CN101674102B - Randomness detecting method based on pseudo-random sequence of sample - Google Patents

Abstract

The invention discloses a random detecting method based on a pseudo-random sequence, belonging to the technical field of signal detection and mainly solving the problems of limitation and one-sidedness existing in the prior randomness detecting method. The method comprises the following detecting steps: carrying out pretreatment of sampling or sampling modulo 2 addition on sequences to be detected, and carrying out transformation point detection on the sequences obtained after the pretreatment; selecting a standard pseudo-random sequence, and arranging the standard pseudo-random sequence in front of the pretreated sequences to form new sequences; grouping the new sequences, and calculating the accumulative sum of bits in the groups to obtain the difference values of the accumulative sums of the adjacent groups; selecting fractiles and determining critical values; comparing all the difference values with the critical values, if all the difference values are less than or equal to the critical values, confirming that the sequences satisfy the random characteristic, otherwise, confirming that the sequences do not satisfy the random characteristic. The method has the advantages of overall detection result, high reliability and good effectiveness, and can be used in the fields of random simulation, spreading code generation in a CDMA system and key stream generation in a stream cipher system.

Description

Randomness detecting method based on the pseudo random sequence of sampling

Technical field

The invention belongs to the signal detection technique field; Be particularly related to the randomness detecting method of pseudo random sequence, can be used for stochastic simulation, the pseudo-code in the pseudo-random code ranging generates; Spreading code in the cdma system generates, and the key stream in various noise sources generations and the stream cipher system generates.

Background technology

Pseudo random sequence through the randomizer generation; Its randomness directly has influence on the fail safe of application; Therefore to judge this and whether use safety; Must guarantee earlier that the randomness of this pseudo random sequence is functional, and the randomness of pseudo random sequence is detected the difficult point that always is in the detection of sequence randomness.Detecting the characteristic whether a sequence have the true random sequence can consider from several aspects:

1) periodic feature;

2) ratio that symbol " 0 " and " 1 " occur in the sequence;

3) distribution situation of the distance of swimming in the sequence;

4) the out of phase autocorrelation function of sequence;

5) complexity of sequence, for example linear complexity;

6) the compressible situation of sequence;

In order to test a sequence whether to satisfy these character of random sequence multiple pointed randomness detecting method has been proposed, the cyclophysis that for example binary matrix order test and spectrum measurement can cycle testss; Frequency test and piecemeal frequency test can cycle tests in the ratio that occurs of symbol " 0 " and " 1 "; Linear complexity test, the test of maximum order complexity and the test of second order complexity can cycle tests complexity.

There is kind more than 60 in corresponding test; Like frequency test, add up and check, runs test etc.; They all can only be tested to some character of randomness, that is to say each test pass through can only explain that this sequence satisfies certain stochastic behaviour, but can not guarantee that it also meets other characteristic; Promptly all there are limitation and one-sidedness, the accuracy rate that influence detects.

Summary of the invention

The objective of the invention is to overcome the deficiency of above-mentioned prior art; A kind of randomness detecting method of pseudo random sequence is proposed; On the basis that does not influence former randomicity of sequences,, new sequence is tested once more through changing some alignment properties of former sequence; To reach former sequence is more comprehensively tested effect, improve the accuracy rate that detects.

For realizing above-mentioned purpose, the present invention proposes following two kinds of technical schemes:

Technical scheme 1: the randomness detecting method based on the pseudo random sequence of direct sampling comprises following process:

(1) establishing binary sequence to be measured is a ₀, a ₁..., a _n, length is n+1;

(2) treat the order-checking row and sample, establishing the sampling interval is positive integer d, and obtaining sampled sequence is a ₀..., a _Md, a ₁..., a _Md+1..., a _D-1..., a _{Md+ (d-1)}, m=(n+1)/d-1;

(3) add up with the change point method of testing, selected one has been proved to be pseudorandom sequence s ₀, s ₁..., s _lAs standard sequence, place the sampled sequence front, form a new sequence s ₀, s ₁..., s _l, a ₀..., a _Md, a ₁..., a _Md+1..., a _D-1..., a _{Md+ (d-1)}, new sequence is divided into the K group, calculate adding up and Sum of each grouping Nepit position _i(1≤i≤K), obtain one group of statistical value Diff of new sequence _i=(Sum _I+1-Sum _i)/σ ₀(1≤i≤K-1), σ ₀Be sequence Sum ₁, Sum ₂..., Sum _KThe overall standard deviation of corresponding normal random variable sequence;

(4) through the change point method of testing, selected quantile α ₀(0＜α ₀＜1), by α ₀Confirm critical value c with packet count K ₀

(5) with statistical value sequence D iff ₁, Diff ₂..., Diff _K-1In all value and critical value c ₀Compare, if all statistical values all are less than or equal to critical value c ₀, sequence then to be measured satisfies stochastic behaviour; Otherwise sequence to be measured does not have stochastic behaviour.

