JP2005259004A - Random number generating method and device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a new method for generating more disordered random numbers by means of an inexpensive simply-constructed device and to provide a device applicable to the method. <P>SOLUTION: An output result of a first electronic circuit outputting a decisive result and an output result of a second electronic circuit outputting a non-decisive result are computed. Then, the computed results by this computing is digitized for generating random numbers. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a random number generation method and a random number generation device.

  Random numbers that are completely chaotic and have the same appearance frequency as a whole are widely used for numerical simulations of social and physical phenomena. In addition, random numbers play an important role as encryption technology, and their demand is high in the field of information protection. Currently, various methods for generating random numbers have been developed. Most of them are generation of software pseudo-random numbers using algorithms.

  Random number generation by an algorithm is widely used because it has a certain degree of reliability and can generate random numbers at high speed. However, since the computer takes only limited information, it has been confirmed that the generated random number has periodicity. Therefore, an accurate solution and sufficient security may not be obtained, and establishment of a more random random number generation method is desired.

  In recent years, a method for generating a physical random number has been developed in order to improve the processing speed and the reliability with the development of hardware. For example, it is known that random numbers generated based on physical phenomena such as thermionic noise and radioactive material decay are ideal random number sequences with high unpredictability. However, these methods often require expensive and large equipment.

  An object of the present invention is to provide a novel method for generating a more random random number using an inexpensive and simple device, and a device applied to the method.

In order to achieve the above object, the present invention provides:
A first step of calculating an output result of a first electronic circuit that outputs a deterministic result and an output result of a second electronic circuit that outputs a non-deterministic result;
A second step of digitizing a calculation result of the calculation and generating a random number;
It is related with the random number generation method characterized by comprising.

  According to the present invention, a random number generation device is configured by a first electronic circuit that outputs a deterministic result and a second electronic circuit that outputs a non-deterministic result. Although a deterministic result is output from the first electronic circuit, a non-deterministic result is output from the second electronic circuit. Therefore, an operation result obtained by calculating these output results is an unpredictable random number. It will be a thing. Therefore, if the calculation result is digitized, a target random number can be obtained.

  In addition, according to the present invention, random number generation is performed based on the output results from the two electronic circuits. Since the output result can be output from the electronic circuit at a relatively high speed, the target random number can be generated at a high speed by performing the calculation on the output result at a high speed using an ultra-high speed calculator or the like. It becomes like this.

  As the first electronic circuit, a computer including an electronic computer can be exemplified. In this case, the deterministic result has a periodicity because it is output as a predetermined numerical value, for example, as a result of an operation by the computer software. However, since it is calculated as a non-deterministic result by the second electronic circuit, the obtained numerical value becomes unpredictable and the desired random number can be obtained as described above. A predetermined control circuit or the like can be used instead of the computer.

  In addition, as the second electronic circuit, a noise generating circuit can be exemplified. The noise generation circuit may include an amplifier circuit, a differential circuit, an analog / digital circuit, and the like as necessary. In this case, the non-deterministic result is noise from the noise generation circuit.

  Further, the operation may be an arithmetic operation such as addition or multiplication, or a logical operation such as AND or OR. Also, arithmetic operations such as differentiation and integration can be used, and several types of operations can be combined.

  In the present invention, in the second step, the numerical operation result obtained as described above is compared with a predetermined threshold value, and a numerical value of “0” or “1” is assigned based on the magnitude relationship with the threshold value. It is also possible to obtain a binary random number.

  Only by calculating the output result from the first electronic circuit and the output result from the second electronic circuit, a sufficiently random random number cannot be obtained, and the purpose for which the random number is used (for example, (Cryptographic random numbers, simulation random numbers, etc.) may not pass the test method for checking whether or not they match. In this case, it is possible to obtain a more random binary random number by appropriately setting the threshold value as described above and taking a magnitude relationship with the threshold value of the calculation result. As a result, random random numbers that can sufficiently pass the above-described test method can be generated.

