Extractors for Jacobian of hyperelliptic curves of genus 2 in odd characteristic

Reza Rezaeian Farashahi*

*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

We propose two simple and efficient deterministic extractors for J(double-struck F signq), the Jacobian of a genus 2 hyperelliptic curve H defined over double-struck F signq, for some odd q. Our first extractor, SEJ, called sum extractor, for a given point D on .J(double-struck F signq), outputs the sum of abscissas of rational points on H in the support of D, considering D as a reduced divisor. Similarly the second extractor, PEJ, called product extractor, for a given point D on the J(double-struck F signq), outputs the product of abscissas of rational points in the support of D. Provided that the point D is chosen uniformly at random in J(double-struck F signq), the element extracted from the point D is indistinguishable from a uniformly random variable in double-struck F signq. Thanks to the Kummer surface K, that is associated to the Jacobian of H over double-struck F signq, we propose the sum and product extractors, SEK and PEK, for K(double-struck F signq). These extractors are the modified versions of the extractors SEJ and PEJ. Provided a point K is chosen uniformly at random in K, the element extracted from the point K is statistically close to a uniformly random variable in double-struck F signq.

Original languageEnglish
Title of host publicationCryptography and Coding - 11th IMA International Conference, Proceedings
EditorsSteven D Galbraith
Pages313-335
Number of pages23
Volume4887 LNCS
Publication statusPublished - 2007
Event11th IMA Conference on Cryptography and Coding - Cirencester, United Kingdom
Duration: 18 Dec 200720 Dec 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4887 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other11th IMA Conference on Cryptography and Coding
CountryUnited Kingdom
CityCirencester
Period18/12/0720/12/07

Keywords

  • Deterministic extractor
  • Hyperelliptic curve
  • Jacobian
  • Kummer surface

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