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GM/T 0005-2012 (GM/T0005-2012, GMT 0005-2012, GMT0005-2012)
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GM/T 0005-2012: PDF in English (GMT 0005-2012) GM/T 0005-2012
GM
CRYPTOGRAPHY INDUSTRY STANDARD
OF THE PEOPLE’S REPUBLIC OF CHINA
ICS 35.040
L 80
RECORD NO.. 36832-2012
Randomness test specification
ISSUED ON. MARCH 21, 2012
IMPLEMENTED ON. MARCH 21, 2012
Issued by. State Cryptography Administration
Table of Contents
Foreword ... 3
1 Scope .. 4
2 Terms and conventions ... 4
3 Symbols and abbreviations ... 8
4 Binary sequence test .. 9
5 Test for random number generator ... 17
Annex A (Informative) Principle for randomness test ... 19
Annex B (Informative) Table of randomness test parameters ... 29
Annex C (Informative) Analytical table of randomness test results .. 30
Foreword
This Standard was drafted in accordance with the rules given in GB/T 1.1-2009.
This Standard is a standard for randomness test and provides scientific basis
for randomness assessment.
Attention is drawn to the possibility that some of the elements of this document
may be the subject of patent rights. The issuer of this document shall not be
held responsible for identifying any or all such patent rights.
Annex A, Annex B and Annex C to this Standard are informative.
This Standard was proposed by and shall be under the jurisdiction of the State
Cryptography Administration of the People’s Republic of China.
The drafting organizations of this Standard. State Cryptography Administration
Commercial Cryptography Testing Center, Institute of Software Chinese
Academy of Sciences.
The main drafters of this Standard. Li Dawei, Feng Dengguo, Chen Hua, Zhang
Chao, Zhou Yongbin, Dong Fang, Fan Limin, Xu Nannan.
Randomness test specification
1 Scope
This Standard specifies the randomness test parameters and test methods in
the commercial cryptography application.
This Standard applies to the randomness test for binary sequence which is
generated by random number generator.
2 Terms and conventions
For the purposes of this document, the following terms and definitions apply.
2.1
binary sequence
Bit string which comprises “0” and “1”.
2.2
random number generator
Random number generator refers to a device or program which generates
random sequences.
2.3
randomness hypothesis
For the randomness test of binary sequence, first make a hypothesis that the
sequence is random, which is called original hypothesis or null hypothesis,
denoted as H0. Alternative hypothesis refers to the hypothesis which is contrary
to original hypothesis, i.e. this sequence is not random, denoted as Hα.
2.4
randomness test
A function or process for binary sequence test, through which it is determined
whether the original hypothesis of randomness is acceptable.
2.5
2.13
frequency test within a block
A statistical test item which is used to test whether the number of ones in the
m-bit subsequences (namely “blocks”) of sequence to be tested is close to m/2.
2.14
poker test
A statistical test item which is used to test whether the number of all modes of
the m-bit non-overlap subsequences in sequence to be tested are close.
2.15
serial test
A statistical test item which is used to test whether the numbers of all modes of
the m-bit overlapping subsequences in sequence to be tested are close.
2.16
runs test
A statistical test item which is used to test whether the total number of runs of
sequence to be tested complies with the randomness requirements.
2.17
runs distribution test
A statistical test item which is used to test whether the numbers of equal-length
runs of sequence to be tested are close to identical.
2.18
test for the longest run of ones in a block
A statistical test item which is used to test whether the distribution of the
maximum “1” runs of all equal-length subsequences of subsequences to be
tested comply with the randomness requirements.
2.19
binary derivative test
A statistical test item. Binary derivative sequence is a new sequence which is
generated by an original sequence; and it is the result which is obtained from
the exclusive-OR operation of two adjacent bits of the original sequence in turn.
The object of binary derivative test is to determine whether the numbers of 0
and 1 in the k-th binary derivative sequence are close to identical.
2.20
autocorrelation test
A statistical test item which is used to test the correlation degree between a
sequence to be tested and a new sequence which is obtained after logic shit of
it by d bits.
