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Performance Analysis for Statistical Testing of Random and Pseudorandom Generators by Entropy Statistics

机译：基于熵统计的随机和伪随机发生器统计测试性能分析

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The topical problem of performance analysis for statistical testing of "pure randomness" for random and pseudorandom cryptographic generators is considered. Statistical tests based on statistical estimators of Rényi and Tsallis entropy functionals for the observed output sequences with some fixed asymptotic significance level are used. To evaluate asymptotic values of power for these tests we consider two useful in practice families of "pure randomness" alternatives. The first one describes the mathematical model of a pseudo-random sequence generator that is close in its probabilistic properties to the "pure random" sequence. The second one is the Markovian alternative. For the alternative hypotheses, asymptotic probability distributions of entropy estimators are also found. Estimates of the power of the developed tests are calculated.
机译：考虑了用于随机和伪随机密码生成器的“纯随机性”统计测试的性能分析的主题问题。使用基于Rényi和Tsallis熵函数的统计估计量的统计检验，对具有固定的渐近显着性水平的观察到的输出序列进行统计。为了评估这些测试的渐近功率值，我们认为在“纯随机性”替代方案的实践系列中有两个有用的方法。第一个描述了伪随机序列生成器的数学模型，该伪随机序列生成器的概率特性与“纯随机”序列接近。第二个是马尔可夫选择。对于替代假设，还发现了熵估计量的渐近概率分布。计算出已开发测试的能力估计值。

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