01046193

j

01046193 Klapper, Andrew Goresky, Mark Feedback shift registers, 2-adic span, and combiners with memory. J. Cryptology 10, No.2, 111-147 (1997). 1997 Springer-Verlag, New York, NY EN binary sequence combiner with memory cryptanalysis 2-adic numbers feedback shift registers arithmetic codes

doi:10.1007/s001459900024

Summary: Feedback shift registers with carry operation (FCSRs) are described, implemented, and analyzed with respect to memory requirements, initial loading, period, and distributional properties of their output sequences. Many parallels with the theory of linear feedback shift registers (LFSRs) are presented, including a synthesis algorithm (analogous to the Berlekamp-Massey algorithm for LFSRs) which, for any pseudo-random sequence, constructs the smallest FCSR which will generate the sequence. These techniques are used to attack the summation cipher. This analysis gives a unified approach to the study of pseudorandom sequences, arithmetic codes, combiners with memory, and the Marsaglia-Zaman random numer generator. Possible variations on the FCSR architecture are indicated at the end.