Abstract
High speed pseudorandom sequence generators have played roles in an array of applications in communications, cryptography, and computing. At the heart of many of these generators are shift registers of various types. Researchers have studied linear feedback shift registers (LFSRs), feedback with carry shift registers (FCSRs), and various generalizations such as ring FCSRS and algebraic feedback shift registers. The analysis of these sequence generators typically proceeds by defining an algebraic structure on the set of infinite output sequences, based on a choice of uniformizing parameter (e.g., power series for LFSRs, N-adic numbers for FCSRs). In this paper we introduce a new generalization of FCSRs in which the uniformizing parameter \(N\in \mathbb {Z}\) is replaced by a square matrix, T, resulting in what we call T-generators. We describe an algebraic structure, the T-adic numbers, and use it to study the periodicity of T-generators.
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Notes
“ ℓ”stands for “long”.
Here “ ℓ” stands for “long”.
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This material is based upon work supported by the National Science Foundation under Grant No. CNS-1420227. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.
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This article is part of the Topical Collection on Sequences and Their Applications.
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Klapper, A. Matrix parametrized shift registers. Cryptogr. Commun. 10, 369–382 (2018). https://doi.org/10.1007/s12095-017-0226-9
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DOI: https://doi.org/10.1007/s12095-017-0226-9