TY - GEN

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

AU - Rezaeian Farashahi, R.

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

U2 - 10.1007/978-3-540-77272-9_19

DO - 10.1007/978-3-540-77272-9_19

M3 - Conference contribution

SN - 978-3-540-77271-2

T3 - Lecture Notes in Computer Science

SP - 313

EP - 335

BT - Proceedings of the 11th IMA International Conference on Cryptography and Coding, 18-20 December 2007, Cirencester, United Kingdom

A2 - Galbraith, S.D.

PB - Springer

CY - Berlin, Germany

T2 - conference; IMA International Conference on Cryptography and Coding 11, Cirencester, United Kingdom; 2007-12-18; 2007-12-20

Y2 - 18 December 2007 through 20 December 2007

ER -