2-adic 1-Lipschitz maps-based nonlinear pseudorandom generators of arbitrary rank having the longest period. (English) Zbl 1525.11084
Summary: Linear congruential method was one of the first one proposed to generate pseudorandom numbers. However, due to drawbacks arising from linearity nonlinear methods of generating pseudorandom numbers were proposed; however, these methods were mostly nonlinear recurrences of rank 1, i.e., iterations of a univariate map. In this paper we propose a generator which is a recurrence of order \(k\) based on 2-adic 1-Lipschitz bijective functions and find conditions under which generator produces sequences with the period of \(k2^t\) of uniformly distributed numbers modulo \(2^t\).
MSC:
| 11K45 | Pseudo-random numbers; Monte Carlo methods |
| 11S82 | Non-Archimedean dynamical systems |
| 37A44 | Relations between ergodic theory and number theory |
References:
| [1] | Stǎnicǎ, P.; Riera, C.; Roy, T.; Sarkar, S., A hybrid inversive congruential pseudorandom number generator with high period, Europ. J. Pure Appl. Math., 14, 1, 1-18 (2021) · doi:10.29020/nybg.ejpam.v14i1.3852 |
| [2] | Anashin, V.; Khrennikov, A., Applied Algebraic Dynamics (2009), Berlin, New York: De Gruyter, Berlin, New York · Zbl 1184.37002 · doi:10.1515/9783110203011 |
| [3] | Eichenauer-Herrmann, J.; Grothe, H., A new inversive congruential pseudorandom number generator with power of two modulus, ACM Trans. Model. Comp. Simul. (TOMACS), 2, 1, 1-11 (1992) · Zbl 0844.11051 · doi:10.1145/132277.132278 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
