Hashing into Hessian curves

Reza Rezaeian Farashahi

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contribution

21 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationProgress in Cryptology, AFRICACRYPT 2011 - 4th International Conference on Cryptology in Africa, Proceedings
EditorsAbderrahmane Nitaj, David Pointcheval
Pages278-289
Number of pages12
Volume6737 LNCS
DOIs
Publication statusPublished - 2011
Event4th International Conference on the Theory and Application of Cryptographic Techniques, AFRICACRYPT 2011 - Dakar, Senegal
Duration: 5 Jul 20117 Jul 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6737 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other4th International Conference on the Theory and Application of Cryptographic Techniques, AFRICACRYPT 2011
CountrySenegal
CityDakar
Period5/07/117/07/11

Keywords

  • Elliptic curve cryptography
  • hashing
  • Hessian curve

Fingerprint Dive into the research topics of 'Hashing into Hessian curves'. Together they form a unique fingerprint.

  • 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