Algorithmic number theory
Finite fields
Multiplicative Character Sums of Recurring Sequences with Rédei Functions
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Finite Fields: Theory and Computation The Meeting Point of Number Theory, Computer Science, Coding Theory and Cryptography
On the linear and nonlinear complexity profile of nonlinear pseudorandom number generators
IEEE Transactions on Information Theory
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
Recent results on recursive nonlinear pseudorandom number generators
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
Multivariate permutation polynomial systems and nonlinear pseudorandom number generators
Finite Fields and Their Applications
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We estimate character sums with inversive and nonlinear recurring sequences `on average' over all initial values and obtain much stronger bounds than known for `individual' sequences. As a consequence, we present results 'on average' about the distribution of power residues and primitive elements in such sequences.On the one hand our bounds can be regarded as results on the pseudorandomness of inversive and nonlinear recurring sequences. On the other hand they shall provide a further step to efficient deterministic algorithms for finding non-powers and primitive elements in a finite field.