大样本条件下随机性检测的误差分析及参数建议  

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

作　　者：孙月玥 范丽敏[2] SUN Yueyue;FAN Limin(School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 100081,China;Trusted Computing and Information Assurance Laboratory,Institute of Software,Chinese Academy of Sciences,Beijing 100190,China)

机构地区：[1]北京理工大学数学与统计学院,北京100081 [2]中国科学院软件研究所可信计算与信息保障实验室,北京100190

出　　处：《计算机科学》2025年第5期322-329,共8页Computer Science

基　　金：国家密码科学基金(2025NCSF02057)。

摘　　要：在信息安全领域,随机性检测在确保密码系统的安全性中起着至关重要的作用。这些测试的稳定性和可靠性直接影响密码系统的整体安全性。检测过程中的误差问题一直是学术界和工业界关注的焦点,特别是在处理大规模样本时,误差的累积更容易导致随机性检测的可靠性降低。因此,研究如何提高随机性检测的准确性和可靠性具有重要意义。GM/T 0005-2021标准中包含了9个具有可变参数的检测项目。针对大样本二元数据的随机性检测问题,根据其特点进行分类,并进行误差量化分析。当待检二元序列比特长度为1×10^(8)时,GM/T 0005-2021标准中的检测参数建议基本合理。对于Maurer通用统计检测,子序列长度取6时p值误差上界为0.0014928,相较于GM/T 0005-2021中建议的参数表现出更高的准确性。对于线性复杂度检测,更小的子序列长度同样会导致更小的误差。随着样本长度的增加,扩展研究了1×10^(9)时的参数选择,分析了不同样本长度和参数下的误差,并给出了样本长度为1×10^(9)时的检测参数建议。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 1×10^(8),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 0.0014928,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 1×10^(9).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 1×10^(9).

关 键 词：随机性检测 大样本 误差分析 检测参数 GM/T 0005-2021 

分 类 号：TN918.1[电子电信—通信与信息系统]