Technical scheme 2. comprises following process based on the randomness detecting method of the pseudo random sequence that adds of sampling mould 2:

1) establishing binary sequence to be measured is a ₀, a ₁..., a _n, length is n+1;

2) treat the order-checking row and sample, establishing the sampling interval is positive integer d, and obtaining sampled sequence is a ₀..., a _Md, a ₁..., a _Md+1..., a _D-1..., a _{Md+ (d-1)}, m=(n+1)/d-1;

3) to above sampled sequence a ₀..., a _Md, a ₁..., a _Md+1..., a _D-1..., a _{Md+ (d-1)}Carrying out mould 2 by turn adds: $b_i=a_{\mathrm{Id}}\⊕a_{\mathrm{Id}+1}\·\·\·\⊕a_{\mathrm{Id}+(d-1)},$ 0≤i≤m, it is b that the mould 2 that obtains sampling adds sequence ₀, b ₁..., b _m

4) add up with the change point method of testing, selected one has been proved to be pseudorandom sequence s ₀, s ₁..., s _lAs standard sequence, place the sampled sequence front, form a new sequence s ₀, s ₁..., s _l, b ₀, b ₁..., b _m, new sequence is divided into K ' group, calculate adding up and CSum of each grouping Nepit position _i(1≤i≤K ') obtains one group of statistical value CDiff of new sequence _i=(CSum _I+1-CSum _i)/σ ₁(1≤i≤K '-1), σ ₁Be sequence C Sum ₁, CSum ₂..., CSum _{K '}The overall standard deviation of corresponding normal random variable sequence;

5) through the change point method of testing, selected quantile α ₁(0＜α ₁＜1), by α ₁Confirm critical value c with packet count K ' ₁

6) with statistical value sequence C Diff ₁, CDiff ₂..., CDiff _{K '-1}In all value and critical value c ₁Compare, if all statistical values all are less than or equal to critical value c ₁, sequence then to be measured satisfies stochastic behaviour; Otherwise sequence to be measured does not have stochastic behaviour.

The present invention has following advantage:

A. the present invention treats to check order to be listed as and carries out preliminary treatment earlier; Add like the mould 2 of sampling or sample afterwards again, obtain new sequence, because new sequence has changed sequence to be measured unicity in the order; The stochastic behaviour that embodies is more; New sequence is tested, can solve previous methods and treat limitation and the one-sidedness that the order-checking row are tested, assay is more comprehensive;

B. the present invention tests to the sequence that obtains after handling, and can avoid the situation of previous methods erroneous judgement, has improved the accuracy rate of assay.

Description of drawings

Fig. 1 the present invention is based on the randomness testing process figure of the pseudo random sequence of sampling

Fig. 2 the present invention preliminary treatment sub-process figure that samples

Fig. 3 the present invention mould 2 of sampling adds preliminary treatment sub-process figure

Embodiment

Embodiment one, realizes that through treating the sampling of order-checking row the randomness of pseudo random sequence detects,

See figures.1.and.2, the concrete performing step of this instance is following:

Step 1 is imported sequence a to be measured ₀, a ₁..., a _n, n=10 ⁶

Step 2 is treated the order-checking row and is sampled, and establishing the sampling interval is positive integer d, and obtaining sampled sequence is a ₀..., a _Md, a ₁..., a _Md+1..., a _D-1..., a _{Md+ (d-1)}, m=(n+1)/(d-1).

Step 3 is to sampled sequence a ₀..., a _Md, a ₁..., a _Md+1..., a _D-1..., a _{Md+ (d-1)}Add up with the change point method of testing:

(3a) get one and be proved to be pseudorandom sequence s ₀, s ₁..., s _l(l=10 ⁶) as standard sequence, place a ₀..., a _Md, a ₁..., a _Md+1..., a _D-1..., a _{Md+ (d-1)}A new sequence s is formed in the front ₀, s ₁..., s _l, a ₀..., a _Md, a ₁..., a _Md+1..., a _D-1..., a _{Md+ (d-1)}

(3b) with all 0 becoming-1 in the new sequence, the sequence after the conversion is c ₁, c ₂..., c _k, k=n+l+2;

(3c) with sequence c ₁, c ₂..., c _kBe divided into N grouping B ₁, B ₂..., B _N, the length of each grouping is B_length=k/N;

(3d) calculate B _iIn all bits add up with, be designated as S _i, obtain and sequence S ₁, S ₂..., S _N

