Adaptive Chi-Square Test and its Application to Some Cryptographic Problems

We address the problem of testing the hypothesis that the letters from some alphabet are distributed uniformly (i.e. ) against the alternative hypothesis that the true distribution is not uniform, in case is large. (It is typical for random number testing and some cryptographic problems where = 2 ~ 2 and more.) In such a case it is difficult to use the chi-square test because the sample size must be greater than .We suggest the which can be successfully applied for testing some kinds of even in case when the sample size is much less than . This statement is confirmed theoretically and experimentally