The CRC Handbook of Finite Fields (hereafter referred to as the Handbook) is a reference
book for the theory and applications of finite fields. It is not intended to be an introductory …

The linear complexity of a sequence is not only a measure for the unpredictability and thus
suitability for cryptography but also of interest in information theory because of its close …

Since the introduction of the Kolmogorov complexity of binary sequences in the 1960s, there
have been significant advancements on the topic of complexity measures for randomness …

Chapter 4 PSEUDORANDOM SEQUENCES Page 1 Chapter 4 PSEUDORANDOM
SEQUENCES Alev Topuzoglu and Arne Winterhof 1. Introduction Sequences, which are …

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 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 …

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 …

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 …

The Nth linear complexity of a sequence is a measure of predictability. Any unpredictable
sequence must have large Nth linear complexity. However, in this paper we show that for q …

Expansion complexity and maximum order complexity are both finer measures of
pseudorandomness than the linear complexity which is the most prominent quality measure …