Advertisement

Clustering Algorithms for Non-profiled Single-Execution Attacks on Exponentiations

  • Johann Heyszl
  • Andreas Ibing
  • Stefan Mangard
  • Fabrizio De Santis
  • Georg Sigl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8419)

Abstract

Most implementations of public key cryptography employ exponentiation algorithms. Side-channel attacks on secret exponents are typically bound to the leakage of single executions due to cryptographic protocols or side-channel countermeasures such as blinding. We propose for the first time, to use a well-established class of algorithms, i.e. unsupervised cluster classification algorithms such as the k-means algorithm to attack cryptographic exponentiations and recover secret exponents without any prior profiling, manual tuning or leakage models. Not requiring profiling is of significant advantage to attackers, as are well-established algorithms. The proposed non-profiled single-execution attack is able to exploit any available single-execution leakage and provides a straight-forward option to combine simultaneous measurements to increase the available leakage. We present empirical results from attacking an FPGA-based elliptic curve scalar multiplication using the \(k\)-means clustering algorithm and successfully exploit location-based leakage from high-resolution electromagnetic field measurements to achieve a low remaining brute-force complexity of the secret exponent. A simulated multi-channel measurement even enables an error-free recovery of the exponent.

Keywords

Exponentiation Side-channel attack Non-profiled Single-execution Unsupervised clustering Simultaneous measurements EM 

Notes

Acknowledgments

This work was partly funded by the German Federal Ministry of Education and Research in the project SIBASE through grant number 01IS13020.

