Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Finite fields
On the distribution of the power generation
Mathematics of Computation
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
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Dynamical systems generated by rational functions
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Exponential sums with Dickson polynomials
Finite Fields and Their Applications
Exponential sums for nonlinear recurring sequences
Finite Fields and Their Applications
Exponential sums of nonlinear congruential pseudorandom number generators with Rédei functions
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
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
Pseudorandom vector sequences derived from triangular polynomial systems with constant multipliers
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
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 class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques studied previously for inversive generators, we bound exponential sums along the orbits of these dynamical systems and show that they admit much stronger estimates ''on average'' over all initial values v@?F"p^m^+^1 than in the general case and thus can be of use for pseudorandom number generation.