Register Synthesis for Algebraic Feedback Shift Registers Based on Non-Primes

Authors:
Andrew Klapper;Jinzhong Xu
Affiliations:
Department of Computer Science, 779A Anderson Hall, University of Kentucky, Lexington, KY 40506-0046 klapper@cs.uky.edu;The American Board of Family Practice, 2224 Young Dr., Lexington, KY 40505 jxu@assesstech.com
Venue:
Designs, Codes and Cryptography
Year:
2004

Citing 8
Cited 8

Analysis and design of stream ciphers

Analysis and design of stream ciphers
Self-dual codes over the integers modulo 4

Journal of Combinatorial Theory Series A
Algebraic feedback shift registers

Theoretical Computer Science - Special issue: cryptography
Shift Register Sequences

Shift Register Sequences
2-Adic Shift Registers

Fast Software Encryption, Cambridge Security Workshop
Improved binary codes and sequence families from Z4-linear codes

IEEE Transactions on Information Theory
Type II codes over Z4

IEEE Transactions on Information Theory
On the non Z4-linearity of certain good binary codes

IEEE Transactions on Information Theory

Design and Properties of a New Pseudorandom Generator Based on a Filtered FCSR Automaton

IEEE Transactions on Computers
Expected Π-Adic Security Measures of Sequences

SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
The asymptotic behavior of π-adic complexity with π2= -2

SSC'07 Proceedings of the 2007 international conference on Sequences, subsequences, and consequences
Expected π-adic security measures of sequences

IEEE Transactions on Information Theory
A survey of feedback with carry shift registers

SETA'04 Proceedings of the Third international conference on Sequences and Their Applications
Algebraic feedback shift registers based on function fields

SETA'04 Proceedings of the Third international conference on Sequences and Their Applications
Periodic sequences with maximal N-adic complexity and large k-error N-adic complexity over Z/(N)

Journal of Complexity
Computing the k-error N-adic complexity of a sequence of period pn

SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications

Quantified Score

Hi-index	0.06

Visualization

Abstract

In this paper, we describe a solution to the register synthesis problem for a class of sequence generators known as algebraic feedback shift registers (AFSRs). These registers are based on the algebra of π-adic numbers, where π is an element in a ring R, and produce sequences of elements in R/(π). We give several cases where the register synthesis problem can be solved by an efficient algorithm. Consequently, any keystreams over R/(π) used in stream ciphers must be unable to be generated by a small register in these classes. This paper extends the analyses of feedback with carry shift registers and algebraic feedback shift registers by Goresky, Klapper, and Xu.