Multivariate Permutation Polynomial Systems and Nonlinear Pseudorandom\n Number Generators

2009/06/21 by Alina Ostafe, Ostafe, Alina · 1 citation
Computer Science · #11K45 #11T23 #Chaos-based Image/Signal Encryption #Coding theory and cryptography #Cryptography and Residue Arithmetic #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0906.3854

openalex publication_date 2009/06/21 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

In this paper we study a class of dynamical systems generated by iterations\nof multivariate permutation polynomial systems which lead to polynomial growth\nof the degrees of these iterations. Using these estimates and the same\ntechniques studied previously for inversive generators, we bound exponential\nsums along the orbits of these dynamical systems and show that they admit much\nstronger estimates on average over all initial values than in the general case\nand thus can be of use for pseudorandom number generation.\n

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• On the Dynamical System Generated by the Möbius Transformation at Smooth Times

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