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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.  ...  Our protocols represent a significant improvement over existing protocols using real hyperelliptic curves.  ...  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

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.  ...  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).  ...  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

Curves and Jacobians:number extractors and efficient arithmetic [article]

Rezaeian Farashahi, R (Reza), Tilborg, HCA (Henk) Van, Lange, T (Tanja), Pellikaan, GR (Ruud)
Farashahi, Extractors for Jacobian of Hyperelliptic Curves of Genus 2 in Odd Characteristic.  ...  The result of this chapter was previously published as: R. R. Farashahi. Extractors for Jacobians of Binary Genus-2 Hyperelliptic Curves.  ...  extractors for binary hyperelliptic curves of genus 2. • We also proposed a way to construct an extractor for the main subgroup based on an extractor of the full group in order to use only the subgroup  ... 
doi:10.6100/ir637900 fatcat:prvylhsj6zdu3hhghr6qypj6ry

An Approach to the Construction of a Recursive Argument of Polynomial Evaluation in the Discrete Log Setting

Sungwook Kim
2022 Electronics  
Polynomial commitment schemes are important building blocks for the construction of SNARks.  ...  Succinct Non-interactive Arguments of Knowledge (SNARks) are receiving a lot of attention as a core privacy-enhancing technology for blockchain applications.  ...  Conflicts of Interest: The author declares no conflict of interest.  ... 
doi:10.3390/electronics11010131 fatcat:j3wly4berffp3lmm75ihoe5olq

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.  ...  One of the central tenets of cryptographic design ...  ...  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