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Extractors for Jacobian of Hyperelliptic Curves of Genus 2 in Odd Characteristic [chapter]

Reza Rezaeian Farashahi
Cryptography and Coding  
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]

Bernadette Faye
2017 arXiv   pre-print
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

A. Stein, R. Scheidler, M. Jacobson
2007 Advances in Mathematics of Communications  
, 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]

Rezaeian Farashahi, R (Reza), Tilborg, HCA (Henk) Van, Lange, T (Tanja), Pellikaan, GR (Ruud)
2008
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]

Min Li, Hua Wang, Ashley Plank, Jianming Yong
Lecture Notes in Computer Science  
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