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Windmill generators a generalization and an observation of how many there are

Smeets, B. J.M. LU orcid and Chambers, W. G. (1988) 6th European Workshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1988 In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 330 LNCS. p.325-330
Abstract

The windmill technique has several practical advantageous over other techniques for high-speed generation or blockwise generation of pn-sequences. In this paper we generalize previous results by showing that if f(t)=α(t v) − β(t −v)t L is the minimal polynomial of a pn-sequence, then the sequence can be generated by a windmill generator. For L = 1,..127, and ν = 4, 8, 16 such that L ≡ ±3 mod 8 no irreducible polynomials f(t) were found. When L ≡ ±1 mod 8 the number of primitive f(t)’s was found to be approximately twice the expected number.

Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
Advances in Cryptology — EUROCRYPT 1988 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings
series title
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
editor
Gunther, Christoph G.
volume
330 LNCS
pages
6 pages
publisher
Springer
conference name
6th European Workshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1988
conference location
Davos, Switzerland
conference dates
1988-05-25 - 1988-05-27
external identifiers
  • scopus:84859784547
ISSN
0302-9743
1611-3349
ISBN
9783540502517
DOI
10.1007/3-540-45961-8_30
language
English
LU publication?
yes
additional info
Funding Information: Part of this work was supported by the National Swedish Board for Technical Development under grant 863759 at the University of Lund. Publisher Copyright: © 1988, Springer-Verlag Berlin Heidelberg.
id
9668b019-6461-4490-8c8f-c7b7e55c8e20
date added to LUP
2021-11-05 02:28:55
date last changed
2024-01-05 19:58:28
@inproceedings{9668b019-6461-4490-8c8f-c7b7e55c8e20,
  abstract     = {{<p>The windmill technique has several practical advantageous over other techniques for high-speed generation or blockwise generation of pn-sequences. In this paper we generalize previous results by showing that if f(t)=α(t <sup>v</sup>) − β(t <sup>−v</sup>)t <sup>L</sup> is the minimal polynomial of a pn-sequence, then the sequence can be generated by a windmill generator. For L = 1,..127, and ν = 4, 8, 16 such that L ≡ ±3 mod 8 no irreducible polynomials f(t) were found. When L ≡ ±1 mod 8 the number of primitive f(t)’s was found to be approximately twice the expected number.</p>}},
  author       = {{Smeets, B. J.M. and Chambers, W. G.}},
  booktitle    = {{Advances in Cryptology — EUROCRYPT 1988 - Workshop on the Theory and Application of Cryptographic Techniques,  Proceedings}},
  editor       = {{Gunther, Christoph G.}},
  isbn         = {{9783540502517}},
  issn         = {{0302-9743}},
  language     = {{eng}},
  pages        = {{325--330}},
  publisher    = {{Springer}},
  series       = {{Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)}},
  title        = {{Windmill generators a generalization and an observation of how many there are}},
  url          = {{http://dx.doi.org/10.1007/3-540-45961-8_30}},
  doi          = {{10.1007/3-540-45961-8_30}},
  volume       = {{330 LNCS}},
  year         = {{1988}},
}