Harald Niederreiter Arne Winterhof Page 1 Applied Number Theory Harald Niederreiter Arne
Winterhof Page 2 Applied Number Theory Page 3 Page 4 Harald Niederreiter • Arne Winterhof …

In this paper, two generic constructions of optimal frequency-hopping sequence (FHS) sets
employing d-form functions with difference-balanced property are presented. They …

This survey article collects recent results on recursive nonlinear pseudorandom number
generators and sketches some important proof techniques. We mention upper bounds on …

The correlation measure of order k is an important measure of pseudorandomness for binary
sequences. This measure tries to look for dependence between several shifted versions of a …

We prove a bound on sums of products of multiplicative characters of shifted Fermat
quotients modulo p. From this bound we derive results on the pseudorandomness of …

We extend the definition of binary threshold sequences from Fermat quotients to Euler
quotients modulo pr with odd prime p and r⩾ 1. Under the condition of 2p− 1≢ 1 (modp2) …

We improve lower bounds on the k th-order nonlinear complexity of pseudorandom
sequences over finite fields, including explicit inversive sequences and sequences obtained …

We give the trace representation of a family of binary sequences derived from Euler
quotients by determining the corresponding defining polynomials. The result extends an …

In the second half of the 1990s Christian Mauduit and András Sárközy [86] introduced a new
quantitative theory of pseudorandomness of binary sequences. Since then numerous …

We combine the concepts of the p-periodic Legendre sequence, the (q-1)-periodic
Sidelnikov sequence and the two-prime generator to introduce a new p (q-1)-periodic …