GB/T 32915-2026Cybersecurity technology — Randomness test methods for binary sequences (English PDF)

3.1 Binary Sequence

A bit string composed of "0" and "1".

NOTE: It is abbreviated as "sequence".

3.2 Randomness Hypothesis

The hypothesis concerning the randomness of the binary sequence to be tested; the decision to accept or reject this hypothesis can be based on the randomness test results.

NOTE: This document assumes that the binary sequence to be tested is random; this is referred to as the null hypothesis.

3.3 Randomness Test

A function or procedure used for binary sequence tests, the result of which is used to determine whether to accept the null hypothesis.

3.4 Significance Level

The probability of incorrectly rejecting the null hypothesis in a randomness test when the null hypothesis is actually true.

3.5 Sample

A binary sequence used for randomness tests.

NOTE: It is also known as a "sequence to be tested".

3.6 Sample Group

A collection of multiple samples.

3.7 Sample Length

The number of bits per sample.

3.8 Sample Size

The number of samples in the sample group.

3.9 Test Parameter

The parameter that needs to be set for randomness tests.

3.10 Run

A subsequence within a sequence, consisting of consecutive "0" or "1", where both the preceding and succeeding elements differ from the elements of the subsequence itself.

5.1 General

This document specifies 15 test techniques for the randomness tests of binary sequences. Each technique is used to test for a specific characteristic property of a binary sequence, with distinct test steps and result determination methods for each.

The randomness tests of binary sequence samples shall comply with the requirements for sample length and test settings specified in Appendix A.

5.2 Monobit Frequency Test

5.2.1 Test objectives

The monobit frequency test is used to test whether a binary sequence exhibits a satisfactory balance between "0" and "1" - that is, whether the numbers of bits "0" and "1" are approximately equal. Test parameter requirements shall comply with the relevant provisions in Appendix A; the test principle is described in B.1 of Appendix B, and an example of the results is provided in C.1 of Appendix C.

5.2.2 Test steps

The steps for the monobit frequency test are as follows:

Step 1: Calculate, converting the "0" and "1" in the sequence to be tested epsilon into "-1" and "1", respectively.

Step 2: Calculate the cumulative sum to obtain.

Step 3: Calculate the statistical value.

Step 4: Calculate.

Step 5: Calculate.

5.2.3 Result determination

Compare the P_value result calculated in 5.2.2 with the significance level alpha. If P_value>=alpha, the binary sequence sample is considered to have passed the monobit frequency test; otherwise, it […]

6.1

A randomness test technique corresponds to at least one randomness test item; if a specific randomness test technique employs different test parameter settings, utilizes distinct test modes (such as the maximum run test within a block or the cumulative sum test), or involves multiple statistical values (such as the overlapping subsequence test), the corresponding aspects shall be tested as separate randomness test items; furthermore, the sample pass rate and distribution uniformity for each test item within the binary sequence sample group shall be evaluated individually to determine compliance. For instance, the cumulative sum test method comprises two modes: forward cumulative sum and backward cumulative sum. These two modes shall be tested as 2 independent test items; furthermore, the sample pass rates and distribution uniformity for the forward and backward cumulative sums within the binary sequence sample group shall be evaluated individually to determine compliance.

The sample size in the binary sequence sample group specified in this document is 1 000.

6.2 Determination of Sample Pass Rate

For each randomness test item defined in 6.1, count the number of samples within the binary sequence sample group that pass the test. Let s denote the sample size in the sample group. If the number of samples passing a specific test item is greater than or equal to, the binary sequence sample group is considered to have passed the test for that item; otherwise, it is considered to have failed.

The significance level alpha specified in this document for the sample pass rate test is 0.01. Based on the sample size and significance level specified in this document, the number of samples within the binary sequence sample group that pass each test item shall be greater than or equal to 981.

6.3 Determination of Sample Distribution Uniformity

For each randomness test item defined in 6.1, the Q_value values of the samples within the binary sequence sample group shall be uniformly distributed within the interval [0, 1]. Let s denote the sample size, and divide the interval [0, 1] into k equal sub-intervals. Count the actual number (Fi) of samples within the binary sequence sample group whose Q_value falls within each sub-interval, where 1<=i<=k. Using the chi2 distribution, compare Fi with the theoretical value s/k, calculate the statistical value, and calculate. When PT is greater than or equal to alphaT, the binary sequence sample group is considered to have passed the test for that item; otherwise, it is considered to have failed. This document specifies a significance level of alphaT=0.000 1 and a number of sub-intervals of k=10 for the sample distribution uniformity test.

6.4 Comprehensive Determination

The binary sequence sample group passes the randomness test specified in this document if and […]

B.1 Monobit Frequency Test

The monobit frequency test is the most fundamental test; it is used to test whether the numbers of "0" and "1" in a binary sequence are approximately equal. Given a binary sequence of length n, let n0 and n1 denote the numbers of "0" and "1" in the sequence, respectively. For a random sequence, when the length is sufficiently large, the statistical value follows a standard normal distribution.

B.2 Frequency Test within a Block

The frequency test within a block is used to test whether the number of "1" in an m-bit subsequence of the sequence to be tested is close to m/2. For a random sequence, the number of "1" in any m-bit subsequence shall be close to m/2.

The frequency test within a block divides the sequence to be tested into N subsequences, each of length m, such that n=Nm. Of course, if n is not divisible by m, there will inevitably be redundant bits; in this case, the redundant bits are discarded. Calculate the proportion of "1" in each subsequence and denote it as. Taking the cumulative sum of the proportions of "1" across all N subsequences as the statistical value, the statistical value follows a chi2 distribution with N degrees of freedom.

B.3 Poker Test

For any positive integer m, there are 2m types of binary sequences of length m. Divide the sequence to be tested into N non-overlapping subsequences of length m, and let represent the number of subsequences of the ith type. The poker test is used to test whether the numbers of subsequences of the 2m types are approximately equal.

The statistical value follows a chi2 distribution with 2m-1 degrees of freedom. […]