Good Is Not Good Enough

Deriving Optimal Distinguishers from Communication Theory
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8731)


We find mathematically optimal side-channel distinguishers by looking at the side-channel as a communication channel. Our methodology can be adapted to any given scenario (device, signal-to-noise ratio, noise distribution, leakage model, etc.). When the model is known and the noise is Gaussian, the optimal distinguisher outperforms CPA and covariance. However, we show that CPA is optimal when the model is only known on a proportional scale. For non-Gaussian noise, we obtain different optimal distinguishers, one for each noise distribution. When the model is imperfectly known, we consider the scenario of a weighted sum of the sensitive variable bits where the weights are unknown and drawn from a normal law. In this case, our optimal distinguisher performs better than the classical linear regression analysis.


Side-channel analysis distinguisher communication channel maximum likelihood correlation power analysis uniform noise Laplacian noise 


  1. 1.
    Akkar, M.-L., Bévan, R., Dischamp, P., Moyart, D.: Power analysis, what is now possible... In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 489–502. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  2. 2.
    Chari, S., Rao, J.R., Rohatgi, P.: Template Attacks. In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 13–28. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  3. 3.
    Coron, J.-S., Kocher, P.C., Naccache, D.: Statistics and Secret Leakage. In: Frankel, Y. (ed.) FC 2000. LNCS, vol. 1962, pp. 157–173. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Doget, J., Prouff, E., Rivain, M., Standaert, F.-X.: Univariate side channel attacks and leakage modeling. J. Cryptographic Engineering 1(2), 123–144 (2011)CrossRefGoogle Scholar
  5. 5.
    Gallager, R.G.: Information theory and reliable communication. Wiley (1968)Google Scholar
  6. 6.
    Kardaun, O.J.W.F.: Classical Methods of Statistics. Springer (2005)Google Scholar
  7. 7.
    Kasper, M., Schindler, W., Stöttinger, M.: A stochastic method for security evaluation of cryptographic FPGA implementations. In: Bian, J., Zhou, Q., Athanas, P., Ha, Y., Zhao, K. (eds.) FPT, pp. 146–153. IEEE (2010)Google Scholar
  8. 8.
    Kocher, P.C., Jaffe, J., Jun, B.: Differential Power Analysis. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 388–397. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  9. 9.
    Lomné, V., Prouff, E., Roche, T.: Behind the scene of side channel attacks. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part I. LNCS, vol. 8269, pp. 506–525. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  10. 10.
    Maghrebi, H., Rioul, O., Guilley, S., Danger, J.-L.: Comparison between Side-Channel Analysis Distinguishers. In: Chim, T.W., Yuen, T.H. (eds.) ICICS 2012. LNCS, vol. 7618, pp. 331–340. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  11. 11.
    Mangard, S., Oswald, E., Standaert, F.-X.: One for All - All for One: Unifying Standard DPA Attacks. Information Security, IET 5(2), 100–111 (2011)CrossRefGoogle Scholar
  12. 12.
    Moore, J.H., Simmons, G.J.: Cycle Structure of the DES with Weak and Semi-weak Keys. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 9–32. Springer, Heidelberg (1987)CrossRefGoogle Scholar
  13. 13.
    Moradi, A., Mousavi, N., Paar, C., Salmasizadeh, M.: A Comparative Study of Mutual Information Analysis under a Gaussian Assumption. In: Youm, H.Y., Yung, M. (eds.) WISA 2009. LNCS, vol. 5932, pp. 193–205. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  14. 14.
    Nadarajah, S.: A generalized normal distribution. Journal of Applied Statistics 32(7), 685–694 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Pelgrom, M.J.M., Duinmaijer, A.C.J., Welbers, A.P.G.: Matching properties of MOS transistors. IEEE Journal of Solid State Circuits 24(5), 1433–1439 (1989)CrossRefGoogle Scholar
  16. 16.
    Prouff, E., Rivain, M.: Theoretical and practical aspects of mutual information-based side channel analysis. International Journal of Applied Cryptography (IJACT) 2(2), 121–138 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Reparaz, O., Gierlichs, B., Verbauwhede, I.: A note on the use of margins to compare distinguishers. In: COSADE, Paris, France, April 14-15. LNCS. Springer (to appear, 2014)Google Scholar
  18. 18.
    Rivain, M.: On the Exact Success Rate of Side Channel Analysis in the Gaussian Model. In: Avanzi, R.M., Keliher, L., Sica, F. (eds.) SAC 2008. LNCS, vol. 5381, pp. 165–183. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  19. 19.
    Schindler, W., Lemke, K., Paar, C.: A Stochastic Model for Differential Side Channel Cryptanalysis. In: Rao, J.R., Sunar, B. (eds.) CHES 2005. LNCS, vol. 3659, pp. 30–46. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  20. 20.
    Souissi, Y., Debande, N., Mekki, S., Guilley, S., Maalaoui, A., Danger, J.-L.: On the Optimality of Correlation Power Attack on Embedded Cryptographic Systems. In: Askoxylakis, I., Pöhls, H.C., Posegga, J. (eds.) WISTP 2012. LNCS, vol. 7322, pp. 169–178. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  21. 21.
    Standaert, F.-X., Koeune, F., Schindler, W.: How to Compare Profiled Side-Channel Attacks? In: Abdalla, M., Pointcheval, D., Fouque, P.-A., Vergnaud, D. (eds.) ACNS 2009. LNCS, vol. 5536, pp. 485–498. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  22. 22.
    Standaert, F.-X., Malkin, T.G., Yung, M.: A Unified Framework for the Analysis of Side-Channel Key Recovery Attacks. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 443–461. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  23. 23.
    Viterbi, A.J., Omura, J.K.: Principles of digital communication and coding. McGraw-Hill series in electrical engineering (2007)Google Scholar
  24. 24.
    Whitnall, C., Oswald, E.: A Fair Evaluation Framework for Comparing Side-Channel Distinguishers. J. Cryptographic Engineering 1(2), 145–160 (2011)CrossRefGoogle Scholar
  25. 25.
    Whitnall, C., Oswald, E., Standaert, F.-X.: The Myth of Generic DPA…and the Magic of Learning. In: Benaloh, J. (ed.) CT-RSA 2014. LNCS, vol. 8366, pp. 183–205. Springer, Heidelberg (2014)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Télécom ParisTech, Institut Mines-Télécom, CNRS LTCI, DepartmentParis Cedex 13France
  2. 2.Secure-IC S.A.S.RennesFrance

Personalised recommendations