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A Bounded-Space Near-Optimal Key Enumeration Algorithm for Multi-subkey Side-Channel Attacks

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Topics in Cryptology – CT-RSA 2017 (CT-RSA 2017)

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Abstract

Enumeration of cryptographic keys in order of likelihood based on side-channel leakages has a significant importance in cryptanalysis. The best optimal-order key enumeration algorithms have a huge space complexity of \(\varOmega (n^{d/2})\) when there are d subkeys and n candidate values per subkey. In this paper, we present a parallelizable algorithm that enumerates the keys in near-optimal order but enjoys a much better space complexity of \(O(d^2w+dn)\) for a design parameter w which can be tuned to available RAM.

Before presenting our algorithm, we provide lower and upper bounds on the guessing entropy of the full key in terms of the easy-to-compute guessing entropies of the individual subkeys. We use these results to quantify the near-optimality of our algorithm’s ranking, and to bound its guessing entropy. Finally, we evaluate our algorithm through extensive simulations, to show the advantages of our new algorithm in practice, on realistic SCA scenarios. We show that our algorithm continues its near-optimal-order enumeration far beyond the rank at which the optimal algorithm fails due to insufficient memory.

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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, Berlin (2003). doi:10.1007/3-540-36400-5_4

    Chapter  Google Scholar 

  2. Anonymous: Anonymous (2015)

    Google Scholar 

  3. Bernstein, D.J., Lange, T., van Vredendaal, C.: Tighter, faster, simpler side-channel security evaluations beyond computing power. Cryptology ePrint Archive, Report 2015/221 (2015). http://eprint.iacr.org/

  4. Bogdanov, A., Kizhvatov, I., Manzoor, K., Tischhauser, E., Witteman, M.: Fast and memory-efficient key recovery in side-channel attacks. In: Dunkelman, O., Keliher, L. (eds.) SAC 2015. LNCS, vol. 9566, pp. 310–327. Springer, Cham (2016). doi:10.1007/978-3-319-31301-6_19

    Chapter  Google Scholar 

  5. 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, Berlin (2004). doi:10.1007/978-3-540-28632-5_2

    Chapter  Google Scholar 

  6. 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, Berlin (2003). doi:10.1007/3-540-36400-5_3

    Chapter  Google Scholar 

  7. David, L., Wool, A.: A bounded-space near-optimal key enumeration algorithm for multi-dimensional side-channel attacks. Cryptology ePrint Archive, Report 2015/1236 (2015). http://eprint.iacr.org/2015/1236

  8. Dichtl, M.: A new method of black box power analysis and a fast algorithm for optimal key search. J. Crypt. Eng. 1(4), 255–264 (2011)

    Article  Google Scholar 

  9. 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, Berlin (2001). doi:10.1007/3-540-44709-1_21

    Chapter  Google Scholar 

  10. Glowacz, C., Grosso, V., Poussier, R., Schüth, J., Standaert, F.-X.: Simpler and more efficient rank estimation for side-channel security assessment. In: Leander, G. (ed.) FSE 2015. LNCS, vol. 9054, pp. 117–129. Springer, Berlin (2015). doi:10.1007/978-3-662-48116-5_6

    Chapter  Google Scholar 

  11. Junod, P., Vaudenay, S.: Optimal key ranking procedures in a statistical cryptanalysis. In: Johansson, T. (ed.) FSE 2003. LNCS, vol. 2887, pp. 235–246. Springer, Berlin (2003). doi:10.1007/978-3-540-39887-5_18

    Chapter  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, Berlin (1999). doi:10.1007/3-540-48405-1_25

    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, Berlin (1996). doi:10.1007/3-540-68697-5_9

    Google Scholar 

  14. Martin, D.P., O’Connell, J.F., Oswald, E., Stam, M.: Counting keys in parallel after a side channel attack. In: Iwata, T., Cheon, J.H. (eds.) ASIACRYPT 2015. LNCS, vol. 9453, pp. 313–337. Springer, Berlin (2015). doi:10.1007/978-3-662-48800-3_13

    Chapter  Google Scholar 

  15. Meier, W., Staffelbach, O.: Analysis of pseudo random sequences generated by cellular automata. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 186–199. Springer, Berlin (1991). doi:10.1007/3-540-46416-6_17