References

  1. 1.
    Agrawal, D., Rao, J.R., Rohatgi, P.: Multi-channel attacks. In: Walter, C.D., Koç, Ç.K., Paar, C. (eds.) CHES 2003. LNCS, vol. 2779, pp. 2–16. Springer, Heidelberg (2003)Google Scholar
  2. 2.
    Amiel, F., Feix, B., Villegas, K.: Power analysis for secret recovering and reverse engineering of public key algorithms. In: Adams, C., Miri, A., Wiener, M. (eds.) SAC 2007. LNCS, vol. 4876, pp. 110–125. Springer, Heidelberg (2007) Google Scholar
  3. 3.
    Batina, L., Gierlichs, B., Lemke-Rust, K.: Differential cluster analysis. In: Clavier, C., Gaj, K. (eds.) CHES 2009. LNCS, vol. 5747, pp. 112–127. Springer, Heidelberg (2009) Google Scholar
  4. 4.
    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) Google Scholar
  5. 5.
    Bauer, S.: Attacking exponent blinding in RSA without CRT. In: Schindler, W., Huss, S.A. (eds.) COSADE 2012. LNCS, vol. 7275, pp. 82–88. Springer, Heidelberg (2012) Google Scholar
  6. 6.
    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) Google Scholar
  7. 7.
    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) Google Scholar
  8. 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) Google Scholar
  9. 9.
    Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification, 2nd edn. Wiley-Interscience, Hoboken (2001)Google Scholar
  10. 10.
    Elaabid, M.A., Meynard, O., Guilley, S., Danger, J.-L.: Combined side-channel attacks. In: Chung, Y., Yung, M. (eds.) WISA 2010. LNCS, vol. 6513, pp. 175–190. Springer, Heidelberg (2011) Google Scholar
  11. 11.
    He, W., de la Torre, E., Riesgo, T.: An interleaved EPE-Immune PA-DPL structure for resisting concentrated EM side channel attacks on FPGA implementation. In: Schindler, W., Huss, S.A. (eds.) COSADE 2012. LNCS, vol. 7275, pp. 39–53. Springer, Heidelberg (2012) Google Scholar
  12. 12.
    Heyszl, J., Mangard, S., Heinz, B., Stumpf, F., Sigl, G.: Localized electromagnetic analysis of cryptographic implementations. In: Dunkelman, O. (ed.) CT-RSA 2012. LNCS, vol. 7178, pp. 231–244. Springer, Heidelberg (2012) Google Scholar
  13. 13.
    Heyszl, J., Merli, D., Heinz, B., De Santis, F., Sigl, G.: Strengths and limitations of high-resolution electromagnetic field measurements for side-channel analysis. In: Mangard, S. (ed.) CARDIS 2012. LNCS, vol. 7771, pp. 248–262. Springer, Heidelberg (2013) Google Scholar
  14. 14.
    Itoh, K., Izu, T., Takenaka, M.: Address-bit differential power analysis of cryptographic schemes OK-ECDH and OK-ECDSA. In: Kaliski, B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 129–143. Springer, Heidelberg (2003) Google Scholar
  15. 15.
    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) Google Scholar
  16. 16.
    Lemke-Rust, K., Paar, C.: Gaussian mixture models for higher-order side channel analysis. In: Paillier, P., Verbauwhede, I. (eds.) CHES 2007. LNCS, vol. 4727, pp. 14–27. Springer, Heidelberg (2007) Google Scholar
  17. 17.
    López, J., Dahab, R.: Fast multiplication on elliptic curves over \(GF(2^{m})\) without precomputation. In: Koç, Ç.K., Paar, C. (eds.) CHES’99. LNCS, vol. 1717, pp. 316–327. Springer, Heidelberg (1999) Google Scholar
  18. 18.
    Mavroeidis, D., Batina, L., van Laarhoven, T., Marchiori, E.: PCA, eigenvector localization and clustering for side-channel attacks on cryptographic hardware devices. In: Flach, P.A., De Bie, T., Cristianini, N. (eds.) ECML PKDD 2012, Part I. LNCS, vol. 7523, pp. 253–268. Springer, Heidelberg (2012) Google Scholar
  19. 19.
    Messerges, T.S., Dabbish, E.A., Sloan, R.H.: Power analysis attacks of modular exponentiation in smartcards. In: Koç, Ç.K., Paar, C. (eds.) CHES 1999. LNCS, vol. 1717, pp. 144–157. Springer, Heidelberg (1999) Google Scholar
  20. 20.
    Perin, G., Torres, L., Benoit, P., Maurine, P.: Amplitude demodulation-based EM analysis of different RSA implementations. In: Design, Automation Test in Europe Conference Exhibition (DATE), 2012, pp. 1167–1172, Mar 2012Google Scholar
  21. 21.
    Schindler, W., Itoh, K.: Exponent blinding does not always lift (partial) SPA resistance to higher-level security. In: Lopez, J., Tsudik, G. (eds.) ACNS 2011. LNCS, vol. 6715, pp. 73–90. Springer, Heidelberg (2011) Google Scholar
  22. 22.
    Souissi, Y., Bhasin, S., Guilley, S., Nassar, M., Danger, J.-L.: Towards different flavors of combined side channel attacks. In: Dunkelman, O. (ed.) CT-RSA 2012. LNCS, vol. 7178, pp. 245–259. Springer, Heidelberg (2012) Google Scholar
  23. 23.
    Standaert, F.-X., Archambeau, C.: Using subspace-based template attacks to compare and combine power and electromagnetic information leakages. In: Oswald, E., Rohatgi, P. (eds.) CHES 2008. LNCS, vol. 5154, pp. 411–425. Springer, Heidelberg (2008) Google Scholar
  24. 24.
    Walter, C.D.: Sliding windows succumbs to big MAC attack. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 286–299. Springer, Heidelberg (2001) Google Scholar
  25. 25.
    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) Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Johann Heyszl
    • 1
  • Andreas Ibing
    • 2
  • Stefan Mangard
    • 3
  • Fabrizio De Santis
    • 2
    • 4
  • Georg Sigl
    • 2
  1. 1.Fraunhofer Institute AISECMunichGermany
  2. 2.Technische Universität MünchenMunichGermany
  3. 3.Graz University of TechnologyGrazAustria
  4. 4.Infineon Technologies AGMunichGermany

Personalised recommendations