Concept

Hyperelliptic curve

Related publications (26)

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On the Static Diffie-Hellman Problem on Elliptic Curves over Extension Fields

Robert Granger

We show that for any elliptic curve

E(\mathbb{F}_{q^n})

, if an adversary has access to a Static Diffie-Hellman Problem (Static DHP) oracle, then by making

O(q^{1-\frac{1}{n+1}})

Static DHP oracle queries during an initial learning phase, for fixed $n>1 ...

Springer Berlin Heidelberg2010

Efficient and side-channel-aware implementations of elliptic curve cryptosystems over prime fields

Yusuf Leblebici

Elliptic curve cryptosystems (ECCs) are utilised as an alternative to traditional public-key cryptosystems, and are more suitable for resource-limited environments because of smaller parameter size. In this study, the authors carry out a thorough investiga ...

2010

Ate Pairing on Hyperelliptic Curves

Robert Granger

In this paper we show that the Ate pairing, originally defined for elliptic curves, generalises to hyperelliptic curves and in fact to arbitrary algebraic curves. It has the following surprising properties: The loop length in Miller’s algorithm can be up t ...

Springer-Verlag Berlin Heidelberg2007

Unsupervised Selective Anisotropic Feature Diffusion for Cortical Surface Registration

Jean-Philippe Thiran, Olivier Cuisenaire

In this paper we use the theory of geometric curve and surface evolution to diffuse an object preserving their important features. We do that using a curvature flow method with a novel influence function. The proposed influence function takes profit from t ...

EUROCAST2003

Computation of the discrete logarithm on elliptic curves of trace one

Jean Monnerat

The security of several elliptic curve cryptosystems is based on the difficulty to compute the discrete logarithm problem. The motivation of using elliptic curves in cryptography is that there is no known sub-exponential algorithm which solves the Elliptic ...

2002

Efficient identity based parameter selection for elliptic curve cryptosystems

Arjen Lenstra

A method is proposed that allows each individual party to an elliptic curve cryptosystem to quickly determine its own unique pair of finite field and Weierstrass equation, in such a way that the resulting pair provides adequate security. Although the choic ...

1999

On the Static Diffie-Hellman Problem on Elliptic Curves over Extension Fields

Robert Granger

We show that for any elliptic curve

E(\mathbb{F}_{q^n})

, if an adversary has access to a Static Diffie-Hellman Problem (Static DHP) oracle, then by making

O(q^{1-\frac{1}{n+1}})

Static DHP oracle queries during an initial learning phase, for fixed $n>1 ...

Springer Berlin Heidelberg2010