Introduction to finite fields and their applications
Introduction to finite fields and their applications
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
On the distribution of inversive congruential pseudorandom numbers in parts of the period
Mathematics of Computation
On the distribution of the power generation
Mathematics of Computation
On the Linear Complexity of the Power Generator
Designs, Codes and 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
Applicable Algebra in Engineering, Communication and Computing
Designs, Codes and Cryptography
On the counting function of the lattice profile of periodic sequences
Journal of Complexity
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Multiplicative Character Sums of Recurring Sequences with Rédei Functions
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
On the Distribution of Nonlinear Congruential Pseudorandom Numbers of Higher Orders in Residue Rings
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Dynamical systems generated by rational functions
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
On the structure of inversive pseudorandom number generators
AAECC'07 Proceedings of the 17th 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
Structure of pseudorandom numbers derived from fermat quotients
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
On the linear complexity profile of the power generator
IEEE Transactions on Information Theory
On the linear and nonlinear complexity profile of nonlinear pseudorandom number generators
IEEE Transactions on Information Theory
Exponential sums with Dickson polynomials
Finite Fields and Their Applications
Finite Fields and Their Applications
Multivariate permutation polynomial systems and nonlinear pseudorandom number generators
Finite Fields and Their Applications
On pseudorandom numbers from multivariate polynomial systems
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
Counting functions and expected values for the lattice profile at n
Finite Fields and Their Applications
The Period Lengths of Inversive Pseudorandom Vector Generations
Finite Fields and Their Applications
On the Distribution and Lattice Structure of Nonlinear Congruential Pseudorandom Numbers
Finite Fields and Their Applications
On the Average Distribution of Inversive Pseudorandom Numbers
Finite Fields and Their Applications
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
The Carlitz rank of permutations of finite fields: A survey
Journal of Symbolic Computation
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This survey article collects recent results on recursive nonlinear pseudorandom number generators and sketches some important proof techniques. We mention upper bounds on additive character sums which imply uniform distribution results. Moreover, we present lower bounds on the linear complexity profile and closely related lattice tests and thus results on the suitability in cryptography. Finally, we give bounds on multiplicative character sums from which one can derive results on the distribution of powers and primitive elements.