(3e) calculate B _iThe overall N of the corresponding stochastic variable normal random variable of institute (0, σ ₂ ²) variances sigma ₂ ², ${\mathrm{\σ}}_2^2=B\_\mathrm{Length}.$ At sequence S ₁, S ₂..., S _NIn, calculate adjacent S _iNormalization difference D _i=(S _I+1-S _i)/σ ₂(1≤i≤N-1), obtain sequence of differences D ₁, D ₂..., D _N-1

Step 4, selected quantile α ₂, utilize following formula to confirm critical value c ₂:

$P\left(\right|D_1|\≤c_2,|D_2|\≤c_2,\·\·\·,|D_{N-1}|\≤c_2)={\∫}_{-c_2}^{c_2}\·\·\·{\∫}_{-c_2}^{c_2}{f}_{N-1}\left(D_{N-1}\right)d{D}_{N-1}=1-{\mathrm{\α}}_2,$ D wherein _N-1=(D ₁, D ₂..., D _N-1) Normal Distribution N (0, C _N-1), $C_{N-1}=\left(\begin{array}{cccccc}2& -1& 0& 0& \·\·\·& 0\\ -1& 2& -1& 0& \·\·\·& 0\\ 0& -1& 2& -1& \·\·\·& 0\\ \·& \·& \·& \·& \·& \·\\ \·& \·& \·& \·& \·& \·\\ \·& \·& \·& \·& \·& \·\\ 0& 0& \·\·\·& 0& -1& 2\end{array}\right)$ Be covariance matrix,

f _N-1(D _N-1) be normal distribution N (0, C _N-1) probability density.For example, selected α ₂=0.05, N=5, then critical value c ₂=3.50.

Step 5 is with D _iWith critical value c ₂Compare, if at D ₁, D ₂... D _N-1The middle existence | D _i|＞c ₂, explain that sequence to be measured does not satisfy stochastic behaviour; Otherwise sequence to be measured has stochastic behaviour.

Embodiment two, add the randomness detection that realizes pseudo random sequence through treating order-checking row sampling mould 2,

With reference to Fig. 1 and Fig. 3, the concrete performing step of this instance is following:

Step 1 is imported sequence a to be measured ₀, a ₁..., a _n, n=10 ⁶

Step 2 is treated the order-checking row and is sampled, and establishing the sampling interval is positive integer d, and obtaining sampled sequence is a ₀..., a _Md, a ₁..., a _Md+1..., a _D-1..., a _{Md+ (d-1)}, m=(n+1)/(d-1).

Step 3 is to above sampled sequence a ₀..., a _Md, a ₁..., a _Md+1..., a _D-1..., a _{Md+ (d-1)}Carrying out mould 2 by turn adds: $b_i=a_{\mathrm{Id}}\⊕a_{\mathrm{Id}+1}\·\·\·\⊕a_{\mathrm{Id}+(d-1)},$ 0≤i≤m, it is b that the mould 2 that obtains sampling adds sequence ₀, b ₁..., b _m

Step 4 adds sequence b to sampling mould 2 ₀, b ₁..., b _mAdd up with the change point method of testing:

(4a) get one and be proved to be pseudorandom sequence s ₀, s ₁..., s _l(l=10 ⁶) as standard sequence, place b ₀, b ₁..., b _mA new sequence s is formed in the front ₀, s ₁..., s _l, b ₀, b ₁..., b _m

(4b) in the new sequence all 0 are become-1, the sequence after the conversion is c ₁, c ₂..., c _{K '}, k '=l+m+1;

(4c) with sequence c ₁, c ₂..., c _{K '}Be divided into the individual grouping CB of N ' ₁, CB ₂..., CB _{N '}, the length C B_length=k ' of each grouping/N ';

(4d) calculate CB _iIn the adding up and (linear with) of all bits, be designated as CS _i, obtain and sequence C S ₁, CS ₂..., CS _{N '}

(4e) calculate CB _iThe overall N of the corresponding stochastic variable normal random variable of institute (0, σ ₃ ²) variances sigma ₃ ², ${\mathrm{\σ}}_3^2=\mathrm{CB}\_\mathrm{Length}.$ At sequence C S ₁, CS ₂..., CS _{N '}In, calculate adjacent C S _iNormalization difference CD _i=(CS _I+1-CS _i)/σ ₃(1≤i≤N '-1) obtains sequence of differences CD ₁, CD ₂..., CD _{N '-1}

Step 5, selected quantile α ₃, utilize following formula to confirm critical value c ₃:

