International audienceThis article generalizes the simplified Shallue–van de Woestijne–Ulas (SWU) method of a deterministic finite field mapping h:Fq→Ea(Fq) to the case of any elliptic Fq-curve Ea : y2 = x3 − ax of j-invariant 1728. In comparison with the (classical) SWU method the simplified SWU method allows to avoid one quadratic residuosity test in the field Fq, which is a quite painful operation in cryptography with regard to timing attacks. More precisely, in order to derive h we obtain a rational Fq-curve C (and its explicit quite simple proper Fq-parametrization) on the Kummer surface K′ associated with the direct product Ea×Ea′, where Ea′ is the quadratic Fq-twist of Ea. Our approach of finding C is based on the fact that every cur...
This book offers the beginning undergraduate student some of the vista of modern mathematics by deve...
Elliptic curve cryptography has received more and more attention from the security industry over the...
Abstract. We provide the first construction of a hash function into ordinary elliptic curves that is...
In this article we produce the simplified SWU encoding to some Barreto--Naehrig curves, including BN...
International audienceIn the article we propose a new compression method (to 2⌈log2(q)⌉+3 bits) for...
International audienceIn the article we propose a new compression method (to 2⌈log2(q)⌉+3 bits) for...
The present article explains how to generalize the hash function SwiftEC (in an elementary quasi-uni...
This article proposes four optimizations of indifferentiable hashing onto (prime-order subgroups of)...
Abstract. Let E be a non-supersingular elliptic curve over a finite field Fq. At CRYPTO 2009, Icart ...
This thesis describes a procedure (the `CM method'), based on the theory of complex multiplication, ...
Dans la thèse deux tâches se posant pour des courbes elliptiques de j-invariants 0; 1728 sont consid...
At Crypto 2010, Brier et al. proposed the first construction of a hash function into ordinary ellipt...
We describe a hashing function from the elements of the finite field double-struck Fq into points on...
Abstract. We provide the first construction of a hash function into ordinary elliptic curves that is...
The BLS Digital Signature Algorithm is a cryptographic scheme using elliptic curves over finite fiel...
This book offers the beginning undergraduate student some of the vista of modern mathematics by deve...
Elliptic curve cryptography has received more and more attention from the security industry over the...
Abstract. We provide the first construction of a hash function into ordinary elliptic curves that is...
In this article we produce the simplified SWU encoding to some Barreto--Naehrig curves, including BN...
International audienceIn the article we propose a new compression method (to 2⌈log2(q)⌉+3 bits) for...
International audienceIn the article we propose a new compression method (to 2⌈log2(q)⌉+3 bits) for...
The present article explains how to generalize the hash function SwiftEC (in an elementary quasi-uni...
This article proposes four optimizations of indifferentiable hashing onto (prime-order subgroups of)...
Abstract. Let E be a non-supersingular elliptic curve over a finite field Fq. At CRYPTO 2009, Icart ...
This thesis describes a procedure (the `CM method'), based on the theory of complex multiplication, ...
Dans la thèse deux tâches se posant pour des courbes elliptiques de j-invariants 0; 1728 sont consid...
At Crypto 2010, Brier et al. proposed the first construction of a hash function into ordinary ellipt...
We describe a hashing function from the elements of the finite field double-struck Fq into points on...
Abstract. We provide the first construction of a hash function into ordinary elliptic curves that is...
The BLS Digital Signature Algorithm is a cryptographic scheme using elliptic curves over finite fiel...
This book offers the beginning undergraduate student some of the vista of modern mathematics by deve...
Elliptic curve cryptography has received more and more attention from the security industry over the...
Abstract. We provide the first construction of a hash function into ordinary elliptic curves that is...