# Extractors for Jacobian of Hyperelliptic Curves of Genus 2 in Odd Characteristic

@inproceedings{Farashahi2007ExtractorsFJ,
title={Extractors for Jacobian of Hyperelliptic Curves of Genus 2 in Odd Characteristic},
author={Reza Rezaeian Farashahi},
booktitle={IMACC},
year={2007}
}
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…
6 Citations
Extracting a uniform random bit-string over Jacobian of Hyperelliptic curves of Genus 2
By using the Mumford’s representation of a reduced divisor D of the Jacobian J(Fq) of a hyperelliptic curve H of genus 2 with odd characteristic, a perfectly random bit string is extracted of the sum of abscissas of rational points on H in the support of D.
Extractors for Jacobians of Binary Genus-2 Hyperelliptic Curves
It is shown that, if D in J(\mathbb{F}_q) is chosen uniformly at random, the bits extracted from Dare are indistinguishable from a uniformly random bit-string of length n.
Linear complexity of some sequences derived from hyperelliptic curves of genus 2
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Cryptogr. Commun.
• 2022
The hyperelliptic analogue of the congruential generator defined by W n = W n − 1 + D for n ≥‬1 and D, W 0 ∈ J C is considered.
Kummer surfaces for primality testing
• Mathematics, Computer Science
• 2020
An algorithm is provided capable of proving the primality or compositeness of most of the integers in these families and the necessary steps to implement this algorithm in a computer are discussed.
Pseudorandom Bits From Points on Elliptic Curves
• Computer Science, Physics
IEEE Transactions on Information Theory
• 2012
These bounds confirm several recent conjectures of Jao, Jetchev, and Venkatesan, related to extracting random bits from various sequences of points on the elliptic curves.
Curves and Jacobians : number extractors and efficient arithmetic
The final author version and the galley proof are versions of the publication after peer review that features the final layout of the paper including the volume, issue and page numbers.

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