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随机数在密码与安全技术方面使用广泛,随机数的产生和使用过程中,需要对随机数的随机性进行检测,统计检测是一种普遍采用的随机数检测方法,其中NIST发布的SP 800-22统计检测包是国际上常采用的统计检测方法,它包含15个检测项目,每个检测项又分为一级检测和二级检测.对于SP 800-22的正态分布型检测项目,我们发现这些检测项目的二级检测是不完备的,即通过这种检测的随机序列仍有可能在所检测的统计特性上存在缺陷.这是因为,正态分布型的检测计算出的P_value适用于一级检测,不适用于二级检测,因为在二级检测中,即使该P_value分布均匀,被测序列通过检测,这个序列也不一定满足所检测性质,为此,不同于原标准二级检测中的P_value均匀性检测,本文提出了Q_value的均匀性检测作为正态分布型检测项目的二级检测,并且给出了Q_value参数的非渐进分布,我们发现相比于P_value,Q_value的分布更接近于均匀分布,用于新的检测能降低误检率提高可靠性.最后,本文通过实验证实Q_value检测能够发现一些更为隐蔽的统计缺陷.
Random numbers are widely used in the fields of cryptography and security technologies. In the process of generating and using random numbers, the randomness of random numbers needs to be tested. Statistical testing is a commonly used random number detection method. Among them, the SP 800- 22 Statistical test package is a commonly used statistical test method in the world, which contains 15 test items, each test item is divided into first-level test and second-level test. For the SP 800-22 normal distributed test items, we It is found that the secondary detection of these test items is not complete, ie, the random sequence passed through this test is still likely to have defects in the statistical properties tested, because the P_value calculated by the test of normal distribution applies to The first level test is not suitable for the second level test because in the second level test, even if the P_value is evenly distributed, the sequence under test does not necessarily satisfy the detected property. Therefore, unlike the second level test In this paper, the detection of uniformity of Q_value is proposed as a second-level detection of normal distribution detection items, and the non-progressive distribution of Q_value parameters is given. We find that phase In P_value, Q_value distribution closer to a uniform distribution, for detecting the new false positive rate can be reduced to improve reliability. Finally, the detection can be confirmed by experiment Q_value find some more subtle defect statistics.