TY - JOUR
AU - Riera, Constanza
AU - Roy, Tapabrata
AU - Sarkar, Santanu
AU - Stanica, Pantelimon
PY - 2021/01/31
Y2 - 2023/12/06
TI - A Hybrid Inversive Congruential Pseudorandom Number Generator with High Period
JF - European Journal of Pure and Applied Mathematics
JA - Eur. J. Pure Appl. Math.
VL - 14
IS - 1
SE -
DO - 10.29020/nybg.ejpam.v14i1.3852
UR - https://ejpam.com/index.php/ejpam/article/view/3852
SP - 1-18
AB - <p class="p1">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<span class="Apple-converted-space">Â </span>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<span class="Apple-converted-space">Â </span>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<span class="Apple-converted-space">Â </span>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.</p>
ER -