Reconstructing truncated integer variables satisfying linear congruences
SIAM Journal on Computing - Special issue on cryptography
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Finite fields
On the distribution of inversive congruential pseudorandom numbers in parts of the period
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
Designs, Codes and Cryptography
Dynamical systems generated by rational functions
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Pseudorandom vector sequences derived from triangular polynomial systems with constant multipliers
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
On stern's attack against secret truncated linear congruential generators
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
Deciphering a linear congruential encryption
IEEE Transactions on Information Theory
Attacking the Pollard Generator
IEEE Transactions on Information Theory
Multivariate permutation polynomial systems and nonlinear pseudorandom number generators
Finite Fields and Their Applications
Exponential sums for nonlinear recurring sequences
Finite Fields and Their Applications
On the Distribution and Lattice Structure of Nonlinear Congruential 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 of maximal period generated by triangular polynomial dynamical systems
Designs, Codes and Cryptography
On the power generator and its multivariate analogue
Journal of Complexity
Predicting masked linear pseudorandom number generators over finite fields
Designs, Codes and Cryptography
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We bound exponential sums along the orbits of essentially arbitrary multivariate polynomial dynamical systems, provided that the orbits are long enough. We use these bounds to derive nontrivial estimates on the discrepancy of pseudorandom vectors generated by such polynomial systems. We generalize several previous results and in particular suggest a new approach that eliminates the need to control the degree growth of the iterations of these polynomial systems, which has been an obstacle in all previous approaches.