Abstract
It should be difficult to extract secret keys using weak side channel leakage from embedded crypto-systems which employ standard counter-measures. Here we consider the case of key re-use with randomised exponent recoding. An optimum strategy is presented and proved, but it has the disadvantage of impracticality for realistic key sizes. Developed from the basis of an optimal decision strategy, some modified, computationally feasible versions are studied for effectiveness. This shows how to modify existing algorithms and pick their parameters for the best results.
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Brier, E., Joye, M.: Weierstraß elliptic curves and side-channel attacks. In: Naccache, D., Paillier, P. (eds.) PKC 2002. LNCS, vol. 2274, pp. 335–345. Springer, Heidelberg (2002)
Chaum, D.: Blind Signatures for Untraceable Payments. In: Chaum, D., Rivest, R.L., Sherman, A.T. (eds.) Advances in Cryptology – Crypto 1982, pp. 199–203. Plenum Press, New York (1983)
Green, P.J., Noad, R., Smart, N.: Further Hidden Markov Model Cryptanalysis. In: Rao, J.R., Sunar, B. (eds.) CHES 2005. LNCS, vol. 3659, pp. 61–74. Springer, Heidelberg (2005)
Ha, J.C., Moon, S.J.: Randomized signed-scalar multiplication of ECC to resist power attacks. In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 551–563. Springer, Heidelberg (2003)
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)
Kocher, P.C.: Timing Attack 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)
Kocher, P.C., Jaffe, J., Jun, B.: Differential Power Analysis. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 388–397. Springer, Heidelberg (1999)
Liardet, P.-Y., Smart, N.P.: Preventing SPA/DPA in ECC Systems using the Jacobi Form. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 391–401. Springer, Heidelberg (2001)
Oswald, E., Aigner, M.: Randomized Addition-Subtraction Chains as a Countermeasure against Power Attacks. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 39–50. Springer, Heidelberg (2001)
Schindler, W.: On the Optimization of Side-Channel Attacks by Advanced Stochastic Methods. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 85–103. Springer, Heidelberg (2005)
Walter, C.D.: Breaking the Liardet-Smart Randomized Exponentiation Algorithm. In: Proc. Cardis 2002, San José, November 2002, pp. 59–68. Usenix Association, Berkeley (2002)
Walter, C.D.: Issues of Security with the Oswald-Aigner Exponentiation Algorithm. In: Okamoto, T. (ed.) CT-RSA 2004. LNCS, vol. 2964, pp. 208–221. Springer, Heidelberg (2004)
Walter, C.D.: Recovering Secret Keys from Weak Side Channel Traces of Differing Lengths. In: Oswald, E., Rohatgi, P. (eds.) CHES 2008. LNCS, vol. 5154, pp. 214–227. Springer, Heidelberg (2008)
Witting, H.: Mathematische Statistik I, Teubner, Stuttgart (1985)
Yen, S.-M., Chen, C.-N., Moon, S.J., Ha, J.C.: Improvement on Ha-Moon Randomized Exponentiation Algorithm. In: Park, C.-s., Chee, S. (eds.) ICISC 2004. LNCS, vol. 3506, pp. 154–167. Springer, Heidelberg (2005)
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Schindler, W., Walter, C.D. (2009). Optimal Recovery of Secret Keys from Weak Side Channel Traces. In: Parker, M.G. (eds) Cryptography and Coding. IMACC 2009. Lecture Notes in Computer Science, vol 5921. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10868-6_27
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DOI: https://doi.org/10.1007/978-3-642-10868-6_27
Publisher Name: Springer, Berlin, Heidelberg
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