Abstract
The MIST algorithm is a randomized version of the division chain exponentiation algorithm and is a side-channel countermeasure. When analyzing the MIST algorithm by ordinary simple power analysis (with only one square-multiply sequence obtained), an attacker cannot retrieve the secret exponent due to the ambiguous relationship between the square-multiply sequence and the computation. We point out the MIST algorithm is still vulnerable to simple power analysis observing multiple power consumption traces and propose a practical method with detailed steps to deduce the secret exponent from multiple square-multiply sequences. Further countermeasures such as exponent blinding are required to prevent the analysis proposed in this paper.
Some part of this research was done while Chien-Ning Chen was a postdoctoral research fellow at the National Central University. The research of Jheng-Hong Tu and Sung-Ming Yen on this work were supported by the National Science Council of the Republic of China under contract NSC 101-2221-E-008-111-MY2.
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Walter, C.D.: Exponentiation using Division Chains. IEEE Transactions on Computers 47(7) (July 1998)
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)
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)
Walter, C.D.: MIST: An Efficient, Randomized Exponentiation Algorithm for Resisting Power Analysis. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, pp. 53–66. Springer, Heidelberg (2002)
Okeya, K.: A Multiple Power Analysis Attack against Side Channel Attack Countermeasure MIST. Technical Report of IEICE, ISEC2002-104, 53–58 (2002) (in Japanese)
Walter, C.D.: Some security aspects of the MIST randomized exponentiation algorithm. In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 276–290. Springer, Heidelberg (2003)
Fouque, P.-A., Valette, F.: The Doubling Attack – Why Upwards Is Better than Downwards. In: Walter, C.D., Koç, Ç.K., Paar, C. (eds.) CHES 2003. LNCS, vol. 2779, pp. 269–280. Springer, Heidelberg (2003)
Oswald, E., Preneel, B.: A Survey on Passive Side-Channel Attacks and their Countermeasures for the NESSIE Public-Key Cryptosystems. Public Reports of the NESSIE Project (2003), https://www.cosic.esat.kuleuven.be/nessie/reports/
Sim, S.G., Park, D.J., Lee, P.J.: New Power Analysis on the Ha-Moon Algorithm and the MIST Algorithm. In: López, J., Qing, S., Okamoto, E. (eds.) ICICS 2004. LNCS, vol. 3269, pp. 291–304. Springer, Heidelberg (2004)
Chevallier-Mames, B., Ciet, M., Joye, M.: Low-Cost Solutions for Preventing Simple Side-Channel Analysis: Side-Channel Atomicity. IEEE Transaction on Computers 53(6), 760–768 (2004)
Courrège, J.-C., Feix, B., Roussellet, M.: Simple Power Analysis on Exponentiation Revisited. In: Gollmann, D., Lanet, J.-L., Iguchi-Cartigny, J. (eds.) CARDIS 2010. LNCS, vol. 6035, pp. 65–79. Springer, Heidelberg (2010)
Yen, S.-M., Lien, W.-C., Chen, C.-N.: Modified Doubling Attack by Exploiting Chosen Ciphertext of Small Order. IEICE Transactions 94-A(10), 1981–1990 (2011)
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Chen, CN., Tu, JH., Yen, SM. (2013). SPA on MIST Exponentiation Algorithm with Multiple Computational Sequences. In: Cuzzocrea, A., Kittl, C., Simos, D.E., Weippl, E., Xu, L. (eds) Security Engineering and Intelligence Informatics. CD-ARES 2013. Lecture Notes in Computer Science, vol 8128. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40588-4_16
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