$P\left(\right|D_1|\≤c_3,|D_2|\≤c_3,\·\·\·,|D_{N^{\′}-1}|\≤c_3)={\∫}_{-c_3}^{c_3}\·\·\·{\∫}_{-c_3}^{c_3}{f}_{N^{\′}-1}\left(D_{N^{\′}-1}\right)d{D}_{N^{\′}-1}=1-{\mathrm{\α}}_3,$ D wherein _{N '-1}=(D ₁, D ₂..., D _{N '-1}) Normal Distribution N (0, C _{N '-1}), $C_{N^{\′}-1}=\left(\begin{array}{cccccc}2& -1& 0& 0& \·\·\·& 0\\ -1& 2& -1& 0& \·\·\·& 0\\ 0& -1& 2& -1& \·\·\·& 0\\ \·& \·& \·& \·& \·& \·\\ \·& \·& \·& \·& \·& \·\\ \·& \·& \·& \·& \·& \·\\ 0& 0& \·\·\·& 0& -1& 2\end{array}\right)$ Be covariance matrix, f _{N '-1}(D _{N '-1}) be normal distribution N (0, C _{N '-1}) probability density.For example, selected α ₃=0.05, N '=5, then critical value c ₃=3.50.

Step 6 is with CD _iWith critical value c ₃Compare, if at CD ₁, CD ₂..., CD _{N '-1}The middle existence | CD _i|＞c ₃, explain that sequence to be measured does not satisfy stochastic behaviour; Otherwise sequence to be measured has stochastic behaviour.

Claims (2)

1. randomness detecting method of pseudo random sequence based on sampling comprises following process:

(1) establishing binary sequence to be measured is a ₀, a ₁..., a _n, length is n+1;

(2) treat the order-checking row and sample, establishing the sampling interval is positive integer d, and obtaining sampled sequence is a ₀..., a _Md, a ₁..., a _Md+1..., a _D-1..., a _{Md+ (d-1)}, m=(n+1)/d-1;

(3) add up with the change point method of testing, selected one has been proved to be pseudorandom sequence s ₀, s ₁..., s _lAs standard sequence, place the sampled sequence front, form a new sequence s ₀, s ₁..., s _l, a ₀..., a _Md, a ₁..., a _Md+1..., a _D-1..., a _{Md+ (d-1)}, new sequence is divided into the K group, calculate adding up and Sum of each grouping Nepit position _i(1≤i≤K), obtain one group of statistical value Diff of new sequence _i=(Sum _I+1-Sum _i)/σ ₀(1≤i≤K-1), σ ₀Be sequence Sum ₁, Sum ₂..., Sum _KThe overall standard deviation of pairing normal random variable sequence;

(4) through the change point method of testing, selected quantile α ₀(0＜α ₀＜1), by α ₀Confirm critical value c with packet count K ₀

(5) with statistical value sequence D iff ₁, Diff ₂..., Diff _K-1In all value and critical value c ₀Compare, if all statistical values all are less than or equal to critical value c ₀, sequence then to be measured satisfies stochastic behaviour; Otherwise sequence to be measured does not have stochastic behaviour.

2. randomness detecting method of pseudo random sequence based on sampling comprises following process:

1) establishing binary sequence to be measured is a ₀, a ₁..., a _n, length is n+1;

2) treat the order-checking row and sample, establishing the sampling interval is positive integer d, and obtaining sampled sequence is a ₀..., a _Md, a ₁..., a _Md+1..., a _D-1..., a _{Md+ (d-1)}, m=(n+1)/d-1;

3) to above sampled sequence a ₀..., a _Md, a ₁..., a _Md+1..., a _D-1..., a _{Md+ (d-1)}Carrying out mould 2 by turn adds:

0≤i≤m, it is b that the mould 2 that obtains sampling adds sequence ₀, b ₁..., b _m

4) add up with the change point method of testing, selected one has been proved to be pseudorandom sequence s ₀, s ₁..., s _lAs standard sequence, place the sampled sequence front, form a new sequence s ₀, s ₁..., s _l, b ₀, b ₁..., b _m, new sequence is divided into K ' group, calculate adding up and CSum of each grouping Nepit position _i(1≤i≤K ') obtains one group of statistical value CDiff of new sequence _i=(CSum _I+1-CSum _i)/σ ₁(1≤i≤K '-1), σ ₁Be sequence C Sum ₁, CSum ₂..., CSum _KThe overall standard deviation of ' pairing normal random variable sequence;

5) through the change point method of testing, selected quantile α ₁(0＜α ₁＜1), by α ₁Confirm critical value c with packet count K ' ₁

6) with statistical value sequence C Diff ₁, CDiff ₂..., CDiff _{K '-1}In all value and critical value c ₁Compare, if all statistical values all are less than or equal to critical value c ₁, sequence then to be measured satisfies stochastic behaviour; Otherwise sequence to be measured does not have stochastic behaviour.

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