Hashing into Hessian curves

Reza Rezaeian Farashahi

doi:10.1007/978-3-642-21969-6_17

Hashing into Hessian curves

Reza Rezaeian Farashahi

School of Computing

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

27 Citations (Scopus)

Abstract

We describe a hashing function from the elements of the finite field double-struck F_q into points on a Hessian curve. Our function features the uniform and smaller size for the cardinalities of almost all fibers compared with the other known hashing functions for elliptic curves. For ordinary Hessian curves, this function is 2:1 for almost all points. More precisely, for odd q, the cardinality of the image set of the function is exactly given by (q + i + 2)/2 for some i = - 1,1. Next, we present an injective hashing function from the elements of ℤ_m into points on a Hessian curve over double-struck F_q with odd q and m = (q + i)/2 for some i = - 1,1,3.

Original language	English
Title of host publication	Progress in Cryptology, AFRICACRYPT 2011 - 4th International Conference on Cryptology in Africa, Proceedings
Editors	Abderrahmane Nitaj, David Pointcheval
Pages	278-289
Number of pages	12
Volume	6737 LNCS
DOIs	https://doi.org/10.1007/978-3-642-21969-6_17
Publication status	Published - 2011
Event	4th International Conference on the Theory and Application of Cryptographic Techniques, AFRICACRYPT 2011 - Dakar, Senegal Duration: 5 Jul 2011 → 7 Jul 2011

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6737 LNCS
ISSN (Print)	03029743
ISSN (Electronic)	16113349

Other

Other	4th International Conference on the Theory and Application of Cryptographic Techniques, AFRICACRYPT 2011
Country/Territory	Senegal
City	Dakar
Period	5/07/11 → 7/07/11

Keywords

Elliptic curve cryptography
hashing
Hessian curve

Access to Document

10.1007/978-3-642-21969-6_17

Cite this

Farashahi, R. R. (2011). Hashing into Hessian curves. In A. Nitaj, & D. Pointcheval (Eds.), Progress in Cryptology, AFRICACRYPT 2011 - 4th International Conference on Cryptology in Africa, Proceedings (Vol. 6737 LNCS, pp. 278-289). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6737 LNCS). https://doi.org/10.1007/978-3-642-21969-6_17

Farashahi, Reza Rezaeian. / Hashing into Hessian curves. Progress in Cryptology, AFRICACRYPT 2011 - 4th International Conference on Cryptology in Africa, Proceedings. editor / Abderrahmane Nitaj ; David Pointcheval. Vol. 6737 LNCS 2011. pp. 278-289 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We describe a hashing function from the elements of the finite field double-struck Fq into points on a Hessian curve. Our function features the uniform and smaller size for the cardinalities of almost all fibers compared with the other known hashing functions for elliptic curves. For ordinary Hessian curves, this function is 2:1 for almost all points. More precisely, for odd q, the cardinality of the image set of the function is exactly given by (q + i + 2)/2 for some i = - 1,1. Next, we present an injective hashing function from the elements of ℤm into points on a Hessian curve over double-struck Fq with odd q and m = (q + i)/2 for some i = - 1,1,3.",

keywords = "Elliptic curve cryptography, hashing, Hessian curve",

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editor = "Abderrahmane Nitaj and David Pointcheval",

booktitle = "Progress in Cryptology, AFRICACRYPT 2011 - 4th International Conference on Cryptology in Africa, Proceedings",

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Farashahi, RR 2011, Hashing into Hessian curves. in A Nitaj & D Pointcheval (eds), Progress in Cryptology, AFRICACRYPT 2011 - 4th International Conference on Cryptology in Africa, Proceedings. vol. 6737 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6737 LNCS, pp. 278-289, 4th International Conference on the Theory and Application of Cryptographic Techniques, AFRICACRYPT 2011, Dakar, Senegal, 5/07/11. https://doi.org/10.1007/978-3-642-21969-6_17

Hashing into Hessian curves. / Farashahi, Reza Rezaeian.
Progress in Cryptology, AFRICACRYPT 2011 - 4th International Conference on Cryptology in Africa, Proceedings. ed. / Abderrahmane Nitaj; David Pointcheval. Vol. 6737 LNCS 2011. p. 278-289 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6737 LNCS).

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

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AU - Farashahi, Reza Rezaeian

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N2 - We describe a hashing function from the elements of the finite field double-struck Fq into points on a Hessian curve. Our function features the uniform and smaller size for the cardinalities of almost all fibers compared with the other known hashing functions for elliptic curves. For ordinary Hessian curves, this function is 2:1 for almost all points. More precisely, for odd q, the cardinality of the image set of the function is exactly given by (q + i + 2)/2 for some i = - 1,1. Next, we present an injective hashing function from the elements of ℤm into points on a Hessian curve over double-struck Fq with odd q and m = (q + i)/2 for some i = - 1,1,3.

AB - We describe a hashing function from the elements of the finite field double-struck Fq into points on a Hessian curve. Our function features the uniform and smaller size for the cardinalities of almost all fibers compared with the other known hashing functions for elliptic curves. For ordinary Hessian curves, this function is 2:1 for almost all points. More precisely, for odd q, the cardinality of the image set of the function is exactly given by (q + i + 2)/2 for some i = - 1,1. Next, we present an injective hashing function from the elements of ℤm into points on a Hessian curve over double-struck Fq with odd q and m = (q + i)/2 for some i = - 1,1,3.

KW - Elliptic curve cryptography

KW - hashing

KW - Hessian curve

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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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Farashahi RR. Hashing into Hessian curves. In Nitaj A, Pointcheval D, editors, Progress in Cryptology, AFRICACRYPT 2011 - 4th International Conference on Cryptology in Africa, Proceedings. Vol. 6737 LNCS. 2011. p. 278-289. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-21969-6_17

Hashing into Hessian curves

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