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

R. Rezaeian Farashahi

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74 Downloads (Pure)

Abstract

We propose two simple and efficient deterministic extractors for J(Fq), the Jacobian of a genus 2 hyperelliptic curve H defined over Fq, for some odd q. Our first extractor, SEJ, called sum extractor, for a given point D on J(Fq), 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(Fq), 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(Fq), the element extracted from the point D is indistinguishable from a uniformly random variable in Fq. Thanks to the Kummer surface K, that is associated to the Jacobian of H over Fq, we propose the sum and product extractors, SEK and PEK, for K(Fq). 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 Fq.
Original languageEnglish
Title of host publicationProceedings of the 11th IMA International Conference on Cryptography and Coding, 18-20 December 2007, Cirencester, United Kingdom
EditorsS.D. Galbraith
Place of PublicationBerlin, Germany
PublisherSpringer
Pages313-335
ISBN (Print)978-3-540-77271-2
DOIs
Publication statusPublished - 2007
Eventconference; IMA International Conference on Cryptography and Coding 11, Cirencester, United Kingdom; 2007-12-18; 2007-12-20 -
Duration: 18 Dec 200720 Dec 2007

Publication series

NameLecture Notes in Computer Science
Volume4887
ISSN (Print)0302-9743

Conference

Conferenceconference; IMA International Conference on Cryptography and Coding 11, Cirencester, United Kingdom; 2007-12-18; 2007-12-20
Period18/12/0720/12/07
OtherIMA International Conference on Cryptography and Coding 11, Cirencester, United Kingdom

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  • Cite this

    Rezaeian Farashahi, R. (2007). Extractors for Jacobian of hyperelliptic curves of genus 2 in odd characteristic. In S. D. Galbraith (Ed.), Proceedings of the 11th IMA International Conference on Cryptography and Coding, 18-20 December 2007, Cirencester, United Kingdom (pp. 313-335). (Lecture Notes in Computer Science; Vol. 4887). Springer. https://doi.org/10.1007/978-3-540-77272-9_19