GB/T 32915-2016 PDF English
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Information security technology - Randomness test methods for binary sequence
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GB/T 32915-2016: Information security technology - Randomness test methods for binary sequence---This is an excerpt. Full copy of true-PDF in English version (including equations, symbols, images, flow-chart, tables, and figures etc.), auto-downloaded/delivered in 9 seconds, can be purchased online: https://www.ChineseStandard.net/PDF.aspx/GBT32915-2016
GB
NATIONAL STANDARD OF THE
PEOPLE’S REPUBLIC OF CHINA
ICS 35.040
L 80
Information security technology -
Randomness test methods for binary sequence
Issued on. AUGUST 29, 2016
Implemented on. MARCH 01, 2017
Issued by. General Administration of Quality Supervision Inspection and
Quarantine of PRC;
Standardization Administration of PRC.
Table of Contents
Foreword... 5
1 Scope... 6
2 Terms and definitions... 6
3 Symbol... 7
4 Randomness test... 9
5 Random number generator test... 23
Appendix A (Informative) Random test principle... 25
Appendix B (Informative) Randomness test parameter setting table... 35
Foreword
This standard was drafted in accordance with the rules given in GB/T 1.1-2009.
Please note that some of the contents of this document may involve patents.
The issuing organization of this document is not responsible for identifying
these patents.
This standard was proposed by the National Cryptography Authority.
This standard shall be under the jurisdiction of the National Information Security
Standardization Technical Committee (SAC/TC 260).
Drafting organizations of this standard. National Cryptographic Authority
Commercial Password Testing Center, Institute of Software of Chinese
Academy of Sciences, Beijing Institute of Information Science and Technology.
The main drafters of this standard. Li Dawei, Feng Dengguo, Chen Hua, Zhang
Chao, Zhou Yongbin, Dong Fang, Fan Limin, Xu Weiwei, Deng Kaiyong, Luo
Peng.
Information security technology -
Randomness test methods for binary sequence
1 Scope
This standard specifies the randomness test indicators and test methods in
commercial password applications.
This standard applies to the randomness test of binary sequences generated
by random number generators.
2 Terms and definitions
The following terms and definitions apply to this document.
2.1
Binary sequence
A bit string consisting of “0” and “1”.
2.2
Random number generator
A device or program that produces a random binary sequence.
2.3
Randomness hypothesis
When performing randomness test on a binary sequence, first assume that
the sequence is random. This assumption is called the original hypothesis
or null hypothesis and is recorded as H0.The hypothesis opposite to the null
hypothesis, that this sequence is not random, is called the alternative
hypothesis, which is denoted as Hα.
2.4
Randomness test
A function or process used for binary sequence test to determine whether to
accept the randomness null hypothesis.
2.5
Significance level
The probability of erroneously determining a random sequence as a non-
random sequence in randomness test, which is represented by α.
3 Symbol
The following symbols apply to this document.
α. Significance level
H0.Original hypothesis (null hypothesis)
Hα. Alternative hypothesis
ε. Sequence to be tested
n. Bit length of the sequence to be tested
4 Randomness test
4.1 Single bit frequency test method
4.1.1 Overview
Single-bit frequency test is the most basic test, which is used to detect whether
the number of 0 and 1 in a binary sequence are similar. That is, if a binary
sequence of length n is known, it is tested whether the sequence has a good 0,
1 balance.
4.1.2 Test procedures
The single-bit frequency test procedures are as follows.
Step 1.This test converts 0 and 1 in the sequence ε to be tested into -1 and 1,
4.1.3 Result determination
The P_value result calculated in 4.1.2 is compared with the significance level α.
If P_value ≥ α, the sequence to be tested is deemed to pass the single bit
frequency test; otherwise, the sequence to be tested is deemed not to pass the
single bit frequency test.
4.2 Block internal frequency test method
4.3 Poker test method
4.3.1 Overview
Poker test is used to test whether the number of 2m subsequence types of
length m is close. For random sequences, the number of 2m subsequences
shall be close.
