TY - GEN

T1 - Extractors for Jacobian of hyperelliptic curves of genus 2 in odd characteristic

AU - Farashahi, Reza Rezaeian

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - Deterministic extractor

KW - Hyperelliptic curve

KW - Jacobian

KW - Kummer surface

UR - http://www.scopus.com/inward/record.url?scp=38149123977&partnerID=8YFLogxK

M3 - Conference proceeding contribution

AN - SCOPUS:38149123977

SN - 9783540772712

VL - 4887 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 313

EP - 335

BT - Cryptography and Coding - 11th IMA International Conference, Proceedings

A2 - Galbraith, Steven D

T2 - 11th IMA Conference on Cryptography and Coding

Y2 - 18 December 2007 through 20 December 2007

ER -