Abstract
On smart-cards, Elliptic Curve Cryptosystems (ECC) can be vulnerable to Side Channel Attacks such as the Refined Power Analysis (RPA). This attack takes advantage of the apparition of special points of the form (0, y). In this paper, we propose a new countermeasure based on co-Z formulæ and an extension of the curve isomorphism countermeasure. It permits to transform the base point P = (x, y) into a base point P′ = (0, y′), which, with − P′, are the only points with a zero X-coordinate. In such case, the RPA cannot be applied. Moreover, the cost of this countermeasure is very low compared to other countermeasures against RPA.
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Akishita, T., Takagi, T.: Zero-Value Point Attacks on Elliptic Curve Cryptosystem. In: Boyd, C., Mao, W. (eds.) ISC 2003. LNCS, vol. 2851, pp. 218–233. Springer, Heidelberg (2003)
Akishita, T., Takagi, T.: On the Optimal Parameter Choice for Elliptic Curve Cryptosystems Using Isogeny. In: Bao, F., Deng, R., Zhou, J. (eds.) PKC 2004. LNCS, vol. 2947, pp. 346–359. Springer, Heidelberg (2004)
Bernstein, D.J., Lange, T.: Explicit-formulas database (2004), http://hyperelliptic.org/EFD
Brier, E., Joye, M.: Fast Point Multiplication on Elliptic Curves through Isogenies. In: Fossorier, M.P.C., Høholdt, T., Poli, A. (eds.) AAECC 2003. LNCS, vol. 2643, pp. 43–50. Springer, Heidelberg (2003)
Ciet, M., Joye, M.: (Virtually) Free Randomization Techniques for Elliptic Curve Cryptography. In: Qing, S., Gollmann, D., Zhou, J. (eds.) ICICS 2003. LNCS, vol. 2836, pp. 348–359. Springer, Heidelberg (2003)
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)
Goubin, L.: A Refined Power-Analysis Attack on Elliptic Curve Cryptosystems. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 199–211. Springer, Heidelberg (2003)
Goundar, R.R., Joye, M., Miyaji, A.: Co-Z Addition Formulæ and Binary Ladders on Elliptic Curves - (Extended Abstract). In: Mangard, S., Standaert, F.-X. (eds.) CHES 2010. LNCS, vol. 6225, pp. 65–79. Springer, Heidelberg (2010)
Goundar, R.R., Joye, M., Miyaji, A., Rivain, M., Venelli, A.: Scalar multiplication on Weierstraß elliptic curves from Co-Z arithmetic. Journal of Cryptographic Engineering 1, 161–176 (2011)
Hutter, M., Joye, M., Sierra, Y.: Memory-Constrained Implementations of Elliptic Curve Cryptography in Co-Z Coordinate Representation. In: Nitaj, A., Pointcheval, D. (eds.) AFRICACRYPT 2011. LNCS, vol. 6737, pp. 170–187. Springer, Heidelberg (2011)
Itoh, K., Izu, T., Takenaka, M.: Efficient Countermeasures against Power Analysis for Elliptic Curve Cryptosystems. In: Proceedings of CARDIS 2004, pp. 99–114. Kluwer Academic Publishers (2004)
Izu, T., Takagi, T.: Exceptional Procedure Attackon Elliptic Curve Cryptosystems. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 224–239. Springer, Heidelberg (2003)
Joye, M.: Smart-Card Implementation of Elliptic Curve Cryptography and DPA-type Attacks. In: Proceedings of CARDIS 2004, pp. 115–126. Kluwer Academic Publisher (2004)
Joye, M.: Highly Regular Right-to-Left Algorithms for Scalar Multiplication. In: Paillier, P., Verbauwhede, I. (eds.) CHES 2007. LNCS, vol. 4727, pp. 135–147. Springer, Heidelberg (2007)
Joye, M., Tymen, C.: Protections against Differential Analysis for Elliptic Curve Cryptography. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 377–390. Springer, Heidelberg (2001)
Joye, M., Yen, S.-M.: The Montgomery Powering Ladder. In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 291–302. Springer, Heidelberg (2003)
Koblitz, N.: Elliptic Curve Cryptosystems. J. Mathematics of Computation 48, 203–209 (1987)
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)
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)
Mamiya, H., Miyaji, A., Morimoto, H.: Efficient Countermeasures against RPA, DPA, and SPA. In: Joye, M., Quisquater, J.-J. (eds.) CHES 2004. LNCS, vol. 3156, pp. 343–356. Springer, Heidelberg (2004)
Meloni, N.: New Point Addition Formulae for ECC Applications. In: Carlet, C., Sunar, B. (eds.) WAIFI 2007. LNCS, vol. 4547, pp. 189–201. Springer, Heidelberg (2007)
Menezes, A.J.: Elliptic Curve Public Key Cryptosystems. Kluwer Academic Publishers (1993)
Miller, V.S.: Use of elliptic curves in cryptography. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 417–426. Springer, Heidelberg (1986)
Okeya, K., Sakurai, K.: Power Analysis Breaks Elliptic Curve Cryptosystems Even Secure against the Timing Attack. In: Roy, B., Okamoto, E. (eds.) INDOCRYPT 2000. LNCS, vol. 1977, pp. 178–190. Springer, Heidelberg (2000)
Smart, N.P.: An Analysis of Goubin’s Refined Power Analysis Attack. In: Walter, C.D., Koç, Ç.K., Paar, C. (eds.) CHES 2003. LNCS, vol. 2779, pp. 281–290. Springer, Heidelberg (2003)
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Danger, JL., Guilley, S., Hoogvorst, P., Murdica, C., Naccache, D. (2013). Low-Cost Countermeasure against RPA. In: Mangard, S. (eds) Smart Card Research and Advanced Applications. CARDIS 2012. Lecture Notes in Computer Science, vol 7771. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37288-9_8
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DOI: https://doi.org/10.1007/978-3-642-37288-9_8
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