Analysis and design of stream ciphers
Analysis and design of stream ciphers
Correlation properties of combiners with memory in stream ciphers
Journal of Cryptology - Eurocrypt '90
On the lattice structure of certain linear congruential sequences related to AWC/SWB generators
Mathematics of Computation
Algebraic feedback shift registers
Theoretical Computer Science - Special issue: cryptography
A New Class of Stream Ciphers Combining LFSR and FCSR Architectures
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
Register Synthesis for Algebraic Feedback Shift Registers Based on Non-Primes
Designs, Codes and Cryptography
Distributional properties of d-FCSR sequences
Journal of Complexity - Special issue on coding and cryptography
On Decimations of $\ell$-Sequences
SIAM Journal on Discrete Mathematics
Arithmetic crosscorrelations of feedback with carry shift register sequences
IEEE Transactions on Information Theory
Fibonacci and Galois representations of feedback-with-carry shift registers
IEEE Transactions on Information Theory
Feedback with carry shift registers synthesis with the Euclidean algorithm
IEEE Transactions on Information Theory
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
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Feedback with carry shift registers (FCSRs) are arithmetic analogs of linear feedback shift registers (LFSRs). In this paper we survey some of the basic properties of FCSRs. For comparison, we first review some basic facts about LFSRs. We then define FCSRs and discuss their relation to the N-adic numbers. This leads to the analysis of periodicity of FCSR sequences, their exponential representation, and a description of maximal period FCSR sequences. We also discuss an arithmetic analog of cross-correlations, the FCSR register synthesis problem, and how FCSRs can be efficiently implemented in parallel architecture.