Table of Contents
Advances in Artificial Intelligence
Volume 2011, Article ID 464971, 10 pages
http://dx.doi.org/10.1155/2011/464971
Research Article

Generalization of the Self-Shrinking Generator in the Galois Field G F ( 𝑝 𝑛 )

1Computer Systems Department, Faculty of Computer Systems and Control, Technical University of Sofia, 8 Kliment Ohridski Street, Sofia 1000, Bulgaria
2Communication and Computer Technique Department, National Military University “Vasil Levski”, 1a Karel Shkorpil Street, Shumen 9701, Bulgaria
3Computer System and Technology Department, University of Shumen “Bishop Konstantin Preslavsky”, 115 Universitetska Street, Shumen 9712, Bulgaria

Received 13 December 2010; Revised 5 February 2011; Accepted 24 February 2011

Academic Editor: Farouk Yalaoui

Copyright © 2011 Antoniya Todorova Tasheva et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The proposed by Meier and Staffelbach Self-Shrinking Generator (SSG) which has efficient hardware implementation only with a single Linear Feedback Shift Register is suitable for low-cost and fast stream cipher applications. In this paper we generalize the idea of the SSG for arbitrary Galois Field G F ( 𝑝 𝑛 ) . The proposed variant of the SSG is called the 𝑝 -ary Generalized Self-Shrinking Generator (pGSSG). We suggest a method for transformation of a non-binary self-shrunken pGSSG sequence into balanced binary sequence. We prove that the keystreams of the pGSSG have large period and good statistical properties. The analysis of the experimental results shows that the pGSSG sequences have good randomness properties. We examine the complexity of exhaustive search and entropy attacks of the pGSSG. We show that the pGSSG is more secure than SSG and Modified SSG against these attacks. We prove that the complexity of the used pGSSG attacks increases with increasing the prime 𝑝 . Previously mentioned properties give the reason to say that the pGSSG satisfy the basic security requirements for a stream chipper and can be useful as a part of modern stream ciphers.