  Examples of the test method include the NIST FIPS140-2 test (monobit test, poker test, run test, long lunch test) which is a famous cryptographic random number test.

  The threshold value can be changed as appropriate so that a sufficiently random random number can be obtained. In this case, it is possible to set the threshold value by including a test process by a predetermined test method after generation of random numbers and obtaining a more random random number based on the test result by the test method.

  In the present invention, the deterministic result output from the first electronic circuit is set to a predetermined numerical value as described above, and the non-deterministic result output from the second electronic circuit is set as the noise or the like. It can be a signal output.

  Furthermore, in the present invention, a predetermined mathematical function can be prepared, and a calculation result of the numerical value and the signal output can be used as an argument of the mathematical function. In this case, the calculation result of the mathematical function based on the argument becomes the basis of the target random number, and the random number can be obtained by digitizing the calculation result. In this case, since the random number is generated through a two-stage operation, the disorder is further improved. Therefore, it is possible to generate a random number that can sufficiently pass the test method as described above.

  In addition, when the calculation result exceeds a preferable range as the mathematical argument of the mathematical function, the calculation result is multiplied or divided by another variable such as a modulation index, By subtracting, the calculation result is set within the preferable range as the mathematical argument.

  Examples of the mathematical function include hypergeometric functions and Mathieu functions collectively called ellipsoidal functions, and various Bessel functions, exponential functions, hyperbolic functions, and the like, but a periodic function is preferably used. In this case, by setting a predetermined threshold value, it becomes possible to easily and appropriately disperse the numerical calculation result by the mathematical function in the vertical direction of the threshold value, and the binary random number as described above. Can be generated in a more disordered state.

  For the same reason, it is preferable to use a trigonometric function such as a sin function or a cos function as the periodic function.

  The periodic function described above has periodicity, but the inverse function is not uniquely determined. That is, the mathematical argument that is the calculation result of the inverse function is not uniquely determined. In other words, the calculation result of the periodic function is obtained using the above-described uncertain mathematical argument, and thus is not obtained as a continuous numerical value having periodicity. Therefore, a more random number can be generated by obtaining a calculation result for the periodic function of the mathematical argument and digitizing it.

  In the present invention, the output result of the first electronic circuit that outputs the deterministic result and the output result of the second electronic circuit that outputs the non-deterministic result are calculated, and the calculation result of the calculation is digitized. It is also possible to generate a random number sequence by repeating a process a plurality of times to obtain a plurality of numerical calculation results and dividing the result into predetermined sections. In this case, the random number sequence belonging to each section constitutes one random number.

  In the repetitive calculation step, a binary arithmetic result obtained by quantifying the first arithmetic result, that is, a binary random number may be used as the non-deterministic result of the second electronic circuit. In other words, in the first step, the output result of the first electronic circuit and the non-deterministic output result of the second electronic circuit are calculated, and the calculation result is compared with a predetermined threshold value. In the process of generating a binary random number and calculating the output result of the first electronic circuit and the non-deterministic output result of the second electronic circuit for the second time and thereafter, the second The binary random number may be used instead of the non-deterministic output result using an electronic circuit.

  As described above, according to the present invention, it is possible to provide a novel method for generating a more random random number using an inexpensive and simple device, and a device applied to the method.

  The details of the present invention and other features and advantages will be described in detail below based on the best mode.

When frequency modulation is performed with noise from a predetermined noise generator for a high-frequency oscillator, the output is
Vo = sin (ωct + mVn) (1)
It can be expressed by a periodic function as follows. Note that Vo is an output voltage, ωc is the frequency of this output voltage, t is time, m is a modulation index, and Vn is a noise voltage. When the noise generator is an analog type, a predetermined A / D converter can be used to appropriately digitize the noise voltage from the noise generator.

  The ωc and the m can be output as a deterministic result, that is, a numerical value from a personal computer as the first electronic circuit. The Vn can be output as a non-deterministic result from a noise generation circuit as the second electronic circuit. Therefore, by multiplying and adding these output results, it becomes a mathematical argument of the periodic function expressed by the equation (1), and the periodic function expressed by the equation (1) is calculated using this mathematical factor. If it is digitized, the target random number can be obtained.

