On next-to-eikonal exponentiation

Horizontal Correlation Analysis on Exponentiation

We introduce in this paper a technique in which we apply correlation analysis using only one execution power curve during an exponentiation to recover the whole secret exponent manipulated by the chip. As in the Big Mac attack from Walter, longer keys may facilitate this analysis and success will depend on the arithmetic coprocessor characteristics. We present the theory of the attack with some...

On multi-exponentiation in cryptography

We describe and analyze new combinations of multi-exponentiation algorithms with representations of the exponents. We deal mainly but not exclusively with the case where the inversion of group elements is fast: This is true for example for elliptic curves, groups of rational divisor classes of hyperelliptic curves, trace zero varieties and XTR. These methods are most attractive with exponents i...

Horizontal Correlation Analysis on Exponentiation

Power Analysis has been widely studied since Kocher et al. presented in 1998 the initial Simple and Differential Power Analysis (SPA and DPA). Correlation Power Analysis (CPA) is nowadays one of the most powerful techniques which requires, as classical DPA, many execution curves for recovering secrets. We introduce in this paper a technique in which we apply correlation analysis using only one ...

An Efficient Solution to the Eikonal Equation on Parametric Manifolds

We present an efficient solution to the eikonal equation on parametric manifolds, based on the fast marching approach. This method overcomes the problem of a non-orthogonal coordinate system on the manifold by creating an appropriate numerical stencil. The method is tested numerically and demonstrated by calculating distances on various parametric manifolds. It is further used for two applicati...

On Exponentiation - A Solution to Tarski's High School Algebra Problem