Hessian elliptic curves and side-channel attacks

Abstract

Side-channel attacks are a recent class of attacks that have been revealed to be very powerful in practice. By measuring some sidechannel information (running time, power consumption,..), an attacker is able to recover some secret data from a carelessly implemented cryptoalgorithm. This paper investigates the Hessian parameterization of an elliptic curve as a step towards resistance against such attacks in the context of elliptic curve cryptography. The idea is to use the same procedure to compute the addition, the doubling or the subtraction of points. As a result, this gives a 33% performance improvement as compared to the best reported methods and requires much less memory.