Error Analysis and Parameter Recommendations for Randomness Test Under Large Sample Conditions

In the field of information security,randomness tests play a crucial role in ensuring the security of cryptographic systems.The stability and reliability of these tests directly impact the overall security of cryptographic systems,making error issues during the testing process a focal point for both academia and industry.Particularly when handling large-scale samples,the accumulation of errors can more readily lead to reliability issues in randomness testing.Consequently,studying methods to enhance the accuracy and reliability of randomness testing is of significant importance.The GM/T 0005-2021 standard outlines 9 tests with variable parameters designed for randomness testing of large binary data samples.This study categorizes these tests according to their characteristics and conducts a quantitative error analysis.Specifically,when the bit length of the binary sequence under test is 1×10⁸,the parameters recommended by the GM/T 0005-2021 standard are generally reasonable.For the Maurer universal statistical test,a subsequence length of 6 results in upper bound p-value error of 0.001 492 8,demonstrating higher accuracy compared to the parameters suggested in the GM/T 0005-2021 standard.Similarly,for the linear complexity test,using smaller subsequence lengths results in smaller errors. With the increase in sample length,this study extends the analysis to parameter selection for a sample length of 1×10⁹.It systematically examines the errors associated with different sample lengths and parameter configurations,providing refined parameter recommendations for randomness testing when the sample length reaches 1×10⁹.