Abstract
A popular effective countermeasure to protect block cipher implementations against differential power analysis (DPA) attacks is to mask the internal operations of the cryptographic algorithm with random numbers. While the masking technique resists against first-order (univariate) DPA attacks, higher-order (multivariate) attacks were able to break masked devices. In this paper, we formulate a statistical model for higher-order DPA attack. We derive an analytic success rate formula that distinctively shows the effects of algorithmic confusion property, signal-noise-ratio (SNR), and masking on leakage of masked devices. It further provides a formal proof for the centered product combination function being optimal for higher-order attacks in very noisy scenarios. We believe that the statistical model fully reveals how the higher-order attack works around masking, and would offer good insights for embedded system designers to implement masking techniques.
Chapter PDF
Similar content being viewed by others
References
Brier, E., Clavier, C., Olivier, F.: Correlation power analysis with a leakage model. In: Joye, M., Quisquater, J.-J. (eds.) CHES 2004. LNCS, vol. 3156, pp. 16–29. Springer, Heidelberg (2004)
Gierlichs, B., Batina, L., Tuyls, P., Preneel, B.: Mutual information analysis. In: Oswald, E., Rohatgi, P. (eds.) CHES 2008. LNCS, vol. 5154, pp. 426–442. Springer, Heidelberg (2008)
Chari, S., Rao, J., 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)
Gierlichs, B., Lemke-Rust, K., Paar, C.: Templates vs. stochastic methods: A performance analysis for side channel cryptanalysis. In: Goubin, L., Matsui, M. (eds.) CHES 2006. LNCS, vol. 4249, pp. 15–29. Springer, Heidelberg (2006)
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)
Chari, S., Jutla, C., Rao, J., Rohatgi, P.: A cautionary note regarding evaluation of AES candidates on smart-cards. In: Second Advanced Encryption Standard Candidate Conf., pp. 22–23 (1999)
Blömer, J., Guajardo, J., Krummel, V.: Provably secure masking of AES. In: Handschuh, H., Hasan, M.A. (eds.) SAC 2004. LNCS, vol. 3357, pp. 69–83. Springer, Heidelberg (2004)
Oswald, E., Mangard, S., Pramstaller, N., Rijmen, V.: A side-channel analysis resistant description of the AES S-box. In: Gilbert, H., Handschuh, H. (eds.) FSE 2005. LNCS, vol. 3557, pp. 413–423. Springer, Heidelberg (2005)
Canright, D., Batina, L.: A very compact “Perfectly masked” S-box for AES. In: Bellovin, S.M., Gennaro, R., Keromytis, A.D., Yung, M. (eds.) ACNS 2008. LNCS, vol. 5037, pp. 446–459. Springer, Heidelberg (2008)
Messerges, T.S.: Using second-order power analysis to attack DPA resistant software. In: Paar, C., Koç, Ç.K. (eds.) CHES 2000. LNCS, vol. 1965, pp. 238–251. Springer, Heidelberg (2000)
Joye, M., Paillier, P., Schoenmakers, B.: On second-order differential power analysis. In: Rao, J.R., Sunar, B. (eds.) CHES 2005. LNCS, vol. 3659, pp. 293–308. Springer, Heidelberg (2005)
Chari, S., Jutla, C.S., Rao, J.R., Rohatgi, P.: Towards sound approaches to counteract power-analysis attacks. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 398–412. Springer, Heidelberg (1999)
Schramm, K., Paar, C.: Higher order masking of the AES. In: Pointcheval, D. (ed.) CT-RSA 2006. LNCS, vol. 3860, pp. 208–225. Springer, Heidelberg (2006)
Gierlichs, B., Batina, L., Preneel, B., Verbauwhede, I.: Revisiting higher-order DPA attacks: In: Pieprzyk, J. (ed.) CT-RSA 2010. LNCS, vol. 5985, pp. 221–234. Springer, Heidelberg (2010)
Oswald, E., Mangard, S., Herbst, C., Tillich, S.: Practical second-order DPA attacks for masked smart card implementations of block ciphers. In: Pointcheval, D. (ed.) CT-RSA 2006. LNCS, vol. 3860, pp. 192–207. Springer, Heidelberg (2006)
Prouff, E., Rivain, M., Bevan, R.: Statistical analysis of second order differential power analysis. IEEE Trans. on Computers, 799–811 (2009)
Standaert, F.-X., Veyrat-Charvillon, N., Oswald, E., Gierlichs, B., Medwed, M., Kasper, M., Mangard, S.: The world is not enough: Another look on second-order DPA. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 112–129. Springer, Heidelberg (2010)
Prouff, E., Rivain, M.: Masking against side-channel attacks: A formal security proof. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 142–159. Springer, Heidelberg (2013)
Fei, Y., Luo, Q., Ding, A.A.: A statistical model for DPA with novel algorithmic confusion analysis. In: Prouff, E., Schaumont, P. (eds.) CHES 2012. LNCS, vol. 7428, pp. 233–250. Springer, Heidelberg (2012)
Luo, Q., Fei, Y.: Algorithmic collision analysis for evaluating cryptographic systems and side-channel attacks. In: IEEE Int. Symp. Hardware Oriented Security & Trust, pp. 75–80 (June 2011)
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)
Fischer, H.: A history of the Central Limit Theorem: From classical to modern probability theory. Springer (2011)
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)
Fei, Y., Ding, A.A., Lao, J., Zhang, L.: A statistics-based fundamental model for side-channel attack analysis. Cryptology ePrint Archive, Report 2014/152 (2014), http://eprint.iacr.org/
Thillard, A., Prouff, E., Roche, T.: Success through confidence: Evaluating the effectiveness of a side-channel attack. In: Bertoni, G., Coron, J.-S. (eds.) CHES 2013. LNCS, vol. 8086, pp. 21–36. Springer, Heidelberg (2013)
Dabosville, G., Doget, J., Prouff, E.: A new second-order side channel attack based on linear regression. IEEE Transactions on Computers 62(8), 1629–1640 (2013)
Runnalls, A.: Kullback-leibler approach to gaussian mixture reduction. IEEE Transactions on Aerospace and Electronic Systems 43(3), 989–999 (2007)
Seneta, E.: A tricentenary history of the law of large numbers. Bernoulli 19(4), 1088–1121 (2013)
Akkar, M.-L., Giraud, C.: An implementation of DES and AES, secure against some attacks. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 309–318. Springer, Heidelberg (2001)
Lewis, T.G., Payne, W.H.: Generalized feedback shift register pseudorandom number algorithm. Journal of the ACM (JACM) 20(3), 456–468 (1973)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ding, A.A., Zhang, L., Fei, Y., Luo, P. (2014). A Statistical Model for Higher Order DPA on Masked Devices. In: Batina, L., Robshaw, M. (eds) Cryptographic Hardware and Embedded Systems – CHES 2014. CHES 2014. Lecture Notes in Computer Science, vol 8731. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44709-3_9
Download citation
DOI: https://doi.org/10.1007/978-3-662-44709-3_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44708-6
Online ISBN: 978-3-662-44709-3
eBook Packages: Computer ScienceComputer Science (R0)