The serial test for a nonlinear pseudorandom number generator

Kato, Takashi; Wu, Li-Ming; Yanagihara, Niro

doi:10.1090/S0025-5718-96-00712-0

The serial test for a nonlinear pseudorandom number generator
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by Takashi Kato, Li-Ming Wu and Niro Yanagihara PDF

Math. Comp. 65 (1996), 761-769 Request permission

Abstract:

Let $M = 2^{w},$ and $G_{M} = \{1,3,...,M-1 \}.$ A sequence $\{y_{n} \}, y_{n} \in G_{M},$ is obtained by the formula $y_{n+1} \equiv a{\overline {y}_{n}} + b + cy_{n} \; \mathrm {mod} \; M.$ The sequence $\{x_{n} \}, x_{n}=y_{n}/M,$ is a sequence of pseudorandom numbers of the maximal period length $M/2$ if and only if $a+c \equiv 1$ (mod 4), $b \equiv 2$ (mod 4). In this note, the uniformity is investigated by the 2-dimensional serial test for the sequence. We follow closely the method of papers by Eichenauer-Herrmann and Niederreiter.

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