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Extra info for A statistical test suite for random and pseudorandom number generators for cryptographic applications (SuDoc C 13.10:800-22)

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Additional input used by the function, but supplied by the testing code: ε The sequence of bits as generated by the RNG or PRNG being tested; this exists as a global structure at the time of the function call; ε = ε1, ε2, … , εn. 3 Test Statistic and Reference Distribution ∇ψ2m(obs) and∇ 2ψ2m(obs): A measure of how well the observed frequencies of m-bit patterns match the expected frequencies of the m-bit patterns. 2-26 A STATISTICAL TEST SUITE FOR RANDOM AND PSEUDORANDOM NUMBER GENERATORS FOR CRYPTOGRAPHIC APPLICATIONS The reference distribution for the test statistic is the χ2 distribution.

324652 )2 (1 ! 182617 )2 ( obs ) = + ( 1 ! 142670 (1 ! 106645 )2 + (1 ! 077147 )2 + (1 ! 167729. 166269 2 (5) & 5 ' 2 ( obs ) # !. $2, ! 167729 # , ! 274932. 01, then conclude that the sequence is non-random. Otherwise, conclude that the sequence is random. 274932), the conclusion is that the sequence is random. 01) and 4) a conclusion of non-randomness would have resulted. , n ≥ 106). Various values of m may be selected, but for the time being, NIST recommends m = 9 or m = 10. If other values are desired, please choose these values as follows: • n ≥ MN.

The reference distribution for the test statistic is the χ2 distribution. 4 (1) Test Description Partition the sequence into N independent blocks of length M. For example, if ε = 10100100101110010110, then n = 20. If N = 2 and M = 10, then the two blocks would be 1010010010 and 1110010110. (2) Let Wj (j = 1, …, N) be the number of times that B (the template) occurs within the block j. Note that j = 1,…,N. The search for matches proceeds by creating an m-bit window on the sequence, comparing the bits within that window against the template.

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