A and F are difficult to occur region for measurement values si are far against the expected value E _v, the measured value si enters these areas The probability is 5%. Region C and region E are difficult to occur region for measurement values si are too close to the expected value E _v, the probability measure si is entering these areas C, E is 1%. The remaining 94% falls into region B and region E. Depending on which areas A to F the computer application 16 (see FIG. 1) uses, the above five types of determination conditions are selected.

As an example of using one determination condition to the comparison determination unit 49 from the statistic determining means 14 discards the measured value si which are far against the expected value E _v is, if you are far the larger adopted sometimes discard area a by using only the lower limit determination value a _v. In this case, 97.5% of the generated random numbers is used.

As an example of using two determination conditions to the comparison determination unit 49 from the statistic determining means 14, but rejects the measurements far against the expected value E _v, I want to adopt a measured value si close to the expected value E _v Sometimes, the upper limit determination value B _v and the lower limit determination value C _v are not determined, and the region A and the region F are discarded using the upper limit determination value D _v and the lower limit determination value A _v . In this case, 99% of the generated random numbers is adopted.

As an example in which three comparison determination conditions are used for the comparison determination means 49 from among the statistic determination means 14, when only regions that occur with a low probability of occurrence are employed as in the case of determining winning, for example, the regions D and F Is used, the expected value _Ev , the lower limit determination value _Cv, and the maximum upper limit determination value _Dv are used. In this case, 3% of the generated random numbers is adopted. As an example of using four determination conditions for the comparison determination condition 49, the case where the region B and the region E are employed, that is, the determination condition J is used. In this case, 94% of the generated random numbers is adopted.

Determination value used for statistic determining means 14 but is two lower limit X _L and the upper limit value X _H, considering conditions of the adoption / non-adoption of the calculator application 16, from (6-1) (6 -4) Four types of determination values A _{v to} D _v corresponding to the equation may be used.

  In addition, when the statistic determination unit 14 uses the comparison determination unit 49 to determine 1% as the significance level and adopts 99%, the statistic determination unit 14 is not adopted once out of 100 trials. If you have any doubts about the ratio, you should test the distribution of statistics using a KS test.

  In the comparison / determination unit 49 provided in the statistic determination unit 14, the random number test apparatus 10 shown in FIGS. This random number inspection apparatus 10 has the same effects as those shown in the statistic conversion means 14, the integer random number conversion means 35, and the frequency distribution measurement means 36A and 36B.

The block diagram which shows embodiment of the random number inspection apparatus which concerns on this invention. The block diagram which shows the exponent conversion means with which the random number inspection apparatus of FIG. 1 is equipped. The figure which shows the concrete index conversion means with which the said random number test | inspection apparatus is equipped. The block diagram which shows the statistic determination means with which the said random number inspection apparatus is equipped. The figure which shows the integer random number conversion means with which the said random number test | inspection apparatus is equipped. (A) And (B) is a figure which shows a frequency distribution measurement means of a different type, respectively. The block diagram which shows the integer type digital comparison circuit with which the statistic determination means of the said random number test | inspection apparatus is equipped. The figure which excites the determination conditions of the said integer type digital comparison circuit.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Random number inspection apparatus 11 Random number generator 12 Random number preservation | save means 13 Statistics calculation means 14 Statistics determination means 15 Output control means 16 Computer application 19 Exponential conversion means 20 Section conversion means 21 Encoding part 22 Encoding part 23 Exponential part 24 Exponential setting Means 25 Mantissa part 26 Mantissa setting means 27 Floating point type storage format 30 Measuring means 31 Degree of freedom converting means 32 Statistics calculating means 33 Measured value determining means 35 Random number converting means 36A, 36B Frequency distribution measuring means 37 Binary random number measuring means ( counter)
38 counter 39 shift register 40 counter 44 integer type digital comparison circuit 45 judgment value holding circuit 46 measurement value counter 47 digital comparison circuit 49 comparison judgment means

Claims (9)

Random number storage means for storing random numbers generated by the random number generation means;
A statistic calculating means for calculating a statistic of random numbers output from the random number storing means;
A statistic determination means for determining the calculated statistic;
Output control means for outputting the random number stored in the random number storage means to the application according to the determination result from the statistic determination means,
The random number inspection apparatus, wherein the output control means outputs a random number required by the application. The statistic calculation means includes:
A sign setting means for setting a sign in the sign part, an exponent setting means for setting a value in the exponent part, and an exponent conversion means for converting a random number into an exponent from a mantissa setting means for setting a random number bit string in the mantissa part;
2. The random number inspection device according to claim 1, further comprising: interval conversion means for converting an output from the exponent conversion means into a property of random numbers required by the application and a use interval. The statistic determination means includes measurement means for obtaining M measurement values;
Degree-of-freedom conversion means for converting the degree of freedom into a measured value of 1,
The random number inspection device according to claim 1, further comprising a determination unit that divides the measurement value into a plurality of groups and compares the measurement value with a predetermined determination value. The statistic determination means includes
Random number conversion means for converting an integer random number into a random number of degrees of freedom;
The random number inspection device according to claim 1, further comprising a determination unit that directly compares the measured value with a predetermined determination value. 5. The random number inspection device according to claim 3, wherein the statistic determination unit includes a frequency distribution measurement unit that measures a frequency distribution of a part of the N-dimensional space as a statistic. 5. The random number inspection device according to claim 3, wherein the statistic determination unit includes a frequency distribution measurement unit that measures a continuous frequency distribution as a statistic. 7. The random number inspection device according to claim 1, wherein said statistic determination means comprises an integer type digital comparison circuit for comparing a determination value storage function and a measured value as determination means. The random number inspection device according to claim 1, wherein the statistic determination unit is configured to perform one to four types of comparisons as the determination unit. Save the generated physical random number or pseudo-random number,
Calculate the statistics of the stored random numbers,
Determine the statistic of the calculated random number,
A random number inspection method, comprising: outputting a random number required by an application from the random number statistics.

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