1. Introduction

This repo is an implementation of GM/T 0005-2021, a randomness testing standard in China.

The Chinese version's document is available here.

We can use it to test a random number generator (RNG): if most random numbers generated by the RNG pass the test suite, we can consider this RNG reliable.

This work includes 15 test units. We will compute the p_value for each sample in each test unit, if the given value is equal or greater than 0.01, we may consider this sample passes the test unit. Total, the number of samples is 1000, and there should be more than 981 samples passing the test if the RNG is reliable. In addition, we also compute the q_value for each test unit, in which the significant value should be 0.0001.

The GM/T document defines the recommended length for the sample bits and the corresponding parameters. Available sizes: 2 * 10^4, 10^6 and 10^8.

1.1 Test units

	Test unit
Monobit Test	Frequency Test within a block	Runs Test
Test for the longest Run of Ones in a block	Binary Matrix Rank Test	Discrete Fourier Transform Test
Maurer's "Universal Statistical" Test	Linear Complexity Test	Serial Test
Approximate Entropy Test	Cumulative Test	Poker Test
Runs Distribution Test	Binary Derivative Test	Autocorrelation Test

1.2 Difference between NIST and GM/T

Both the NIST standard and the GM/T standard require very similar test units. However, Poker test, Runs distribution test, Binary derivative test, and Autocorrelation test are only available in GM/T standard, while Excursion Test, Random Excursion Variant Test,Non-overlapping Template Matching Test, and Overlapping Template Matching Test are only available in NIST standards.

The GM/T standard also requires the q_value and the sample size.

Also, there are some different parameters in the discrete Fourier transform test and the test for the longest run of ones in a block. Please check comments in source codes for details.

1.3 References

https://github.com/dj-on-github/sp800_22_tests

https://github.com/InsaneMonster/NistRng

https://github.com/stevenang/randomness_testsuite

2. Usage

Execution Environment

Python >= 3.9.0

Requirements

pip install -r requirements.txt

Generating tested samples

We need to generate tested random numbers and write them into a binary file before we run the script. Example here:

import os 

with open("data_20000","wb") as f:
        for i in range(1000):
                f.write(os.urandom(2500))
                f.flush()

Users can use your own RNG.

Execution

Example

import numpy
# import our libs
from gmt_random_test.gmt_randomness_test import GmtRandomnessTest
from gmt_random_test.test import Result

if __name__ == "__main__":
    # create the test instance with the sample size
    gmt_test: GmtRandomnessTest = GmtRandomnessTest(20000)
    # also you can choose other sizes 
    # gmt_test: GmtRandomnessTest = GmtRandomnessTest(1000000)
    # gmt_test: GmtRandomnessTest = GmtRandomnessTest(100000000)

    # read binary sequences
    bits: numpy.ndarray = None
    with open("data/data_20000","rb") as f:
       bits = numpy.unpackbits(numpy.frombuffer(f.read(2500), dtype=numpy.uint8))
    # run all tests   
    gmt_test.run_all_battery_with_bits(bits)
    # run tests by name
    gmt_test.run_by_name_with_bits(bits, "serial_3")
    gmt_test.run_by_name_with_bits(bits, "serial_5")
    # file as input
    gmt_test.run_all_battery_with_file("data/data_20000")

Unit Test:

Please check the test file.

3. Results

20000-bits

GMT randomness test (samples size: 1000)
Types of test:  Passes:         Distribution:
Monobit         992     0.19376653751100414
Frequency Within Block (m=1000)         993     0.6287904561747886
Poker (m=4)     992     0.9774801795691433
Poker (m=8)     983     0.010988016145239969
Runs)   989     0.5810821521175091
RunsDistribution)       989     0.6204652616810549
Binary Derivative (d=3)         994     0.8628831961771974
Binary Derivative (d=7)         989     0.35864134122843766
Autocorrelation (k=2)   987     0.5523828823144027
Autocorrelation (k=8)   990     0.5081718433121454
Autocorrelation (k=16)  991     0.004085375625386839
Approximate Entropy (m=2)       990     0.7791877161648364
Approximate Entropy (m=5)       996     0.5261047121948592
Discrete Fourier Transform                      991     0.12961959133276194
Serial (m=3)                    985     0.8891175958894987, 0.33768835649023937
Serial (m=5)                    984     0.03756608354257083, 0.6371194071693984
Longest Runs In A Block                         983     0.18555523463043544, 0.9929519746920032
Cumulative Sums                         991     0.8237245548918524, 0.4559371952206618