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Bernoulli at the Root of Horizontal Side Channel Attacks

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Smart Card Research and Advanced Applications (CARDIS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14530))

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Abstract

Vertical side-channel attacks represent a major threat to the confidentiality of enclosed secrets in hardware devices. Fortunately, countermeasures such as blinding or masking are nowadays quasi-systematically used to protect implementations of asymmetric cryptographic algorithms (RSA, ECDSA). Horizontal attacks thus constitute an interesting alternative for adversaries. They aim at recovering the secret exponent or scalar using a single trace, thus bypassing the blinding countermeasure. Several attacks have been proposed, based for instance on statistical distinguisher or clustering techniques. However, the success of these attacks relies heavily on the selection of Points of Interest (PoI) carrying leakage, extracted from acquired signals.

In this context, this work aims at providing a framework for the selection of PoI in the context of noisy traces. It is based on statistical tests applied to the distribution of each point; these tests have been derived from the analysis of noise impact on distributions. Experiments performed with this framework emphasize a gap reduction in terms of attack success rates between unsupervised and supervised attacks.

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References

  1. MbedTLS library. https://github.com/Mbed-TLS/mbedtls/

  2. Batina, L., Hogenboom, J., van Woudenberg, J.G.J.: Getting more from PCA: first results of using principal component analysis for extensive power analysis. In: Dunkelman, O. (ed.) CT-RSA 2012. LNCS, vol. 7178, pp. 383–397. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-27954-6_24

    Chapter  Google Scholar 

  3. Bauer, A., Jaulmes, E., Prouff, E., Wild, J.: Horizontal collision correlation attack on elliptic curves. In: Lange, T., Lauter, K., Lisoněk, P. (eds.) SAC 2013. LNCS, vol. 8282, pp. 553–570. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-43414-7_28

    Chapter  Google Scholar 

  4. 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). https://doi.org/10.1007/978-3-540-28632-5_2

    Chapter  Google Scholar 

  5. Chari, S., Rao, J.R., Rohatgi, P.: Template attacks. In: Kaliski, B.S., Koç, K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 13–28. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36400-5_3

    Chapter  Google Scholar 

  6. Clavier, C., Feix, B., Gagnerot, G., Roussellet, M., Verneuil, V.: Horizontal correlation analysis on exponentiation. In: Soriano, M., Qing, S., López, J. (eds.) ICICS 2010. LNCS, vol. 6476, pp. 46–61. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17650-0_5

    Chapter  Google Scholar 

  7. Clavier, C., Feix, B., Gagnerot, G., Roussellet, M., Verneuil, V.: Square always exponentiation. In: Bernstein, D.J., Chatterjee, S. (eds.) INDOCRYPT 2011. LNCS, vol. 7107, pp. 40–57. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25578-6_5

    Chapter  Google Scholar 

  8. Coron, J.-S.: Resistance against differential power analysis for elliptic curve cryptosystems. In: Koç, Ç.K., Paar, C. (eds.) CHES 1999. LNCS, vol. 1717, pp. 292–302. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48059-5_25

    Chapter  Google Scholar 

  9. Diop, I., Linge, Y., Ordas, T., Liardet, P.-Y., Maurine, P.: From theory to practice: horizontal attacks on protected implementations of modular exponentiations. J. Cryptogr. Eng. 9(1), 37 (2019)

    Article  Google Scholar 

  10. Heyszl, J., Ibing, A., Mangard, S., De Santis, F., Sigl, G.: Clustering algorithms for non-profiled single-execution attacks on exponentiations. In: Francillon, A., Rohatgi, P. (eds.) CARDIS 2013. LNCS, vol. 8419, pp. 79–93. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08302-5_6

    Chapter  Google Scholar 

  11. Johnson, D., Menezes, A., Vanstone, S.: The elliptic curve digital signature algorithm (ECDSA). Int. J. Inf. Secur. 1(1), 36–63 (2001)

    Article  Google Scholar 

  12. Kocher, P., Jaffe, J., Jun, B.: Differential power analysis. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 388–397. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48405-1_25

    Chapter  Google Scholar 

  13. Kocher, P.C.: Timing attacks on implementations of Diffie-Hellman, RSA, DSS, and other systems. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 104–113. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-68697-5_9

    Chapter  Google Scholar 

  14. Nascimento, E., Chmielewski, L.: Horizontal clustering side-channel attacks on embedded ECC implementations (extended version). Number 1204 (2017)

    Google Scholar 

  15. Perin, G., Chmielewski, Ł: A semi-parametric approach for side-channel attacks on protected RSA implementations. In: Homma, N., Medwed, M. (eds.) CARDIS 2015. LNCS, vol. 9514, pp. 34–53. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-31271-2_3

    Chapter  Google Scholar 

  16. Perin, G., Chmielewski, Ł., Batina, L., Picek, S.: Keep it unsupervised: horizontal attacks meet deep learning. IACR Trans. Cryptogr. Hardw. Embedded Syst., 343–372 (2021)

    Google Scholar 

  17. Perin, G., Imbert, L., Torres, L., Maurine, P.: Attacking randomized exponentiations using unsupervised learning. In: Prouff, E. (ed.) COSADE 2014. LNCS, vol. 8622, pp. 144–160. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10175-0_11

    Chapter  Google Scholar 

  18. Benadjila, R., Prouff, E., Strullu, R., Cagli, E., Dumas, C.: Study of deep learning techniques for side-channel analysis and introduction to ASCAD database (2018). Report Number: 053

    Google Scholar 

  19. Rivest, R.L., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21(2), 120–126 (1978)

    Article  MathSciNet  Google Scholar 

  20. Schindler, W., Walter, C.D.: Optimal recovery of secret keys from weak side channel traces. In: Parker, M.G. (ed.) IMACC 2009. LNCS, vol. 5921, pp. 446–468. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10868-6_27

    Chapter  Google Scholar 

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Correspondence to Gauthier Cler .

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Cler, G., Ordas, S., Maurine, P. (2024). Bernoulli at the Root of Horizontal Side Channel Attacks. In: Bhasin, S., Roche, T. (eds) Smart Card Research and Advanced Applications. CARDIS 2023. Lecture Notes in Computer Science, vol 14530. Springer, Cham. https://doi.org/10.1007/978-3-031-54409-5_6

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  • DOI: https://doi.org/10.1007/978-3-031-54409-5_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-54408-8

  • Online ISBN: 978-3-031-54409-5

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