4.3.3 Result determination
The P_value result calculated in 4.3.2 is compared with the significance level α.
If P_value ≥ α, the sequence to be tested is deemed to pass the poker test;
otherwise, the sequence to be tested is deemed not to pass the poker test.
4.4 Overlapping subsequence test method
4.4.1 Overview
For any positive integer m, the binary sequence of length m has 2m types.
Overlapping subsequence test divides the sequence to be tested (length n) into
n superimposable m-bit subsequences. For a random binary sequence, the
probability of occurrence of each mode of the m-bit superimposable
subsequence shall be close due to its uniformity.
4.4.3 Result determination
Compare the two P_value results calculated in 4.4.2 with the significance level
α. If P_value1 ≥ α and P_value2 ≥ α, the sequence to be tested is deemed to
pass the overlapping subsequence test.
4.5 Total run number test method
4.5.1 Overview
A run is a subsequence in a sequence consisting of consecutive “0” or “1”, and
the preamble and successor elements of the subsequence are different from
their own elements. The total run number test mainly tests whether the total
number of runs in the sequence to be tested obeys the randomness
requirements.
4.7 Maximum “1” run test method in block
4.7.1 Overview
The maximum “1” run test in the block divides the sequence to be tested into N
subsequences of length m, where. The longest “1” run length in each
subsequence is counted, and by assigning it to the corresponding set, the
randomness of the sequence to be tested is evaluated in accordance with the
distribution of the largest 1 run in each subsequence.
4.7.3 Result determination
Compare the P_value result calculated in 4.7.2 with the significance level α. If
P_value ≥ α, then the sequence to be tested is deemed to pass the largest “1”
run test in the block.
4.8 Binary derivation test method
4.8.1 Overview
The purpose of the binary derivation test is to determine whether the number of
0 and 1 in the kth binary derivation sequence is close to coincide.
4.8.2 Test procedures
The binary derivation test procedures are as follows.
Step 1.For the sequence ε, perform XOR operation for the adjacent two bits in
the initial sequence to obtain a new sequence ε', that is, ε'i = εi εi + 1.
4.8.3 Result determination
Compare the P_value result calculated in 4.8.2 with the significance level α. If
P_value ≥ α, the sequence to be tested is deemed to pass the binary derivation
test.
4.9 Autocorrelation test method
4.10 Matrix rank test method
4.10.1 Overview
Matrix rank test is used to test the linear independence between subsequences
of a given length in the sequence to be tested. Construct a matrix from the
sequence to be tested, then test the linear independence between the rows or
columns of the matrix, the degree of offset of the matrix rank can give an
understanding of the amount of linear independence, thereby affecting the
evaluation of the randomness of the binary sequence.
4.11 Cumulative sum test methods
4.11.1 Overview
The cumulative sum test determine the randomness of the sequence to be
tested by determining the maximum offset (between 0) in each subsequence of
the sequence to be tested, that is, the comparison between the maximum
accumulation and the maximum offset that a random sequence shall have.
4.12 Approximate entropy test method
4.12.1 Overview
The approximate entropy test evaluates the randomness by comparing the
frequency of the m-bit overlappable subsequence mode with the frequency of
the (m+1)-bit overlappable subsequence mode.
4.12.2 Test procedures
The approximate entropy test procedures are as follows.
4.12.3 Result determination
The P_value result calculated in 4.12.2 is compared to the significance level α.
If P_value ≥ α, the sequence to be tested is deemed to pass the approximate
entropy test.
4.13 Linear complexity test method
4.13.3 Result determination
The P_value result calculated in 4.13.2 is compared to the significance level α.
If P_value ≥ α, the sequence to be tested is deemed to pass the linear
complexity test.
......
Source: Above contents are excerpted from the full-copy PDF -- translated/reviewed by: www.ChineseStandard.net / Wayne Zheng et al.
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