  At this time, if a predetermined threshold value is set, the calculation result of the periodic function expressed by the equation (1) is compared with the threshold value, and “0” or “1” is assigned according to the magnitude relationship, A binary random number can be obtained. In addition, if the threshold value is appropriately changed according to the calculation result, a random random number can be generated more easily.

  It is also possible to generate a random number sequence by obtaining a plurality of calculation results for the periodic function represented by equation (1), digitizing the result, and dividing the result into predetermined sections. In this case, each random number sequence forms one random number.

  The calculation based on the mathematical factor of the periodic function of the equation (1) can be performed using the same personal computer as described above, or a computer such as a different ultrahigh-speed electronic computer can be used.

(Example)
A noise generating circuit using a predetermined personal computer and a diode shown in FIG. 1 was used, and the noise from the noise generating circuit was digitized by an A / D converter and taken into the personal computer as a noise voltage Vn. The noise voltage Vn was changed within the range of +2047 to -2048. On the other hand, in the personal computer, the frequency ωc is increased from 0 by 0.314 to 6280, and the modulation index m is changed in the range of 0.01 to 10 ¹⁵ .

  Based on the mathematical argument obtained under such conditions, the periodic function shown in Equation (1) was calculated, and then the calculation result was digitized. Next, a plurality of obtained numerical calculation results were compared with a threshold of 0 level, and “0” or “1” was assigned according to the magnitude relationship to obtain a plurality of binary numerical values. Next, the binary numbers were divided into 8 bits each to be a decimal number, and as shown in FIG. 2, odd numbers were assigned to the horizontal axis and even numbers were assigned to the horizontal axis for plotting.

  As is apparent from FIG. 2, it can be seen that the plots are evenly distributed in the front of the figure and are random numbers. In addition, when m is 0.1 or more, it passed the FIPS140-2 test of NIST, USA. However, when m was 0.01, the poker test and the run test were rejected. Therefore, it can be seen that sufficiently random numbers can be obtained by setting m to 0.1 or more.

  As described above, the present invention has been described in detail based on the embodiments of the present invention with specific examples. However, the present invention is not limited to the above contents, and all modifications and changes are made without departing from the scope of the present invention. It can be changed.

  For example, a noise generation circuit with higher speed can be used instead of the noise generation circuit shown in FIG. FIG. 3 is a circuit diagram showing an example of an oscillator used for speeding up. In this case, the output terminal of the noise generating circuit shown in FIG. 1 is connected to the noise input terminal of the circuit shown in FIG. 3, and the signal output from the oscillator shown in FIG. 3 is digitized by an A / D converter. A noise signal can be obtained at high speed. This aspect is advantageous when the speed of a computer such as an electronic computer used is increased.

  The conversion speed of the A / D converter is about 10,000 to 100,000 times per second. On the other hand, the calculation speed of a computer such as an electronic computer may be increased to about 100 million times per second. In such a case, the output of the A / D converter is insufficient, and the same noise signal (noise voltage) is used in the calculation when generating the random number, and the randomness of the random number deteriorates. May end up.

  As a countermeasure, for example, 20,000 digitized noise signals from the noise generator are sampled at a certain first time, and another 20,000 samples are sampled at the next certain time, and these are multiplied in vector. 20,000 x 20,000 2D vector data is created. Since the noise signal obtained at each time is nondeterministic and uncertain, the two-dimensional vector data is uncertain. Therefore, the two-dimensional vector data can be used as a non-deterministic result instead of the noise signal.

  In this case, it is preferable to use diagonal elements of the two-dimensional vector data because short periodicity tends to appear when the elements in the column direction or the row direction are used in the two-dimensional vector data.

  When each element of the 20,000 × 20,000 two-dimensional vectors is used up, a procedure for newly collecting a digitized noise signal from the noise generator is repeated. As a result, new non-deterministic results can always be obtained.

