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

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3 Test Statistic and Reference Distribution χ2(obs): A measure of how well the observed number of occurrences of fixed length LFSRs matches the expected number of occurrences under an assumption of randomness. The reference distribution for the test statistic is the χ2 distribution. 4 Test Description (1) Partition the n-bit sequence into N independent blocks of M bits, where n = MN. (2) Using the Berlekamp-Massey algorithm5, determine the linear complexity Li of each of the N blocks (i = 1,…,N).

Xk + . + Xn For the example in this section, S1 = -1 S2 = 0 S3 = 1 S4 = 0 S5 = 1 S6 = 2 S7 = 1 S8 = 2 S9 = 1 S10 = 2 The set S = {-1, 0, 1, 0, 1, 2, 1, 2, 1, 2}. (3) Form a new sequence S' by attaching zeros before and after the set S. That is, S' = 0, s1, s2, … , sn, 0. 2-38 A STATISTICAL TEST SUITE FOR RANDOM AND PSEUDORANDOM NUMBER GENERATORS FOR CRYPTOGRAPHIC APPLICATIONS For the example, S' = 0, -1, 0, 1, 0, 1, 2, 1, 2, 1, 2, 0. The resulting random walk is shown below. Example Random Walk (S') (4) For each of the eighteen non-zero states of x, compute ξ(x) = the total number of times that state x occurred across all J cycles.

5374383 # ! 767189. Note ! 2 1 . 338 % " For the example in this section, P-value = erfc $$ that the expected value and variance for L = 2 are not provided in the above table, since a block of length two is not recommended for testing. ” 2-22 A STATISTICAL TEST SUITE FOR RANDOM AND PSEUDORANDOM NUMBER GENERATORS FOR CRYPTOGRAPHIC APPLICATIONS example. The value for the expected value and variance for the case where L = 2, although not shown in the above table, were taken from the indicated reference3.

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