This work studies the best attacks against some of the most popular pairings and proposes new key sizes using an analysis which is more precise than the analysis in a recent article of Menezes, Sarkar and Singh.Expand

This paper presents two FPGA-based high speed pairing designs using the Residue Number System and lazy reduction, and shows that by combining RNS, which is naturally suitable for parallel architectures, and lazy Reduction, the speed of pairing computation in hardware can be largely increased.Expand

This work optimize formulae for basic operations arising in leak-resistant arithmetic on elliptic curves (unified addition, Montgomery ladder) in order to minimize the number of modular reductions.Expand

This paper gives an explicit description of the Kummer surface and uses these new objects to give a very fast scalar multiplication algorithm for hyperelliptic curve cryptography in characteristic 2.Expand

Abstract By using the so-called elliptic curve Chabauty method, N. Bruin [1], V. Flynn and J. Wetherell [6] have extended Chabauty's method to some cases where the rank of the Jacobian may not be… Expand

This work generalizes the Montgomery method for scalar multiplication to the jacobian of genus 2 curves to obtain an algorithm that is competitive compared to the usual methods of scalarmultiplication and that has additional properties such as resistance to timings attacks.Expand

This work deduced the best form of hyperelliptic curves of genus 2 in characteristic 2 to use in cryptography, just as the short Weierstrass form for elliptic curves.Expand

The complete list of integral points on elliptic curves of the form y2 = f(X) is computed and it is proved that this list is exhaustive by using the methods of Tzanakis and de Weger, together with bounds on linear forms in elliptic logarithms due to S. David.Expand

This work generalizes Montgomery ladder for scalar multiplication to the Jacobian of genus 2 curves in characteristic 2 and obtains an algorithm that is competitive compared to usual methods of scaler multiplication and that has additional properties such as resistance to simple side-channel attacks.Expand