  Further, by repeating the above-described operation, three-dimensional vector data, four-dimensional vector data, or even more multidimensional vector data can be used instead of the two-dimensional vector data.

It is a block diagram which shows an example of the noise generation circuit used in the random number generation method of this invention. It is a figure which shows distribution of 20,000 random numbers obtained by the random number generation method of this invention. It is a circuit diagram showing an example of an oscillator used for speeding up.

Claims (22)

A first step of calculating an output result of a first electronic circuit that outputs a deterministic result and an output result of a second electronic circuit that outputs a non-deterministic result;
A second step of digitizing a calculation result of the calculation and generating a random number;
A random number generation method characterized by comprising:   In the second step, the numerical calculation result is compared with a predetermined threshold value, and a numerical value of “0” or “1” is assigned based on the magnitude relation of the calculation result with the threshold value. The random number generation method according to claim 1, wherein the random number is generated.   The random number generation method according to claim 2, wherein the threshold value is changed based on a test result of a predetermined random number test method.   In the first step, the first electronic circuit outputs a numerical value as a deterministic result, the second electronic circuit outputs a predetermined signal as a non-deterministic result, and the numerical value and the output value of the signal The random number generation method according to claim 1, wherein the random number is calculated.   In the second step, a predetermined mathematical function is set, an operation result of the numerical value and the output value of the signal is used as an argument of the mathematical function, and an operation result of the mathematical function by the argument is a numerical value. The random number generation method according to claim 4, wherein the random number is generated by generating a random number.   The random number generation method according to claim 5, wherein the mathematical function is a periodic function.   The random number generation method according to claim 6, wherein the periodic function is a trigonometric function.   The random number generation method according to claim 1, wherein the first electronic circuit includes a computer in which predetermined software is incorporated.   The random number generation method according to claim 1, wherein the second electronic circuit includes a noise generation circuit. A first step of calculating an output result of a first electronic circuit that outputs a deterministic result and an output result of a second electronic circuit that outputs a non-deterministic result;
A second step of digitizing the calculation result of the calculation;
A third step of dividing a plurality of numerical calculation results obtained by repeating the first step and the second step into predetermined sections and generating a random number sequence;
A random number generation method characterized by comprising: In the second step, the operation result that has been digitized is compared with a predetermined threshold value, and a numerical value of “0” or “1” is assigned based on the magnitude relationship between the operation result and the threshold value. Get the result,
In the third step, a plurality of binary arithmetic results are obtained, the plurality of binary arithmetic results are divided into predetermined sections, and the random number sequence is generated. Item 11. The random number generation method according to Item 10.   The binary arithmetic operation result in the second step is used as the non-deterministic result of the second electronic circuit in the first step in the third step. 11. The random number generation method according to 11.   The random number generation method according to claim 11 or 12, wherein the threshold value is changed based on a test result of a predetermined random number test method.   In the first step, the first electronic circuit outputs a numerical value as a deterministic result, the second electronic circuit outputs a predetermined signal as a non-deterministic result, and outputs the mathematical variable and the signal. The random number generation method according to claim 10, wherein a value is calculated.   In the second step, a predetermined mathematical function is set, an operation result of the numerical value and the output value of the signal is used as an argument of the mathematical function, and an operation result of the mathematical function by the argument is a numerical value. The random number generation method according to claim 14, wherein:   The method according to claim 15, wherein the mathematical function is a periodic function.   The random number generation method according to claim 16, wherein the periodic function is a trigonometric function.   18. The random number generation method according to claim 10, wherein the first electronic circuit includes a computer in which predetermined software is incorporated.   The random number generation method according to claim 10, wherein the second electronic circuit includes a noise generation circuit.   A random number generator comprising: a first electronic circuit that outputs a deterministic result; and a second electronic circuit that outputs a non-deterministic result.   21. The random number generation device according to claim 20, wherein the first electronic circuit includes a computer in which predetermined software is incorporated.   The random number generation device according to claim 20 or 21, wherein the second electronic circuit includes a noise generation circuit.

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