Method for detecting randomicity of pseudorandom sequence based on random permutation

A pseudo-random sequence, randomness detection technology, applied in the field of randomness detection of pseudo-random sequences, to achieve the effect of comprehensive test results

Inactive Publication Date: 2010-04-21
XIDIAN UNIV
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  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

[0007] 5) The complexity of the sequence, such as linear complexity;
[0010] There are more than 60 kinds of corresponding tests, however, they can only be tested for certain properties of randomness, that is to say, the passing of each test can only show that the sequence satisfies a certain random characteristic, but it does not guarantee it. It also meets other characteristics, that is, there are limitations and one-sidedness, and these tests can only explain the necessary conditions for the randomness of the sequence

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  • Method for detecting randomicity of pseudorandom sequence based on random permutation

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Experimental program
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Effect test

Embodiment 1

[0034] Embodiment 1, the randomness detection of the pseudo-random sequence is realized by inverting the sequence to be tested. Specific steps are as follows:

[0035] Step 1, input the sequence to be tested a 1 , a 2 ,...,a n , n=10 6 .

[0036] Step 2, find the sequence to be tested a 1 , a 2 ,...,a n The inverse sequence, get a n , a n-1 ,...,a 1 .

[0037] Step 3, use the Cramér-von Mises test method to perform statistics on the reverse sequence:

[0038] a) set the length to 10 6 the reverse sequence of a n , a n-1 ,...,a 1 Divide into 100 small groups with a length of 10000, record m=10000, N=100, where 10000 and 100 are optional;

[0039] b) let x 1ij Represents the j-th bit in the i-th small group, i=1, 2, L, N, j=1, 2, L, m, construct statistics

[0040] c) put x 1(i) Sort x from smallest to largest 1(1) ≤x1(2) ≤L≤x 1(N) ;

[0041] d) put x 1(i) bring in Find the statistical value T of the reverse sequence 1 , F(x 1(i) ) is the standard no...

Embodiment 2

[0050] In the second embodiment, the randomness detection of the pseudo-random sequence is realized by inverting the sequence to be tested. Specific steps are as follows:

[0051] Step 1, input the sequence to be tested a 1 , a 2 ,...,a n , n=10 6 .

[0052] Step 2, find the sequence to be tested a 1 , a 2 ,...,a n The inverse sequence, get a 1 , a 2 ,...,a n , where a i =(1+a i ) mod 2, 1≤i≤n.

[0053] Step 3, use the Cramér-von Mises test method to perform statistics on the reverse sequence:

[0054] 1) set the length to 10 6 the reverse sequence of a 1 , a 2 ,...,a n Divide into 20 small groups with a length of 50000, record m=50000, N=20, where 50000 and 20 are optional;

[0055] 2) let x 2ij Represents the j-th bit in the i-th small group, i=1, 2, L, N, j=1, 2, L, m, construct statistics

[0056] 3) put x 2(i) Sort x from smallest to largest 2(1) ≤x 2(2) ≤L≤x 2(N) ;

[0057] 4) put x 2(i) bring in Find the statistical value T of the reverse s...

Embodiment 3

[0064] In the third embodiment, the randomness detection of the pseudo-random sequence is realized by performing random interleaving on the sequence to be tested. Specific steps are as follows:

[0065] Step A, input the sequence to be tested a 1 , a 2 ,...,a n , n=10 6 .

[0066] Step B, the sequence to be tested a 1 , a 2 ,...,a n Perform random interleaving.

[0067] According to the length n of the sequence to be tested, initialize the set I={1, 2, L, n}, randomly select an integer s from the set I 1 denoted as S(1), and s 1 Deleted from set I, the new set obtained is denoted as I 1 ;

[0068] At step k, from set I k-1 ={s∈I, s≠s 1 ,L,s k-1 } randomly selects an integer s k denoted as S(k), and s k from set I k-1 deleted, and the new set obtained is denoted as I k , k=2,3,L,n;

[0069] When k=n, S(n) is obtained, and random interleaving is completed;

[0070] According to the S(1), S(2), L, S(n) obtained above, the random interleaving...

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Abstract

The invention discloses a method for detecting the randomicity of a pseudorandom sequence based on random permutation, which belongs to the field of detection and mainly solves the problems of limitation and onesidedness existing in the traditional randomicity detection method. A series of random permutation processing, such as inversion or negative or random interleaving, is carried out on a sequence to be detected; statistics is carried out on an inverse sequence or a negative sequence or a random interleaving sequence obtained after the random permutation processing by a Cramer-von Mises detection method, a statistical value corresponding to the sequence is obtained, and the statistical value corresponding to the sequence is compared with a selected standard statistical value; if the statistical value is smaller than the standard statistical value, the sequence to be detected meets random properties; and contrarily, the sequence to be detected does not have the random properties. The invention enables the randomicity detection of the pseudorandom sequence to be more comprehensive in a detection result and can be applied to the fields of secret communication, aerospace, distance measurement, cryptography and automatic control.

Description

technical field [0001] The invention belongs to the detection field, in particular to a randomness detection method of a pseudo-random sequence, which can be used for modulation and demodulation in a spread spectrum communication system, key stream generation in a stream cipher system, and the like. Background technique [0002] The randomness of the pseudo-random sequence generated by the random number generator directly affects the security of the application. Therefore, to judge whether the application is safe, it must first ensure that the randomness of the pseudo-random sequence is good. Randomness detection has always been a difficult point in sequence randomness detection. To detect whether a sequence has the characteristics of a truly random sequence, several aspects can be considered: [0003] 1) periodic characteristics; [0004] 2) The proportion of symbols "0" and "1" in the sequence; [0005] 3) The distribution of runs in the sequence; [0006] 4) The out-o...

Claims

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Application Information

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IPC IPC(8): H04L25/03H04B1/707H04B1/7105
Inventor 马文平陈秋丽殷浩
Owner XIDIAN UNIV
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