Applied Mathematicsematics

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Additional 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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Form the set S = {Si}. S1 = X1 S2 = X1 + X2 S3 = X1 + X2 + X3 . Sk = X1 + X2 + X3 + … + X k . Sn = X1 + X2 + X3 + … + 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. For the example in this section, S' = 0, -1, 0, 1, 0, 1, 2, 1, 2, 1, 2, 0. The resulting random walk is shown below.

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. • N should be chosen so that N • (min πi) > 5.

5776 • 2 ) (2 ! 1 ! 1 ! 2888 • 2 Compute P " value = e " ! 596953. Since there are 3 classes in the example, the P-value for the 2 & ' (obs ) # !! 741948. 01, then conclude that the sequence is non-random. Otherwise, conclude that the sequence is random. 741948), the conclusion is that the sequence is random. Note that large values of ! 2 ( obs ) (and hence, small P-values) would have indicated a deviation of the rank distribution from that corresponding to a random sequence. 7 Input Size Recommendation The probabilities for M = Q = 32 have been calculated and inserted into the test code.

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