Abstract
In the execution on a smart card, elliptic curve cryptosystems have to be secure against side channel attacks such as the simple power analysis (SPA), the differential power analysis (DPA), and the refined power analysis (RPA), and so on. MMM-algorithm proposed by Mamiya, Miyaji, and Morimoto is a scalar multiplication algorithm secure against SPA, DPA, and RPA, which can decrease the computational complexity by increasing the size of a pre-computed table. However, it provides only 4 different cases of pre-computed tables. From the practical point of view, a wider range of time-memory tradeoffs is usually desired. This paper generalizes MMM-algorithm to improve the flexibility of tables as well as the computational complexity. Our improved algorithm is secure, efficient and flexible for the storage size.
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References
Avanzi, R., Cohen, H., Doche, C., Frey, G., Lange, T., Nguyen, K., Vercauteren, F.: Handbook of Elliptic and Hyperelliptic Curve Cryptography. Chapman & Hall/CRC (2006)
Blake, I.F., Seroussi, G., Smart, N.P.: Elliptic Curves in Cryptology. In: LMS, vol. 265. Cambridge University Press, Cambridge (1999)
Ciet, M., Joye, M.: (Virtually) Free randomization technique for elliptic curve cryptography. In: Qing, S., Gollmann, D., Zhou, J. (eds.) ICICS 2003. LNCS, vol. 2836, pp. 348–359. Springer, Heidelberg (2003)
Ciet, M., Joye, M., Lauter, K., Montgomey, P.L.: Trading inversions for multiplications in elliptic curve cryptography. Designs, Codes and Cryptography 39(2), 189–206 (2006)
Cohen, H., Miyaji, A., Ono, T.: Efficient elliptic curve exponentiation. In: Han, Y., Quing, S. (eds.) ICICS 1997. LNCS, vol. 1334, pp. 282–290. Springer, Heidelberg (1997)
Cohen, H., Miyaji, A., Ono, T.: Efficient elliptic curve exponentiation using mixed coordinates. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 51–65. Springer, Heidelberg (1998)
Doche, C., Icart, T., Kohel, D.R.: Efficient scalar multiplication by isogeny decompositions. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T.G. (eds.) PKC 2006. LNCS, vol. 3958, pp. 191–206. Springer, Heidelberg (2006)
Eisenträger, K., Lauter, K., Montgomey, P.L.: Fast elliptic curve arithmetic and improved Weil pairing evaluation. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 343–354. Springer, Heidelberg (2003)
Goubin, L.: A Refined Power-Analysis Attack on Elliptic Curve Cryptosystems. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 199–210. Springer, Heidelberg (2002)
Itoh, K., Takenaka, M., Torii, N., Temma, S., Kurihara, Y.: Fast implementation of public-key cryptography on DSP TMS320C6201. In: Koç, Ç.K., Paar, C. (eds.) CHES 1999. LNCS, vol. 1717, pp. 61–72. Springer, Heidelberg (1999)
Itoh, K., Izu, T., Takenaka, M.: Efficient countermeasures against power analysis for elliptic curve cryptosystems. In: Proceedings of CARDIS 2004, pp. 99–114. Kluwer, Dordrecht (2004)
Lim, C.H., Lee, P.J.: More flexible exponentiation with precomputation. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 95–107. Springer, Heidelberg (1994)
Pippenger, N.: On the evaluation of powers and related problems (preliminary version). In: 17th annual symposium on foundations of computer science, pp. 258–263. IEEE Computer Society, Los Alamitos (1976)
Mamiya, H., Miyaji, A., Morimoto, H.: Secure elliptic curve exponentiation against RPA, ZRA, DPA, and SPA. IEICE Trans. Fundamentals E89-A(8), 2207–2215 (2006)
Mishra, P.K., Sarkar, P.: Application of Montgomery’s trick to scalar multiplication for EC and HEC using fixed base point. In: Bao, F., Deng, R., Zhou, J. (eds.) PKC 2004. LNCS, vol. 2947, pp. 41–57. Springer, Heidelberg (2004)
Möller, B.: Parallelizable elliptic curve point multiplication method with resistance against side-channel attacks. In: Chan, A.H., Gligor, V.D. (eds.) ISC 2002. LNCS, vol. 2433, pp. 402–413. Springer, Heidelberg (2002)
Montgomery, P.L.: Speeding the Pollard and elliptic curve methods for factorization. Mathematics of Computation 48, 243–264 (1987)
Standard for efficient cryptography group, specification of standards for efficient cryptography, available from: http://www.secg.org
Yen, S.M., Lien, W.C., Moon, S., Ha, J.: Power analysis by exploiting chosen message and internal collisions - Vulnerability of checking mechanism for RSA-Decryption. In: Dawson, E., Vaudenay, S. (eds.) Mycrypt 2005. LNCS, vol. 3715, pp. 183–195. Springer, Heidelberg (2005)
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Miyaji, A. (2007). Generalized MMM-Algorithm Secure Against SPA, DPA, and RPA. In: Nam, KH., Rhee, G. (eds) Information Security and Cryptology - ICISC 2007. ICISC 2007. Lecture Notes in Computer Science, vol 4817. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76788-6_23
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DOI: https://doi.org/10.1007/978-3-540-76788-6_23
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