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Profiled Attacks Against the Elliptic Curve Scalar Point Multiplication Using Neural Networks

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Network and System Security (NSS 2021)

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Abstract

In recent years, machine learning techniques have been successfully applied to improve side-channel attacks against different cryptographic algorithms. In this work, we deal with the use of neural networks to attack elliptic curve-based cryptosystems. In particular, we propose a deep learning based strategy to retrieve the scalar from a double-and-add scalar-point multiplication. As a proof of concept, we conduct an effective attack against the scalar-point multiplication on NIST standard curve P-256 implemented in BearSSL, a timing side-channel hardened public library. The experimental results show that our attack strategy allows to recover the secret scalar value with a single trace from the attacked device and an exhaustive search over a set containing a few hundreds of the sought secret.

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References

  1. Agrawal, D., Archambeault, B., Rao, J.R., Rohatgi, P.: The EM side—channel(s). In: Kaliski, B.S., Koç, K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 29–45. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36400-5_4

    Chapter  Google Scholar 

  2. Barthelmeh, J.: WolfSSL (formerly cyassl) library: a small, fast, portable implementation of TLS/SSL for embedded devices (2016). https://github.com/wolfSSL/wolfssl

  3. 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 

  4. 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 

  5. Bishop, C.: Pattern Recognition and Machine Learning. Information Science and Statistics, Springer, New York (2006)

    MATH  Google Scholar 

  6. Brumley, D., Boneh, D.: Remote timing attacks are practical. In: Proceedings of the 12th USENIX Security Symposium, Washington, D.C., USA, 4–8 August 2003, pp. 1–13. USENIX Association (2003). https://www.usenix.org/conference/12th-usenix-security-symposium/remote-timing-attacks-are-practical

  7. Cagli, E., Dumas, C., Prouff, E.: Convolutional neural networks with data augmentation against jitter-based countermeasures. In: Fischer, W., Homma, N. (eds.) CHES 2017. LNCS, vol. 10529, pp. 45–68. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66787-4_3

    Chapter  Google Scholar 

  8. Carbone, M., et al.: Deep learning to evaluate secure RSA implementations. IACR Trans. Cryptogr. Hardw. Embed. Syst. 2019(2), 132–161 (2019). https://doi.org/10.13154/tches.v2019.i2.132-161

    Article  Google Scholar 

  9. 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 

  10. Danger, J.-L., Guilley, S., Hoogvorst, P., Murdica, C., Naccache, D.: Improving the big mac attack on elliptic curve cryptography. In: Ryan, P.Y.A., Naccache, D., Quisquater, J.-J. (eds.) The New Codebreakers. LNCS, vol. 9100, pp. 374–386. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49301-4_23

    Chapter  MATH  Google Scholar 

  11. Denis, F.: The Sodium cryptography library. Libsodium (2013). https://doc.libsodium.org/

  12. Duchi, J.C., Hazan, E., Singer, Y.: Adaptive subgradient methods for online learning and stochastic optimization. In: Kalai, A.T., Mohri, M. (eds.) COLT 2010 - The 23rd Conference on Learning Theory, Haifa, Israel, 27–29 June 2010, pp. 257–269. Omnipress (2010). http://colt2010.haifa.il.ibm.com/papers/COLT2010proceedings.pdf#page=265

  13. Gandolfi, K., Mourtel, C., Olivier, F.: Electromagnetic analysis: concrete results. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 251–261. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44709-1_21

    Chapter  Google Scholar 

  14. 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). https://doi.org/10.1007/978-3-540-85053-3_27

    Chapter  Google Scholar 

  15. Gierlichs, B., Lemke-Rust, K., Paar, C.: Templates vs. stochastic methods. In: Goubin, L., Matsui, M. (eds.) CHES 2006. LNCS, vol. 4249, pp. 15–29. Springer, Heidelberg (2006). https://doi.org/10.1007/11894063_2

    Chapter  Google Scholar 

  16. Gilmore, R., Hanley, N., O’Neill, M.: Neural network based attack on a masked implementation of AES. In: IEEE International Symposium on Hardware Oriented Security and Trust, HOST 2015, Washington, DC, USA, 5–7 May 2015, pp. 106–111. IEEE Computer Society (2015). https://doi.org/10.1109/HST.2015.7140247

  17. Hanley, N., Kim, H.S., Tunstall, M.: Exploiting collisions in addition chain-based exponentiation algorithms using a single trace. In: Nyberg, K. (ed.) CT-RSA 2015. LNCS, vol. 9048, pp. 431–448. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-16715-2_23

    Chapter  MATH  Google Scholar 

  18. Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. In: Bengio, Y., LeCun, Y. (eds.) 3rd International Conference on Learning Representations, ICLR 2015, Conference Track Proceedings, San Diego, CA, USA, 7–9 May 2015 (2015). http://arxiv.org/abs/1412.6980

  19. 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 

  20. 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 

  21. Maas, A.L., Hannun, A.Y., Ng, A.Y.: Rectifier nonlinearities improve neural network acoustic models. In: ICML Workshop on Deep Learning for Audio, Speech and Language Processing (2013)

    Google Scholar 

  22. Maghrebi, H.: Assessment of common side channel countermeasures with respect to deep learning based profiled attacks. In: 31st International Conference on Microelectronics, ICM 2019, Cairo, Egypt, 15–18 December 2019, pp. 126–129. IEEE (2019). https://doi.org/10.1109/ICM48031.2019.9021728

