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.
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Klapper, A., Xu, J. Register Synthesis for Algebraic Feedback Shift Registers Based on Non-Primes. Designs, Codes and Cryptography 31, 227–250 (2004). https://doi.org/10.1023/B:DESI.0000015886.71135.e1
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DOI: https://doi.org/10.1023/B:DESI.0000015886.71135.e1