On the Lattice Structure of Pseudorandom Numbers Generated over Arbitrary Finite Fields

被引：0

作者：

Harald Niederreiter

Arne Winterhof

机构：

[1] Department of Mathematics,

[2] National University of Singapore,undefined

[3] 2 Science Drive 2,undefined

[4] Singapore 117543,undefined

[5] Republic of Singapore (e-mail: nied@math.nus.edu.sg),undefined

[6] Institute of Discrete Mathematics,undefined

[7] Austrian Academy of Sciences,undefined

[8] Sonnenfelsgasse 19,undefined

[9] 1010 Vienna,undefined

[10] Austria (e-mail: arne.winterhof@oeaw.ac.at),undefined

来源：

Applicable Algebra in Engineering, Communication and Computing | 2001年 / 12卷

关键词：

Keywords: Pseudorandom number generator, Nonlinear method, Marsaglia's lattice test.;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Marsaglia's lattice test for congruential pseudorandom number generators modulo a prime is extended to a test for generators over arbitrary finite fields. A congruential generator η0,η1,…, generated by ηn=g(n), n = 0, 1,…, passes Marsaglia's s-dimensional lattice test if and only if s≤ deg(g). It is investigated how far this conditin holds true for polynomials over arbitrary finite fields Fq, particularly for polynomials of the form gd(x)=α(x+β)d+γ, α, β, γ∈Fq, α≠ 0, 1 ≤d≤q− 1.

引用

页码：265 / 272

页数：7