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

In this paper, we describe a solution to the register synthesis problem for a class of sequence generators known as Algebraic Feedback Shift Registers. These registers are based on the algebra of -adic numbers, where is an element in a ring R, and produce sequences of elements in R/(). We give several cases where the register synthesis problem can be solved by an efficient algorithm. Consequently, any keystreams over R/() 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. Key words: Feedback shift register, pseudorandom generator, stream cipher, register synthesis, N-adic numbers.

• Type: Conference
• Year: 2004
• Where: DCC
• Authors: Andrew Klapper, Jinzhong Xu
• Keywords: Algebraic Feedback Shift, Computer Graphics, DCC 2004, Feedback Shift Registers, Register Synthesis Problem