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
The Newton Polygon of Plane Curves with Many Rational Points
Designs, Codes and Cryptography
Extracting randomness from samplable distributions
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
Designs, Codes and Cryptography
The Quadratic Extension Extractor for (Hyper)Elliptic Curves in Odd Characteristic
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
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
Extractors for Jacobian of hyperelliptic curves of genus 2 in odd characteristic
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
Efficient doubling on genus two curves over binary fields
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
The Twist-AUgmented technique for key exchange
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
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Extractors are an important ingredient in designing key exchange protocols and secure pseudorandom sequences in the standard model. Elliptic and hyperelliptic curves are gaining more and more interest due to their fast arithmetic and the fact that no subexponential attacks against the discrete logarithm problem are known.In this paper we propose two simple and efficient deterministic extractors for $J(\mathbb{F}_q)$, the Jacobian of a genus 2 hyperelliptic curve Hdefined over $\mathbb{F}_q$, where q= 2n, called the sumand productextractors.For non-supersingular hyperelliptic curves having a Jacobian with group order 2m, where mis odd, we propose the modified sumand productextractors for the main subgroup of $J(\mathbb{F}_q)$. We show that, if $D\in J(\mathbb{F}_q)$ is chosen uniformly at random, the bits extracted from Dare indistinguishable from a uniformly random bit-string of length n.