Cryptographic Hardware and Embedded Systems — CHES 2001

Volume 2162 of the series Lecture Notes in Computer Science pp 402-410


Hessian Elliptic Curves and Side-Channel Attacks

  • Marc JoyeAffiliated withCard Security Group, Gemplus Card International
  • , Jean-Jacques QuisquaterAffiliated withUCL Crypto Group, Université catholique de Louvain


Side-channel attacks are a recent class of attacks that have been revealed to be very powerful in practice. By measuring some side-channel information (running time, power consumption,...), an attacker is able to recover some secret data from a carelessly implemented crypto-algorithm. 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.


Elliptic curves Cryptography Side-channel attacks Implementation Smart-cards