Extractors for jacobians of binary genus-2 hyperelliptic curves

Reza Rezaeian Farashahi

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

1 Citation (Scopus)

Abstract

Extractors are an important ingredient in designing key exchange protocols and secure pseudorandom sequences in the standard model. Elliptic and hyperelliptic curves are gaining more and more interest due to their fast arithmetic and the fact that no subexponential attacks against the discrete logarithm problem are known. In this paper we propose two simple and efficient deterministic extractors for , the Jacobian of a genus 2 hyperelliptic curve H defined over , where q∈=∈2 n , called the sum and product extractors. For non-supersingular hyperelliptic curves having a Jacobian with group order 2m, where m is odd, we propose the modified sum and product extractors for the main subgroup of . We show that, if is chosen uniformly at random, the bits extracted from D are indistinguishable from a uniformly random bit-string of length n.

Original languageEnglish
Title of host publicationInformation Security and Privacy - 13th Australasian Conference, ACISP 2008, Proceedings
EditorsYi Mu, Willy Susilo, Jennifer Seberry
Pages447-462
Number of pages16
Volume5107 LNCS
DOIs
Publication statusPublished - 2008
Event13th Australasian Conference on Information Security and Privacy, ACISP 2008 - Wollongong, NSW, Australia
Duration: 7 Jul 20089 Jul 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5107 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other13th Australasian Conference on Information Security and Privacy, ACISP 2008
CountryAustralia
CityWollongong, NSW
Period7/07/089/07/08

Keywords

  • Deterministic extractor
  • Hyperelliptic curve
  • Jacobian

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