Families of sequences with good family complexity and cross-correlation measure

Autor:	Doğan, Kenan, Şahin, Murat, Yayla, Oğuz
Rok vydání:	2020
Předmět:	Computer Science - Information Theory Computer Science - Cryptography and Security Mathematics - Number Theory 11K45 94A55 94A60
Druh dokumentu:	Working Paper
Popis:	In this paper we study pseudorandomness of a family of sequences in terms of two measures, the family complexity ($f$-complexity) and the cross-correlation measure of order $\ell$. We consider sequences not only on binary alphabet but also on $k$-symbols ($k$-ary) alphabet. We first generalize some known methods on construction of the family of binary pseudorandom sequences. We prove a bound on the $f$-complexity of a large family of binary sequences of Legendre-symbols of certain irreducible polynomials. We show that this family as well as its dual family have both a large family complexity and a small cross-correlation measure up to a rather large order. Next, we present another family of binary sequences having high $f$-complexity and low cross-correlation measure. Then we extend the results to the family of sequences on $k$-symbols alphabet. Comment: 15 pages. Comments are welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2004.13938 Zobrazit plný text záznamu View this record from Arxiv