Add to ORKGInternational audienceUsing powerful tools on genus 2 curves like the Kummer variety, we generalize the Montgomery method for scalar multiplication to the jacobian of these curves. Previously this method was only known for elliptic curves. We obtain an algorithm that is competitive compared to the usual methods of scalar multiplication and that has additional properties such as resistance to timings attacks. This algorithm has very important applications in cryptography using hyperelliptic curves and more particularly for people interested in cryptography on smart cards
Elliptic Curve Cryptography (ECC) was independently introduced by Koblitz and Miller in the eighties...
Abstract. Genus 2 curves have been an object of much mathematical interest since eighteenth century ...
International audienceThree decades ago, Montgomery introduced a new elliptic curve model for use in...
Hyperelliptic curves of low genus obtained a lot of attention in the recent past for cryptographic a...
In 1986, D. V. Chudnovsky and G. V. Chudnovsky proposed to use formulae coming from Theta functions...
Abstract. In 1986, D. V. Chudnovsky and G. V. Chudnovsky proposed to use formulae coming from Theta ...
International audienceWe give one-and two-dimensional scalar multiplication algorithms for Jacobians...
We give a general framework for uniform, constant-time one-and two-dimensional scalar multiplication...
Abstract. This paper presents a new projective coordinate system and new explicit algorithms which t...
In this paper we highlight the benefits of using genus 2 curves in public-key cryptography. Compared...
The Montgomery ladder is a remarkably simple method of computing scalar multiples of points on a bro...
This paper presents an algorithm to construct cryptographically strong genus 2 curves and their Kumm...
Elliptic Curve Cryptography (ECC) was independently introduced by Koblitz and Miller in the eighties...
Abstract. Genus 2 curves have been an object of much mathematical interest since eighteenth century ...
International audienceThree decades ago, Montgomery introduced a new elliptic curve model for use in...
Hyperelliptic curves of low genus obtained a lot of attention in the recent past for cryptographic a...
In 1986, D. V. Chudnovsky and G. V. Chudnovsky proposed to use formulae coming from Theta functions...
Abstract. In 1986, D. V. Chudnovsky and G. V. Chudnovsky proposed to use formulae coming from Theta ...
International audienceWe give one-and two-dimensional scalar multiplication algorithms for Jacobians...
We give a general framework for uniform, constant-time one-and two-dimensional scalar multiplication...
Abstract. This paper presents a new projective coordinate system and new explicit algorithms which t...
In this paper we highlight the benefits of using genus 2 curves in public-key cryptography. Compared...
The Montgomery ladder is a remarkably simple method of computing scalar multiples of points on a bro...
This paper presents an algorithm to construct cryptographically strong genus 2 curves and their Kumm...
Elliptic Curve Cryptography (ECC) was independently introduced by Koblitz and Miller in the eighties...
Abstract. Genus 2 curves have been an object of much mathematical interest since eighteenth century ...
International audienceThree decades ago, Montgomery introduced a new elliptic curve model for use in...