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Extractors for Jacobian of Hyperelliptic Curves of Genus 2 in Odd Characteristic
[chapter]
Cryptography and Coding
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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. ...
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. ...
The author thanks to the anonymous referees for several useful suggestions. ...
doi:10.1007/978-3-540-77272-9_19
dblp:conf/ima/Farashahi07
fatcat:bdg4zxjkgbf5njcbtq7otpbsjq
Extracting a uniform random bit-string over Jacobian of Hyperelliptic curves of Genus 2
[article]
2017
arXiv
pre-print
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By using the Mumford's representation of a reduced divisor D of the Jacobian J(F_q) of a hyperelliptic curve H of genus 2 with odd characteristic, we extract a perfectly random bit string of the sum of ...
By this new approach, we reduce in an elementary way the upper bound of the statistical distance of the deterministic randomness extractors defined over F_q where q=p^n, for some positive integer n≥ 1 ...
Ciss for useful comments and suggestions on an earlier draft of this paper. ...
arXiv:1703.08151v1
fatcat:zawcse3yangtjktw7uyuanbd5q
Cryptographic protocols on real hyperelliptic curves
2007
Advances in Mathematics of Communications
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, the distance problem, in the real model of a hyperelliptic curve. ...
The first two authors are supported in part by NSERC of Canada. ...
Acknowledgements We would like to thank the referees very much for their valuable comments and suggestions. ...
doi:10.3934/amc.2007.1.197
fatcat:njwlkremovhipafbuet436wvqe
Curves and Jacobians:number extractors and efficient arithmetic
[article]
2008
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A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
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Farashahi, Extractors for Jacobian of Hyperelliptic Curves of Genus 2 in Odd Characteristic. ...
A surface related to the Jacobian in odd characteristic In this section we introduce a surface related to the Jacobian of a genus-2 hyperelliptic curve over a finite field with odd characteristic. ...
curve C, defined over F q 2 , where q is some power of an odd prime. • In Chapter 6, we proposed the first extractors for the Jacobian of a genus 2 hyperelliptic curve H over F q . ...
doi:10.6100/ir637900
fatcat:prvylhsj6zdu3hhghr6qypj6ry
Advanced Permission-Role Relationship in Role-Based Access Control
[chapter]
Lecture Notes in Computer Science
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In this paper we address security of cookie-based authenticationusing the concept of strong locked same originpolicy for browsers introduced at ACM CCS'07. ...
For the past several decades, cryptographers have consistently provided us with stronger and more capable primitives and protocols that have found many applications in security systems in everyday life ...
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= ...
doi:10.1007/978-3-540-70500-0_29
fatcat:sdoiqrtlnrczleab3nyms3kjom