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Bits remaining at the end of the sequence that do not form a complete L-bit block are discarded. The first Q blocks are used to initialize the test. The remaining K blocks are the test blocks (K = n/L - Q). 2-20 A STATISTICAL TEST SUITE FOR RANDOM AND PSEUDORANDOM NUMBER GENERATORS FOR CRYPTOGRAPHIC APPLICATIONS For example, if ε = 01011010011101010111, then n = 20. If L = 2 and Q = 4, then K = n/L Q = 20/2 - 4 = 6 . The initialization segment is 01011010; the test segment is 011101010111.

N ≥ 106). 01 for each of the eighteen states of x, accept the sequence as random. 2-40 A STATISTICAL TEST SUITE FOR RANDOM AND PSEUDORANDOM NUMBER GENERATORS FOR CRYPTOGRAPHIC APPLICATIONS 3. Technical Description of Tests This section contains the mathematical background for the tests in the NIST test suite. Each subsection corresponds to the appropriate subsection in Section 2. The relevant references for each subsection are provided at the end of that subsection. 1 Frequency (Monobits) Test The most basic test is that of the null hypothesis: in a sequence of independent identically distributed Bernoulli random variables (X's or ε's, where X = 2ε-1, and so Sn = X1 + … + Xn = 2(ε1 + … + εn) – n), the probability of ones is 1/2.

2) Determine the frequency of all possible overlapping m-bit blocks, all possible overlapping (m-1)bit blocks and all possible overlapping (m-2)-bit blocks. im ! 2 denote the frequency of the (m-2)-bit pattern i1…im-2. For the example in this section, when m = 3, then (m-1) = 2, and (m-2) = 1. The frequency of all 3-bit blocks is: v000 = 0, v001 = 1, v010 = 1, v011 = 2, v100 = 1, v101 = 2, v110 = 2, v111 = 0. The frequency of all possible (m-1)-bit blocks is: v00 = 1, v01 = 3, v10 = 3, v11 = 3.

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