A pseudo-random bit generator based on elliptic logarithms
Proceedings on Advances in cryptology---CRYPTO '86
Journal of Cryptology
Pseudorandomness and Cryptographic Applications
Pseudorandomness and Cryptographic Applications
Extracting randomness from samplable distributions
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
An algorithm for solving the discrete log problem on hyperelliptic curves
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
The Twist-AUgmented technique for key exchange
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
How to turn loaded dice into fair coins
IEEE Transactions on Information Theory
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
Extractors for Jacobians of Binary Genus-2 Hyperelliptic Curves
ACISP '08 Proceedings of the 13th Australasian conference on Information Security and Privacy
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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.