A Hybrid Inversive Congruential Pseudorandom Number Generator with High Period


  • Constanza Riera
  • Tapabrata Roy
  • Santanu Sarkar
  • Pantelimon Stanica Naval Postgraduate School Applied Mathematics Department




Pseudorandom numbers, congruences, period, lattice test


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.

Author Biography

Pantelimon Stanica, Naval Postgraduate School Applied Mathematics Department

Professor of Applied Mathematics




How to Cite

Riera, C., Roy, T., Sarkar, S., & Stanica, P. (2021). A Hybrid Inversive Congruential Pseudorandom Number Generator with High Period. European Journal of Pure and Applied Mathematics, 14(1), 1–18. https://doi.org/10.29020/nybg.ejpam.v14i1.3852



Nonlinear Analysis