  23. Maghrebi, H., Portigliatti, T., Prouff, E.: Breaking cryptographic implementations using deep learning techniques. In: Carlet, C., Hasan, M.A., Saraswat, V. (eds.) SPACE 2016. LNCS, vol. 10076, pp. 3–26. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-49445-6_1

    Chapter  Google Scholar 

  24. Mangard, S., Oswald, E., Popp, T.: Power Analysis Attacks - Revealing the Secrets of Smart Cards. Springer, Boston (2007). https://doi.org/10.1007/978-0-387-38162-6

    Book  MATH  Google Scholar 

  25. Masure, L., Dumas, C., Prouff, E.: A comprehensive study of deep learning for side-channel analysis. IACR Cryptology ePrint Archive 2019/439 (2019). https://eprint.iacr.org/2019/439

  26. Perin, G., Chmielewski, L., Batina, L., Picek, S.: Keep it unsupervised: horizontal attacks meet deep learning. IACR Trans. Cryptogr. Hardw. Embed. Syst. 2021(1), 343–372 (2021). https://doi.org/10.46586/tches.v2021.i1.343-372

    Article  Google Scholar 

  27. Pornin, T.: BearSSL, a smaller SSL/TLS library (2016). https://bearssl.org/index.html

  28. Poussier, R., Zhou, Y., Standaert, F.-X.: A systematic approach to the side-channel analysis of ECC implementations with worst-case horizontal attacks. In: Fischer, W., Homma, N. (eds.) CHES 2017. LNCS, vol. 10529, pp. 534–554. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66787-4_26

    Chapter  Google Scholar 

  29. Quisquater, J.J., Samyde, D.: Eddy current for magnetic analysis with active sensor. In: Proceedings of Esmart 2002, Nice, France, pp. 185–194, September 2002

    Google Scholar 

  30. Reed, R.D., Marks, R.J.: Neural Smithing: Supervised Learning in Feedforward Artificial Neural Networks. MIT Press, Cambridge (1998)

    Google Scholar 

  31. Roelofs, N., Samwel, N., Batina, L., Daemen, J.: Online template attack on ECDSA: extracting keys via the other side. In: Nitaj, A., Youssef, A. (eds.) AFRICACRYPT 2020. LNCS, vol. 12174, pp. 323–336. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-51938-4_16

    Chapter  Google Scholar 

  32. Srivastava, N., Hinton, G.E., Krizhevsky, A., Sutskever, I., Salakhutdinov, R.: Dropout: a simple way to prevent neural networks from overfitting. J. Mach. Learn. Res. 15(1), 1929–1958 (2014)

    MathSciNet  MATH  Google Scholar 

  33. Weissbart, L., Chmielewski, Ł, Picek, S., Batina, L.: Systematic side-channel analysis of Curve25519 with machine learning. J. Hardw. Syst. Secur. 4(4), 314–328 (2020). https://doi.org/10.1007/s41635-020-00106-w

    Article  Google Scholar 

  34. Weissbart, L., Picek, S., Batina, L.: One trace is all it takes: machine learning-based side-channel attack on EdDSA. In: Bhasin, S., Mendelson, A., Nandi, M. (eds.) SPACE 2019. LNCS, vol. 11947, pp. 86–105. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-35869-3_8

    Chapter  Google Scholar 

  35. Witteman, M.F., van Woudenberg, J.G.J., Menarini, F.: Defeating RSA multiply-always and message blinding countermeasures. In: Kiayias, A. (ed.) CT-RSA 2011. LNCS, vol. 6558, pp. 77–88. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19074-2_6

    Chapter  MATH  Google Scholar 

  36. Zhou, Y., Standaert, F.X.: Simplified single-trace side-channel attacks on elliptic curve scalar multiplication using fully convolutional networks. In: 40th WIC Symposium on Information Theory in the Benelux (2019). https://dial.uclouvain.be/pr/boreal/object/boreal:226275

  37. Zotkin, Y., Olivier, F., Bourbao, E.: Deep learning vs template attacks in front of fundamental targets: experimental study. IACR Cryptology ePrint Archive 2018/1213 (2018). https://eprint.iacr.org/2018/1213

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Author information

Authors and Affiliations

  1. Politecnico di Milano, Milan, Italy

    Alessandro Barenghi & Gerardo Pelosi

  2. STMicroelectronics, Agrate Brianza, Italy

    Diego Carrera, Silvia Mella, Andrea Pace & Ruggero Susella

  3. RadBoud University, Nijmegen, The Netherlands

    Silvia Mella

Authors
  1. Alessandro Barenghi
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  2. Diego Carrera
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  3. Silvia Mella
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  4. Andrea Pace
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  5. Gerardo Pelosi
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  6. Ruggero Susella
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Corresponding author

Correspondence to Gerardo Pelosi .

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Editors and Affiliations

  1. Fudan University, Shanghai, China

    Min Yang

  2. James Cook University, Townsville, QLD, Australia

    Chao Chen

  3. Nanyang Technological University, Singapore, Singapore

    Yang Liu

A Details of Double-and-Add Algorithm

A Details of Double-and-Add Algorithm

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Barenghi, A., Carrera, D., Mella, S., Pace, A., Pelosi, G., Susella, R. (2021). Profiled Attacks Against the Elliptic Curve Scalar Point Multiplication Using Neural Networks. In: Yang, M., Chen, C., Liu, Y. (eds) Network and System Security. NSS 2021. Lecture Notes in Computer Science(), vol 13041. Springer, Cham. https://doi.org/10.1007/978-3-030-92708-0_15

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  • DOI: https://doi.org/10.1007/978-3-030-92708-0_15

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