A Matrix Model for the Linear Feedback Shift Register

Abstract

In this report, a matrix model is used to discover some of the properties of the linear feedback shift register (LFSR) and to consider its application to security systems. First the hardware and operation of the LFSR is briefly discussed. Then a representation of the LFSR as a finite state device is used to obtain the matrix model for the LFSR. The matrix model is employed to derive a number of known results about the period of an LFSR as well as some new results concerning subperiods of an LFSR. Cryptographic applications are suggested by the randomness properties of the LFSR bit stream output. The matrix model provides a concise treatment of the cryptanalysis of the simple LFSR system. Some suggestions are made to improve the security of LFSR secrecy systems.

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Document Details

Document Type
Technical Report
Publication Date
Jul 06, 1989
Accession Number
ADA212351

Entities

People

  • W. P. Wardlaw

Organizations

  • United States Naval Research Laboratory

Tags

DTIC Thesaurus Topics

  • Biometric Security
  • Classification
  • Equations
  • Feedback
  • Identification
  • Identification Systems
  • Identities
  • Mathematics
  • Military Research
  • Notation
  • Permutations
  • Polynomials
  • Security
  • Sequences
  • Shift Registers
  • Vector Spaces

Fields of Study

  • Computer science
  • Mathematics

Readers

  • Computer Programming and Software Development.
  • Linear Algebra