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

R. Rezaeian Farashahi

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

3 Citaten (Scopus)
115 Downloads (Pure)

Samenvatting

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.
Originele taal-2Engels
TitelProceedings of the 11th IMA International Conference on Cryptography and Coding, 18-20 December 2007, Cirencester, United Kingdom
RedacteurenS.D. Galbraith
Plaats van productieBerlin, Germany
UitgeverijSpringer
Pagina's313-335
ISBN van geprinte versie978-3-540-77271-2
DOI's
StatusGepubliceerd - 2007
Evenementconference; IMA International Conference on Cryptography and Coding 11, Cirencester, United Kingdom; 2007-12-18; 2007-12-20 -
Duur: 18 dec 200720 dec 2007

Publicatie series

NaamLecture Notes in Computer Science
Volume4887
ISSN van geprinte versie0302-9743

Congres

Congresconference; IMA International Conference on Cryptography and Coding 11, Cirencester, United Kingdom; 2007-12-18; 2007-12-20
Periode18/12/0720/12/07
AnderIMA International Conference on Cryptography and Coding 11, Cirencester, United Kingdom

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