Abstract
Belief propagation, or the sum-product algorithm, is a powerful and well known method for inference on probabilistic graphical models, which has been proposed for the specific use in side channel analysis by Veyrat-Charvillon et al. [14].
We define a novel metric to capture the importance of variable nodes in factor graphs, we propose two improvements to the sum-product algorithm for the specific use case in side channel analysis, and we explicitly define and examine different ways of combining information from multiple side channel traces. With these new considerations we systematically investigate a number of graphical models that “naturally” follow from an implementation of AES. Our results are unexpected: neither a larger graph (i.e. more side channel information) nor more connectedness necessarily lead to significantly better attacks. In fact our results demonstrate that in practice the (on balance) best choice is to utilise an acyclic graph in an independent graph combination setting, which gives us provable convergence to the correct key distribution. We provide evidence using both extensive simulations and a final confirmatory analysis on real trace data.
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Notes
- 1.
A factor graph can also be constructed for non-iterative functions but this is not necessary for our work.
References
Banciu, V., Oswald, E.: Pragmatism vs. elegance: comparing two approaches to simple power attacks on AES. In: Constructive Side-Channel Analysis and Secure Design - 5th International Workshop, COSADE 2014, Paris, France, 13–15 April 2014, Revised Selected Papers, pp. 29–40 (2014)
Green, J., Roy, A., Oswald, E.: A systematic study of the impact of graphical models on inference-based attacks on AES. Cryptology ePrint Archive, Report 2018/671 (2018). https://eprint.iacr.org/2018/671
Green, P.J., Noad, R., Smart, N.P.: Further hidden markov model cryptanalysis. In: Rao, J.R., Sunar, B. (eds.) CHES 2005. LNCS, vol. 3659, pp. 61–74. Springer, Heidelberg (2005). https://doi.org/10.1007/11545262_5
Grosso, V., Standaert, F.-X.: ASCA, SASCA and DPA with enumeration: which one beats the other and when? In: Iwata, T., Cheon, J.H. (eds.) ASIACRYPT 2015. LNCS, vol. 9453, pp. 291–312. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48800-3_12
Grosso, V., Standaert, F.-X.: Masking proofs are tight (and how to exploit it in security evaluations). Cryptology ePrint Archive, Report 2017/116 (2017). http://eprint.iacr.org/2017/116
Karlof, C., Wagner, D.: Hidden markov model cryptanalysis. In: Walter, C.D., Koç, Ç.K., Paar, C. (eds.) CHES 2003. LNCS, vol. 2779, pp. 17–34. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45238-6_3
MacKay, D.J.C.: Information Theory, Inference, and Learning Algorithms. Cambridge University Press, New York (2003)
Mangard, S.: A simple power-analysis (SPA) attack on implementations of the AES key expansion. In: Lee, P.J., Lim, C.H. (eds.) ICISC 2002. LNCS, vol. 2587, pp. 343–358. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36552-4_24
Martin, D.P., Mather, L., Oswald, E., Stam, M.: Characterisation and estimation of the key rank distribution in the context of side channel evaluations. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10031, pp. 548–572. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53887-6_20
McCann, D., Oswald, E., Whitnall, C.: Towards practical tools for side channel aware software engineering: ‘grey box’ modelling for instruction leakages. In: 26th USENIX Security Symposium, USENIX Security 2017, Vancouver, BC, Canada, 16–18 August 2017, pp. 199–216 (2017)
Mezard, M., Montanari, A.: Information, Physics, and Computation. Oxford University Press Inc., New York (2009)
Oswald, E.: Enhancing simple power-analysis attacks on elliptic curve cryptosystems. In: Kaliski, B.S., Koç, K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 82–97. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36400-5_8
Primas, R., Pessl, P., Mangard, S.: Single-trace side-channel attacks on masked lattice-based encryption. In: Fischer, W., Homma, N. (eds.) CHES 2017. LNCS, vol. 10529, pp. 513–533. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66787-4_25
Veyrat-Charvillon, N., Gérard, B., Standaert, F.-X.: Soft analytical side-channel attacks. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8873, pp. 282–296. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-45611-8_15
Acknowledgements
Joey Green has been funded by an NCSC studentship. Arnab Roy and Elisabeth Oswald were funded in part by EPSRC under grant agreement EP/N011635/1 (LADA) and the ERC via the grant SEAL (Project Reference 725042).
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Appendix
Appendix
Factor graph representing the computation of a column in the first round of AES FURIOUS. (Color figure online)
Graph combination methods using graphs \(G_1\) and \(G_{1}^{A}\), SNR \(2^{-1}\)
Graph combination methods using graphs \(G_1\) and \(G_{1}^{A}\), SNR \(2^{-6}\)
Reduced graph comparison using SNRs \(2^{-1}\) and \(2^{-6}\) respectively
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Green, J., Roy, A., Oswald, E. (2019). A Systematic Study of the Impact of Graphical Models on Inference-Based Attacks on AES. In: Bilgin, B., Fischer, JB. (eds) Smart Card Research and Advanced Applications. CARDIS 2018. Lecture Notes in Computer Science(), vol 11389. Springer, Cham. https://doi.org/10.1007/978-3-030-15462-2_2
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