A Hybrid Inversive Congruential Pseudorandom Number Generator with High Period
TLDR
In this paper, a hybrid inversive congruential generator (HICG) based on a second order recurrence using the inversive modulo M, a power of 2, was proposed.Abstract:
Though generating a sequence of pseudorandom numbers by linear methods (Lehmer generator) displays acceptable behavior under some conditions of the parameters, it also has undesirable features, which makes the sequence unusable for various stochastic simulations. An extension which showed promise for such applications is a generator obtained by using a first-order recurrence based upon the inversive modulo a prime or a prime power, called inversive congruential generator (ICG). A lot of work has been dedicated to investigate the periods (under some conditions of the parameters), the lattice test passing, discrepancy and other statistical properties of such a generator. Here, we propose a new method, which we call hybrid inversive congruential generator (HICG), based upon a second order recurrence using the inversive modulo M, a power of 2. We investigate the period of this pseudorandom numbers generator (PRNG) and give necessary and sufficient conditions for our PRNG to have periods M (thereby doubling the period of the classical ICG) and M/2 (matching the one of the ICG). Moreover, we show that the lattice test complexity for a binary sequence associated to (a full period) HICG is precisely M/2.read more
Citations
More filters
Journal ArticleDOI
Process schemes of ethanol coupling to C4 olefins based on a genetic algorithm for back propagation neural network optimization
TL;DR: In this paper , a comprehensive evaluation system of an experimental scheme was constructed based on the Analytic Hierarchy Process/Entropy Weight Method-Technique for Order Preference by Similarity to Ideal Solution (AHP/EWM-TOPSIS) and Chemical production indicators.
References
More filters
Journal ArticleDOI
Further combinatorial identities deriving from the n th power of a 2 × 2 matrix
TL;DR: A formula for the nth power of a 2 × 2 matrix A (in terms of the entries in A) is used to derive various combinatorial identities and it is shown that if m and n are positive integers and s ∈ {0,1,2,..., ⌊(mn-1)/2⌋}, then
Journal ArticleDOI
On generalized inversive congruential pseudorandom numbers
TL;DR: The inversive congruential method with prime modulus for generating uniform pseudorandom numbers has several very promising properties, such as statistical independence properties as discussed by the authors, which is a generalization of composite moduli.
Journal ArticleDOI
Pseudorandom Bits From Points on Elliptic Curves
TL;DR: These bounds confirm several recent conjectures of Jao, Jetchev, and Venkatesan, related to extracting random bits from various sequences of points on the elliptic curves.