Matrix parametrized shift registers

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 car...

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Bibliographic Details
Published in:Cryptography and communications 2018-03, Vol.10 (2), p.369-382
Main Author: Klapper, Andrew
Format: Article
Language:English
Subjects:
Algebra
Circuits
Coding and Information Theory
Communications Engineering
Computer Science
Cryptography
Data Structures and Information Theory
Feedback
Generators
Information and Communication
Linear feedback shift registers
Mathematics of Computing
Matrices (mathematics)
Networks
Periodic variations
Power series
Pseudorandom sequences
Registers
Shift registers
Special Issue on Sequences and Their Applications
Citations: Items that this one cites
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Summary: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 ∈ 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.
ISSN:1936-2447
1936-2455
DOI:10.1007/s12095-017-0226-9