International Workshop on Cryptographic Hardware and Embedded Systems

CHES 2001: Cryptographic Hardware and Embedded Systems — CHES 2001 pp 402-410

Hessian Elliptic Curves and Side-Channel Attacks

  • Marc Joye
  • Jean-Jacques Quisquater
Conference paper

DOI: 10.1007/3-540-44709-1_33

Volume 2162 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Joye M., Quisquater JJ. (2001) Hessian Elliptic Curves and Side-Channel Attacks. In: Koç Ç.K., Naccache D., Paar C. (eds) Cryptographic Hardware and Embedded Systems — CHES 2001. CHES 2001. Lecture Notes in Computer Science, vol 2162. Springer, Berlin, Heidelberg


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 curvesCryptographySide-channel attacksImplementationSmart-cards
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Marc Joye
    • 1
  • Jean-Jacques Quisquater
    • 2
  1. 1.Card Security GroupGemplus Card InternationalGémenosFrance
  2. 2.UCL Crypto GroupUniversité catholique de LouvainLouvain-la-NeuveBelgium