Elliptic twin prime conjecture

John Friedlander; Igor E. Shparlinski

doi:10.1007/978-3-642-01877-0_8

Elliptic twin prime conjecture

John Friedlander, Igor E. Shparlinski

School of Computing

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

3 Citations (Scopus)

Abstract

Motivated by a recent application to hash functions suggested by O. Chevassut, P.-A. Fouque, P. Gaudry and D. Pointcheval, we study the frequency with which both an elliptic curve over a finite field, and its quadratic twist are cryptographically suitable. Here, we obtain heuristic estimates for the number of such curves for which both the curve and its twist have a number of points which is prime. In a work in progress theoretical extimates are obtained wherein the number of such points on both curves has a prescribed arithmetic structure.

Original language	English
Title of host publication	Coding and Cryptology - Second International Workshop, IWCC 2009, Proceedings
Editors	Yeow Meng Chee, San Ling, Huaxiong Wang, Chaoping Xing
Place of Publication	Berlin; Heidelberg
Publisher	Springer, Springer Nature
Pages	77-81
Number of pages	5
Volume	5557 LNCS
ISBN (Electronic)	9783642018770
ISBN (Print)	3642018130, 9783642018138
DOIs	https://doi.org/10.1007/978-3-642-01877-0_8
Publication status	Published - 2009
Event	2nd International Workshop on Coding and Cryptology, IWCC - 2009 - Zhangjiajie, China Duration: 1 Jun 2009 → 5 Jun 2009

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5557 LNCS
ISSN (Print)	03029743
ISSN (Electronic)	16113349

Other

Other	2nd International Workshop on Coding and Cryptology, IWCC - 2009
Country/Territory	China
City	Zhangjiajie
Period	1/06/09 → 5/06/09

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10.1007/978-3-642-01877-0_8

Cite this

Friedlander, J., & Shparlinski, I. E. (2009). Elliptic twin prime conjecture. In Y. M. Chee, S. Ling, H. Wang, & C. Xing (Eds.), Coding and Cryptology - Second International Workshop, IWCC 2009, Proceedings (Vol. 5557 LNCS, pp. 77-81). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5557 LNCS). Springer, Springer Nature. https://doi.org/10.1007/978-3-642-01877-0_8

Friedlander, John ; Shparlinski, Igor E. / Elliptic twin prime conjecture. Coding and Cryptology - Second International Workshop, IWCC 2009, Proceedings. editor / Yeow Meng Chee ; San Ling ; Huaxiong Wang ; Chaoping Xing. Vol. 5557 LNCS Berlin; Heidelberg : Springer, Springer Nature, 2009. pp. 77-81 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "Motivated by a recent application to hash functions suggested by O. Chevassut, P.-A. Fouque, P. Gaudry and D. Pointcheval, we study the frequency with which both an elliptic curve over a finite field, and its quadratic twist are cryptographically suitable. Here, we obtain heuristic estimates for the number of such curves for which both the curve and its twist have a number of points which is prime. In a work in progress theoretical extimates are obtained wherein the number of such points on both curves has a prescribed arithmetic structure.",

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Friedlander, J & Shparlinski, IE 2009, Elliptic twin prime conjecture. in YM Chee, S Ling, H Wang & C Xing (eds), Coding and Cryptology - Second International Workshop, IWCC 2009, Proceedings. vol. 5557 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5557 LNCS, Springer, Springer Nature, Berlin; Heidelberg, pp. 77-81, 2nd International Workshop on Coding and Cryptology, IWCC - 2009, Zhangjiajie, China, 1/06/09. https://doi.org/10.1007/978-3-642-01877-0_8

Elliptic twin prime conjecture. / Friedlander, John; Shparlinski, Igor E.
Coding and Cryptology - Second International Workshop, IWCC 2009, Proceedings. ed. / Yeow Meng Chee; San Ling; Huaxiong Wang; Chaoping Xing. Vol. 5557 LNCS Berlin; Heidelberg: Springer, Springer Nature, 2009. p. 77-81 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5557 LNCS).

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

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AB - Motivated by a recent application to hash functions suggested by O. Chevassut, P.-A. Fouque, P. Gaudry and D. Pointcheval, we study the frequency with which both an elliptic curve over a finite field, and its quadratic twist are cryptographically suitable. Here, we obtain heuristic estimates for the number of such curves for which both the curve and its twist have a number of points which is prime. In a work in progress theoretical extimates are obtained wherein the number of such points on both curves has a prescribed arithmetic structure.

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SN - 9783642018138

VL - 5557 LNCS

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

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Friedlander J, Shparlinski IE. Elliptic twin prime conjecture. In Chee YM, Ling S, Wang H, Xing C, editors, Coding and Cryptology - Second International Workshop, IWCC 2009, Proceedings. Vol. 5557 LNCS. Berlin; Heidelberg: Springer, Springer Nature. 2009. p. 77-81. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-01877-0_8

Elliptic twin prime conjecture

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