Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
On the p-Divisibility of Fermat quotients
Mathematics of Computation
On the counting function of the lattice profile of periodic sequences
Journal of Complexity
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
Counting functions and expected values for the lattice profile at n
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
Boolean functions derived from Fermat quotients
Cryptography and Communications
Pseudorandomness and Dynamics of Fermat Quotients
SIAM Journal on Discrete Mathematics
Linear complexity of pseudorandom sequences generated by Fermat quotients and their generalizations
Information Processing Letters
Linear complexity of binary sequences derived from Euler quotients with prime-power modulus
Information Processing Letters
Linear complexity of binary sequences derived from polynomial quotients
SETA'12 Proceedings of the 7th international conference on Sequences and Their Applications
On the linear complexity of binary threshold sequences derived from Fermat quotients
Designs, Codes and Cryptography
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We study the distribution of s-dimensional points of Fermat quotients modulo p with arbitrary lags. If no lags coincide modulo p the same technique as in [21] works. However, there are some interesting twists in the other case. We prove a discrepancy bound which is unconditional for s = 2 and needs restrictions on the lags for s 2.We apply this bound to derive results on the pseudorandomness of the binary threshold sequence derived from Fermat quotients in terms of bounds on the well-distribution measure and the correlation measure of order 2, both introduced by Mauduit and Sárközy. We also prove a lower bound on its linear complexity profile. The proofs are based on bounds on exponential sums and earlier relations between discrepancy and both measures above shown by Mauduit, Niederreiter and Sárközy. Moreover, we analyze the lattice structure of Fermat quotients modulo p with arbitrary lags.