Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Finite fields
Handbook of Applied Cryptography
Handbook of Applied Cryptography
On the Distribution of Nonlinear Recursive Congruential Pseudorandom Numbers of Higher Orders
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Iterations of Multivariate Polynomials and Discrepancy of Pseudorandom Numbers
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Multivariate permutation polynomial systems and nonlinear pseudorandom number generators
Finite Fields and Their Applications
On the Average Distribution of Inversive Pseudorandom Numbers
Finite Fields and Their Applications
Recent results on recursive nonlinear pseudorandom number generators
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
Pseudorandom vector sequences of maximal period generated by triangular polynomial dynamical systems
Designs, Codes and Cryptography
On the power generator and its multivariate analogue
Journal of Complexity
On pseudorandom numbers from multivariate polynomial systems
Finite Fields and Their Applications
Predicting masked linear pseudorandom number generators over finite fields
Designs, Codes and Cryptography
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In this paper we study a new class of dynamical systems generated by iterations of a class of multivariate permutation polynomial systems. Using the same techniques studied previously for other generators, we bound exponential sums along the orbits of these dynamical systems and show that they admit stronger estimates than in the general case and thus can be of use for pseudorandom number generation. We also prove a nontrivial bound "on average" over all initial values v ε Fmp on the discrepancy for pseudorandom vectors generated by these iterations.