Best Information is Most Successful

Mutual Information and Success Rate in Side-Channel Analysis

  • Eloi de Chérisey LTCI, Télécom ParisTech, 46 rue Barrault, 75013 Paris
  • Sylvain Guilley LTCI, Télécom ParisTech, 46 rue Barrault, 75013 Paris; Secure-IC S.A.S., 15 Rue Claude Chappe, Bât. B, ZAC des Champs Blancs, 35 510 Cesson-Sévigné; École Normale Supérieure, 45 rue d’Ulm, 75005 Paris
  • Olivier Rioul LTCI, Télécom ParisTech, 46 rue Barrault, 75013 Paris
  • Pablo Piantanida LSS, Centrale-Supélec 8-10 rue Joliot-Curie, 91190 Gif-sur-Yvette
Keywords: Side-Channel Analysis, Information Theory, Guessing Entropy, Success, Rate

Abstract

Using information-theoretic tools, this paper establishes a mathematical link between the probability of success of a side-channel attack and the minimum number of queries to reach a given success rate, valid for any possible distinguishing rule and with the best possible knowledge on the attacker’s side. This link is a lower bound on the number of queries highly depends on Shannon’s mutual information between the traces and the secret key. This leads us to derive upper bounds on the mutual information that are as tight as possible and can be easily calculated. It turns out that, in the case of an additive white Gaussian noise, the bound on the probability of success of any attack is directly related to the signal to noise ratio. This leads to very easy computations and predictions of the success rate in any leakage model.

Published
2019-02-28
How to Cite
de Chérisey, E., Guilley, S., Rioul, O., & Piantanida, P. (2019). Best Information is Most Successful. IACR Transactions on Cryptographic Hardware and Embedded Systems, 2019(2), 49-79. https://doi.org/10.13154/tches.v2019.i2.49-79
Section
Articles