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Low-Cost Countermeasure against RPA

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Smart Card Research and Advanced Applications (CARDIS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7771))

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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References

  1. 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)

    Chapter  Google Scholar 

  2. 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)

    Chapter  Google Scholar 

  3. Bernstein, D.J., Lange, T.: Explicit-formulas database (2004), http://hyperelliptic.org/EFD

  4. 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)

    Chapter  Google Scholar 

  5. 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)

    Chapter  Google Scholar 

  6. 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)

    Chapter  Google Scholar 

  7. 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)

    Chapter  Google Scholar 

  8. 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)

    Chapter  Google Scholar 

  9. 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)

    Article  Google Scholar 

  10. 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)

    Chapter  Google Scholar 

  11. 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)

    Google Scholar 

  12. 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)

    Chapter  Google Scholar 

  13. 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)

    Google Scholar 

  14. 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)

    Chapter  Google Scholar 

  15. 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)

    Chapter  Google Scholar 

  16. 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)

    Chapter  Google Scholar 

  17. Koblitz, N.: Elliptic Curve Cryptosystems. J. Mathematics of Computation 48, 203–209 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  18. 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 

  19. 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)

    Chapter  Google Scholar 

  20. 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)

    Chapter  Google Scholar 

  21. 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)

    Chapter  Google Scholar 

  22. Menezes, A.J.: Elliptic Curve Public Key Cryptosystems. Kluwer Academic Publishers (1993)

    Google Scholar 

  23. 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)

    Google Scholar 

  24. 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)

    Chapter  Google Scholar 

  25. 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)

    Chapter  Google Scholar 

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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

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37287-2

  • Online ISBN: 978-3-642-37288-9

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