A simple unpredictable pseudo random number generator
SIAM Journal on Computing
Algebraic feedback shift registers
Theoretical Computer Science - Special issue: cryptography
Shift Register Sequences
Distributional properties of d-FCSR sequences
Journal of Complexity - Special issue on coding and cryptography
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
Distributional properties of d-FCSR sequences
Journal of Complexity - Special issue on coding and cryptography
Some Results on the Arithmetic Correlation of Sequences
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Expected Π-Adic Security Measures of Sequences
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Expected π-adic security measures of sequences
IEEE Transactions on Information Theory
SETA'10 Proceedings of the 6th 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
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A d-feedback-with-carry shift register (d-FCSR) is a finite state machine, similar to a linear feedback shift register (LFSR), in which a small amount of memory and a delay (by d-clock cycles) is used in the feedback algorithm (see Goresky and Klapper [4,5]). The output sequences of these simple devices may be described using arithmetic in a ramified extension field of the rational numbers. In this paper we show how many of these sequences may also be described using simple integer arithmetic, and consequently how to find such sequences with large periods. We also analyze the “arithmetic cross-correlation” between pairs of these sequences and show that it often vanishes identically.