    Google Scholar 

  16. Oren, Y., Weisse, O., Wool, A.: A new framework for constraint-based probabilistic template side channel attacks. In: Batina, L., Robshaw, M. (eds.) CHES 2014. LNCS, vol. 8731, pp. 17–34. Springer, Berlin (2014). doi:10.1007/978-3-662-44709-3_2

    Google Scholar 

  17. Pan, J., Woudenberg, J.G.J., Hartog, J.I., Witteman, M.F.: Improving DPA by peak distribution analysis. In: Biryukov, A., Gong, G., Stinson, D.R. (eds.) SAC 2010. LNCS, vol. 6544, pp. 241–261. Springer, Berlin (2011). doi:10.1007/978-3-642-19574-7_17

    Chapter  Google Scholar 

  18. Poussier, R., Grosso, V., Standaert, F.-X.: Comparing approaches to rank estimation for side-channel security evaluations. In: Homma, N., Medwed, M. (eds.) CARDIS 2015. LNCS, vol. 9514, pp. 125–142. Springer, Cham (2016). doi:10.1007/978-3-319-31271-2_8

    Chapter  Google Scholar 

  19. Poussier, R., Standaert, F.-X., Grosso, V.: Simple key enumeration (and rank estimation) using histograms: an integrated approach. In: Gierlichs, B., Poschmann, A.Y. (eds.) CHES 2016. LNCS, vol. 9813, pp. 61–81. Springer, Berlin (2016). doi:10.1007/978-3-662-53140-2_4

    Chapter  Google Scholar 

  20. Quisquater, J.-J., Samyde, D.: ElectroMagnetic analysis (EMA): measures and counter-measures for smart cards. In: Attali, I., Jensen, T. (eds.) E-smart 2001. LNCS, vol. 2140, pp. 200–210. Springer, Berlin (2001). doi:10.1007/3-540-45418-7_17

    Chapter  Google Scholar 

  21. 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, Berlin (2009). doi:10.1007/978-3-642-01001-9_26

    Chapter  Google Scholar 

  22. Veyrat-Charvillon, N., Gérard, B., Renauld, M., Standaert, F.-X.: An optimal key enumeration algorithm and its application to side-channel attacks. In: Knudsen, L.R., Wu, H. (eds.) SAC 2012. LNCS, vol. 7707, pp. 390–406. Springer, Berlin (2013). doi:10.1007/978-3-642-35999-6_25

    Chapter  Google Scholar 

  23. Veyrat-Charvillon, N., Gérard, B., Standaert, F.-X.: Security evaluations beyond computing power. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 126–141. Springer, Berlin (2013). doi:10.1007/978-3-642-38348-9_8

    Chapter  Google Scholar 

  24. Ye, X., Eisenbarth, T., Martin, W.: Bounded, yet sufficient? how to determine whether limited side channel information enables key recovery. In: Joye, M., Moradi, A. (eds.) CARDIS 2014. LNCS, vol. 8968, pp. 215–232. Springer, Cham (2015). doi:10.1007/978-3-319-16763-3_13

    Google Scholar 

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Authors and Affiliations

  1. School of Electrical Engineering, Tel Aviv University, 69978, Ramat Aviv, Israel

    Liron David & Avishai Wool

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  1. Liron David
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  2. Avishai Wool
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Correspondence to Liron David or Avishai Wool .

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Editors and Affiliations

  1. Cryptography Research Inc. , San Francisco, California, USA

    Helena Handschuh

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David, L., Wool, A. (2017). A Bounded-Space Near-Optimal Key Enumeration Algorithm for Multi-subkey Side-Channel Attacks. In: Handschuh, H. (eds) Topics in Cryptology – CT-RSA 2017. CT-RSA 2017. Lecture Notes in Computer Science(), vol 10159. Springer, Cham. https://doi.org/10.1007/978-3-319-52153-4_18

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  • DOI: https://doi.org/10.1007/978-3-319-52153-4_18

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  • Print ISBN: 978-3-319-52152-7

  • Online ISBN: 978-3-319-52153-4

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