We propose efficient algorithms and formulas that improve the performance of side-channel protected elliptic curve computations, with special focus on scalar multiplication exploiting the GallantLambert-Vanstone (CRYPTO 2001) and Galbraith-Lin-Scott (EUROCRYPT 2009) methods. Firstly, by adapting Feng et al.’s recoding to the GLV setting, we derive new regular algorithms for variable-base scalar...

Assuming sufficiently many terms of an n-dimensional table defined over a field are given, we aim at guessing the linear recurrence relations with either constant or polynomial coefficients they satisfy. In applications, come along structure: for instance, may be zero outside cone, built from Gröbner basis ideal invariant under action finite group. Thus, show how to take advantage this structur...

A generalization of recent group-theoretic matrix multiplication algorithms to an analogue of the theory of partial matrix multiplication is presented. We demonstrate that the added flexibility of this approach can in some cases improve upper bounds on the exponent of matrix multiplication yielded by group-theoretic full matrix multiplication. The group theory behind our partial matrix multipli...

This paper presents a new scheme for the hardware evaluation of elementary functions, based on a piecewise second order minimax approximation. The novelty is that this evaluation requires only one small rectangular multiplication. Therefore the resulting architecture combines a small table size, thanks to second-order evaluation, with a short critical path: Consisting of one table lookup, the r...

This paper deals with Euclidean space codes obtained from two-level group codes of length n over a Generalized Quaternion Group Q,, m23, with 2"' elements, with generators x and y, given by the presentation Q,,,= using a matched labelling of a 4-dimensional signal set with 2" elements with Q,. I. TWO LEVEL GROUP CODES OVER e,. Four dimensional signal sets in conne...

This paper presents a new scheme for the hardware evaluation of elementary functions, based on a piecewise second order minimax approximation. The novelty is that this evaluation requires only one small rectangular multiplication. Therefore the resulting architecture combines a small table size, thanks to second-order evaluation, with a short critical path: Consisting of one table lookup, the r...

In the recent paper (Casselman, 2001) I described how a number of ideas due to Fokko du Cloux and myself could be incorporated into a reasonably efficient program to carry out multiplication in arbitrary Coxeter groups. At the end of that paper I discussed how this algorithm could be used to build the reflection table of minimal roots, which could in turn form the basis of a much more efficient...

This paper addresses multiple precision integer multiplication on GPUs. In this paper, we propose a novel data-structure named a product digit table and present a GPU algorithm to perform the multiplication with the product digit table. Experimental results on a 3.10 GHz Intel Core i3-2100 CPU and an NVIDIA GeForce GTX480 GPU show that the proposed GPU algorithm respectively runs over 71.4 time...

A direct numerical method is proposed for the determination of all isolated zeros of a system of multivariate polynomial equations. By “polynomial combination”, the system is reduced to a special form which may be interpreted as a multiplication table for power products modulo the system. The zeros are then formed from an ordinary eigenvalue problem for the matrix of the multiplication table. D...