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Date: 2013
Language: eng
Resource Type: conference paper
Identifier: http://hdl.handle.net/1959.14/217822
Description: This paper presents new explicit formulae for the point doubling, tripling and addition for ordinary Weierstraß elliptic curves with a point of order 3 and their equivalent Hessian curves over finite ... More
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/178617
Description: Edwards curves are an alternate model for elliptic curves, which have attracted notice in cryptography. We give exact formulas for the number of Fq-isomorphism classes of Edwards curves and twisted Ed ... More
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/195239
Description: We obtain explicit formulas for the number of nonisomorphic elliptic curves with a given group structure (considered as an abstract abelian group) and the number of distinct group structures of all el ... More
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/174485
Description: 6 page(s)
Reviewed: Reviewed
Date: 2011
Language: eng
Resource Type: conference paper
Identifier: http://hdl.handle.net/1959.14/151255
Description: We describe a hashing function from the elements of the finite field double-struck Fq into points on a Hessian curve. Our function features the uniform and smaller size for the cardinalities of almost ... More
Reviewed: Reviewed
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/130338
Description: We give explicit formulas for the number of distinct elliptic curves over a finite field (up to isomorphism over the algebraic closure of the ground field) in several families of curves of cryptograph ... More
Reviewed: Reviewed
Date: 2008
Language: eng
Resource Type: conference paper
Identifier: http://hdl.handle.net/1959.14/346455
Description: This paper presents a new shape for ordinary elliptic curves over fields of characteristic 2. Using the new shape, this paper presents the first complete addition formulas for binary elliptic curves, ... More
Reviewed: Reviewed
Date: 2008
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/146721
Description: We propose a simple and efficient deterministic extractor for an ordinary elliptic curve E, defined over F₂n , where n = 2ℓ and ℓ is a positive integer. Our extractor, for a given point P on E, output ... More
Reviewed: Reviewed
Date: 2008
Language: eng
Resource Type: conference paper
Identifier: http://hdl.handle.net/1959.14/346454
Description: 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 ... More
Reviewed: Reviewed
Date: 2007
Language: eng
Resource Type: conference paper
Identifier: http://hdl.handle.net/1959.14/347001
Description: A family of pseudorandom generators based on the decisional Diffie-Hellman assumption is proposed. The new construction is a modified and generalized version of the Dual Elliptic Curve generator propo ... More
Reviewed: Reviewed
Date: 2007
Language: eng
Resource Type: conference paper
Identifier: http://hdl.handle.net/1959.14/346466
Description: 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, ... More
Reviewed: Reviewed
Date: 2007
Language: eng
Resource Type: conference paper
Identifier: http://hdl.handle.net/1959.14/346769
Description: We propose a simple and efficient deterministic extractor for the (hyper)elliptic curve C, defined over Fq², where q is some power of an odd prime. Our extractor, for a given point P on C, outputs the ... More
Reviewed: Reviewed
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