On the lattice structure of pseudorandom numbers generated over arbitrary finite fields
H Niederreiter, A Winterhof - Applicable Algebra in Engineering …, 2001 - Springer
H Niederreiter, A Winterhof
Applicable Algebra in Engineering, Communication and Computing, 2001•SpringerMarsaglia'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 η 0, η
1,…, generated by η n= 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 F q, particularly for polynomials of the form gd (x)= α (x+ β) d+ γ, α, β, γ∈
F q, α≠ 0, 1≤ d≤ q− 1.
extended to a test for generators over arbitrary finite fields. A congruential generator η 0, η
1,…, generated by η n= 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 F q, particularly for polynomials of the form gd (x)= α (x+ β) d+ γ, α, β, γ∈
F q, α≠ 0, 1≤ d≤ q− 1.
Abstract
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 η n =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 F q , particularly for polynomials of the form g d (x)=α(x+β) d +γ, α, β, γ∈F q , α≠ 0, 1 ≤d≤q− 1.
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