Some Notes on Pseudorandom Binary Sequences Derived from Fermat-Euler Quotients

Zhifan YE  Pinhui KE  Shengyuan ZHANG  Zuling CHANG  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E98-A   No.10   pp.2199-2202
Publication Date: 2015/10/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E98.A.2199
Type of Manuscript: LETTER
Category: Cryptography and Information Security
Keyword: 
binary sequence,  linear complexity,  Fermat quotients,  Euler quotients,  balance,  

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Summary: 
For an odd prime p and a positive integer r, new classes of binary sequences with period pr+1 are proposed from Euler quotients in this letter, which include several known classes of binary sequences derived from Fermat quotients and Euler quotients as special cases. The advantage of the new constructions is that they allow one to choose their support sets freely. Furthermore, with some constrains on the support set, the new sequences are proved to possess large linear complexities under the assumption of 2p-1 ≢ 1 mod p2.