A universal statistical test for random bit generators
Journal of Cryptology
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
“Book Stack” as a New Statistical Test for Random Numbers
Problems of Information Transmission
A New Type of Attacks on Block Ciphers
Problems of Information Transmission
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The main problem considered consists in testing the hypothesis H0 that letters of an alphabet A = {a1, a2, …, ak} are generated with equal probabilities 1/k against the alternative complex hypothesis H1, the negation of H0. In many applications, in particular, those connected with cryptography, k is large, but possible deviations from the uniform distribution are small. Therefore, application of Pearson's χ2 test, which is one of the most wide-spread and efficient tests, requires samples of a very large size, certainly exceeding k. We propose a so-called adaptive χ2 test, whose power can be considerably higher than that of the traditional method in the case described. This conclusion is based on the theoretical analysis of the proposed criterion for some classes of alternatives as well as on experimental results related to discriminating between enciphered Russian texts and random sequences.