Book ChapterDOI
On the lattice test for inversive congruential pseudorandom numbers
Wun-Seng Chou,Harald Niederreiter +1 more
- pp 186-197
TLDR
For a given prime modulus p, the optimal behavior of inversive congruential generators occurs when they pass the (p - 2)-dimensional lattice test as discussed by the authors, where p is a Mersenne prime.Abstract:
An important tool for the analysis of inversive congruential pseudorandom numbers is the lattice test. For a given prime modulus p, the optimal behavior of inversive congruential generators occurs when they pass the (p - 2)-dimensional lattice test. We use the connection with permutation polynomials to establish several criteria for passing the (p - 2)-dimensional lattice test. We also prove that if p is a Mersenne prime, then there exists an inversive congruential generator which has period length p and passes the (p - 2)-dimensional lattice test.read more
Citations
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Book ChapterDOI
New Developments in Uniform Pseudorandom Number and Vector Generation
TL;DR: A survey of recent and new developments in the areas of uniform pseudorandom number and uniform Pseudo-Pseudorandom vector generation is presented.
Book ChapterDOI
A survey of quadratic and inversive congruential pseudorandom numbers
TL;DR: A review of nonlinear methods for the generation of uniform pseudorandom numbers in the unit interval can be found in this paper, where the emphasis is on results of the theoretical analysis of quadratic congruential and (recursive) inversive generators, which are scattered over a fairly large number of articles.
Journal ArticleDOI
Lattice Structure and Linear Complexity of Nonlinear Pseudorandom Numbers
TL;DR: It is shown that a q-periodic sequence over the finite field Fq passes an extended version of Marsaglia's lattice test for high dimensions if and only if its linear complexity is large.
References
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Book
Random number generation and quasi-Monte Carlo methods
TL;DR: This chapter discusses Monte Carlo methods and Quasi-Monte Carlo methods for optimization, which are used for numerical integration, and their applications in random numbers and pseudorandom numbers.
Journal ArticleDOI
A non-linear congruential pseudo random number generator
Jürgen Eichenauer,Jürgen Lehn +1 more
TL;DR: A theorem on the period length of sequences produced by this type of generators is proved and it is shown that good results are obtained if a non-linear congruential generator of about the same period length is applied.
Journal ArticleDOI
Inversive congruential pseudorandom numbers : a tutorial
TL;DR: In this paper, the authors dealt exclusively with the problem of pseudorandom number generation in the interval [0, 1] and showed that for a large positive integer m and integers a, b, yo a linear congruential sequence (y, n),n-o of nonnegative integers less than m is defined by
Book
Finite Fields, Coding Theory, and Advances in Communications and Computing
TL;DR: The refereed proceedings of the First International Conference on Finite Fields, Coding Theory, and Advances in Communications and Computing aim to encourage interaction between the theoretical aspects of finite fields and applications in many areas including information theory.