Periodicity and Distribution Properties of Combined FCSR Sequences
نویسندگان
چکیده
This is a study of some of the elementary statistical properties of the bitwise exclusive or of two maximum period feedback with carry shift register sequences. We obtain condition under which the resulting sequences has the maximum possible period, and we obtain bounds on the variation in the distribution of blocks of a fixed length. This may lead to improved design of stream ciphers using FCSRs. Keyword:s Feedback with carry shift register, pseudorandom sequence, stream cipher.
منابع مشابه
Periodicity, correlation, and distribution properties of d-FCSR sequences
A d-feedback-with-carry shift register (d-FCSR) is a finite state machine, similar to a linear feedback shift register, in which a small amount of memory and a delay (by d-clock cycles) is used in the feedback algorithm (see [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 man...
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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 representa...
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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, in which a small amount of memory and a delay (by d-clock cycles) is used in the feedback algorithm (see [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 man...
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