2.21
binary matrix rank test
A statistical test item which is used to test the linear independence between
given-length subsequences of sequences to be tested.
2.22
cumulative test
A statistical test item which is used to determine whether the maximum
deviation of a sequence to be tested is too large or too small, by comparing the
maximum deviation of all subsequences of sequence to be tested (here, it
refers to the maximum deviation from 0, i.e. the maximum cumulative sum) and
the maximum deviation of a random sequence.
2.23
approximate entropy test
A statistical test item which is used to determine the randomness by comparing
the frequency of the m-th bit overlapping sequence mode and the frequency of
the m + 1-bit overlapping subsequence mode.
2.24
linear complexity test
A statistical test item which is used to determine whether the distribution of
linear complexities of a sequence to be test comply with the randomness
requirements.
2.25
Maurer’s “Universal Test”
b) Calculate the length of the longest run of ones in each subsequence and
include them into a corresponding set {v0, v1, ., v6}.
c) Calculate the statistical value . See Annex A.7 for the
definitions of vi and πi.
d) Calculate .
e) If P-value ≥ α, then the sequence to be tested passes the test for the
longest run of ones in a block.
4.4.9 Binary derivative test
a) For the sequence to be tested ε, conduct exclusive-OR operation of two
adjacent bits in the original sequence to obtain a new sequence ε’, i.e.
b) Repeat operation a) for k times. k = 3,7 in this Specification.
c) Convert the 0 and 1 in the new sequence ε’ respectively into -1 and 1 and
then do cumulative summation to obtain .
d) Calculate the statistical value .
e) Calculate .
f) If P-value ≥ α, then the sequence to be tested passes the binary derivative
test.
4.4.10 Autocorrelation test
a) Calculate . d = 1, 2, 8, 16 in this Specification.
b) Calculate the statistical value .
c) Calculate .
d) If P-value ≥ α, then the sequence to be tested passes the autocorrelation
test.
Annex A
(Informative)
Principle for randomness test
A.1 Monobit frequency test
The monobit frequency test is a most basic test which is used to test whether
the numbers of zeros and ones in a binary sequence are close, i.e. if a binary
sequence of length n is known, it is tested whether the sequence has good
balance of zeros and ones. Let n0 and n1 denote the numbers of zeros and ones
in the sequence. For a random sequence, when its length is sufficiently large,
its statistical value V shall be of standard normal distribution.
A.2 Frequency test within a block
The frequency test within a block is used to test whether the number of ones in
the m-bit subsequences of the sequence to be tested is close to m/2. For a
random sequence, the number of ones in the m-bit subsequences of any length
shall be close to m/2.
In the frequency test within a block, the sequence to be tested is divided into N
subsequences, the length of each subsequence m, n = N * m. Certainly, if n
can’t be divided exactly by m, there will definitely be redundant bits, and then
the abundant bits shall be abandoned. Calculate the proportion of ones in each
subsequence, and set πi = . Let the cumulative sum of the
proportions of ones in all N subsequences as the statistical value, and then.
The statistical value shall follow the x2 distribution with degree of freedom N.
A.3 Poker test
For any positive integer m, there are 2m binary sequences of length m. Divide
the sequence to be tested into non-overlapping subsequences of
length m; and use ni (1 ≤ i ≤ 2m) to represent the number of the i-th subsequence
Annex C
(Informative)
Analytical table of randomness test results
Table C.1
S.N. Test item Principle Parameter requirement Fail analysis
Monobit frequency
test
Test whether the numbers of zeros and ones
in the sequence to be tested are close
n >100
Indicate the number of
zeros or ones is too
small
Frequency test
within a block
whether the number of ones in the m-bit
subsequences is close to m/2
n ≥ 100, m ≥ 20
The proportion of zeros
and ones in the m-bit
subsequences is
unbalanced
3 Poker test
The 2m kinds of subsequences of length m.
Use the length to divide the sequence to be
tested and test whether the numbers of
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Source: Above contents are excerpted from the PDF -- translated/reviewed by: www.chinesestandard.net / Wayne Zheng et al.
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