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

B. J.M. Smeets; W. G. Chambers

doi:10.1007/3-540-45961-8_30

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

B. J.M. Smeets, W. G. Chambers

Lund University

King's College London

Research output: Chapter in Book/Report/Conference proceeding › Paper in conference proceeding › peer-review

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.

Original language	English
Title of host publication	Advances in Cryptology — EUROCRYPT 1988 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings
Editors	Christoph G. Gunther
Publisher	Springer
Pages	325-330
Number of pages	6
ISBN (Print)	9783540502517
DOIs	https://doi.org/10.1007/3-540-45961-8_30
Publication status	Published - 1988
Event	6th European Workshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1988 - Davos, Switzerland Duration: 1988 May 25 → 1988 May 27

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	330 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	6th European Workshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1988
Country/Territory	Switzerland
City	Davos
Period	1988/05/25 → 1988/05/27

Bibliographical note

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.

Subject classification (UKÄ)

Mathematical Analysis

Access to Document

10.1007/3-540-45961-8_30

Cite this

Smeets, B. J. M., & Chambers, W. G. (1988). Windmill generators a generalization and an observation of how many there are. In C. G. Gunther (Ed.), Advances in Cryptology — EUROCRYPT 1988 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings (pp. 325-330). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 330 LNCS). Springer. https://doi.org/10.1007/3-540-45961-8_30

Smeets, B. J.M. ; Chambers, W. G. / Windmill generators a generalization and an observation of how many there are. Advances in Cryptology — EUROCRYPT 1988 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings. editor / Christoph G. Gunther. Springer, 1988. pp. 325-330 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Windmill generators a generalization and an observation of how many there are",

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){\textquoteright}s was found to be approximately twice the expected number.",

author = "Smeets, \{B. J.M.\} and Chambers, \{W. G.\}",

note = "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: {\textcopyright} 1988, Springer-Verlag Berlin Heidelberg.; 6th European Workshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1988 ; Conference date: 25-05-1988 Through 27-05-1988",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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Smeets, BJM & Chambers, WG 1988, Windmill generators a generalization and an observation of how many there are. in CG Gunther (ed.), Advances in Cryptology — EUROCRYPT 1988 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 330 LNCS, Springer, pp. 325-330, 6th European Workshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1988, Davos, Switzerland, 1988/05/25. https://doi.org/10.1007/3-540-45961-8_30

Windmill generators a generalization and an observation of how many there are. / Smeets, B. J.M.; Chambers, W. G.
Advances in Cryptology — EUROCRYPT 1988 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings. ed. / Christoph G. Gunther. Springer, 1988. p. 325-330 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 330 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Paper in conference proceeding › peer-review

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AU - Chambers, W. G.

N1 - 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.

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N2 - 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.

AB - 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.

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T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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BT - Advances in Cryptology — EUROCRYPT 1988 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings

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Smeets BJM, Chambers WG. Windmill generators a generalization and an observation of how many there are. In Gunther CG, editor, Advances in Cryptology — EUROCRYPT 1988 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings. Springer. 1988. p. 325-330. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-45961-8_30

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

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