The problem of constructing the most powerful test for random number generators (RNGs) is considered, where the generators are modelled by stationary ergodic processes. At present, RNGs are widely used in data protection, modelling and simulation systems, computer games, and in many other areas where the generated random numbers should look like binary numbers of a Bernoulli equiprobable sequence. Another problem considered is that of constructing effective statistical tests for random number generators (RNG). Currently, effectiveness of statistical tests for RNGs is mainly estimated based on experiments with various RNGs. We find an asymptotic estimate for the $p$-value of an optimal test in the case where the alternative hypothesis is a known stationary ergodic source, and then describe a family of tests each of which has the same asymptotic estimate of the $p$-value for any (unknown) stationary ergodic source. This model appears to be acceptable for binary sequences generated by physical devices that are used in cryptographic data protection systems.

考虑为随机数生成器 (RNG) 构建最强大的测试的问题，其中生成器通过平稳遍历过程建模。目前，RNG 广泛用于数据保护、建模和模拟系统、计算机游戏以及许多其他领域，其中生成的随机数应该看起来像伯努利等概率序列的二进制数。另一个考虑的问题是为随机数生成器 (RNG) 构建有效的统计测试。目前，RNG 统计检验的有效性主要是基于各种 RNG 的实验来估计的。我们找到了一个渐近估计$磷$- 在替代假设是已知平稳遍历源的情况下的最优检验值，然后描述一系列检验，每个检验都具有相同的渐近估计 $磷$- 任何（未知）平稳遍历源的值。对于由用于加密数据保护系统的物理设备生成的二进制序列，该模型似乎是可以接受的。