A statistical test suite for random and pseudorandom number by U.S. National Archives and Records Administration

By U.S. National Archives and Records Administration

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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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The examination proceeded as follows: 5 Defined in The Handbook of Applied Cryptography; A. Menezes, P. Van Oorschot and S. Vanstone; CRC Press, 1997. 2-24 A STATISTICAL TEST SUITE FOR RANDOM AND PSEUDORANDOM NUMBER GENERATORS FOR CRYPTOGRAPHIC APPLICATIONS The first 4 bits and the resulting 5th bit Bits 2-5 and the resulting 6th bit Bits 3-6 and the resulting 7th bit Bits 4-7 and the resulting 8th bit Bits 5-8 and the resulting 9th bit Bits 6-9 and the resulting 10th bit Bits 7-10 and the resulting 11th bit Bits 8-11 and the resulting 12th bit Bits 9-12 and the resulting 13th bit Bit 1 1 1 0 1 0 1 1 1 1 Bit 2 1 0 1 0 1 1 1 1 0 Bit 3 0 1 0 1 1 1 1 0 0 Bit 4 1 0 1 1 1 1 0 0 0 Bit 5 0 1 1 1 1 0 0 0 1 For this block, the trial feedback algorithm works.

Defined in FIPS 186-2. 01, accept the sequence as random. 1 Test Purpose The focus of this test is the length of a linear feedback shift register (LFSR). The purpose of this test is to determine whether or not the sequence is complex enough to be considered random. Random sequences are characterized by longer LFSRs. An LFSR that is too short implies non-randomness. 2 Function Call LinearComplexity(M, n), where: M The length in bits of a block. n The length of the bit string. 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.

2) Compute the partial sums Si of successively larger subsequences, each starting with X1. 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.

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