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Same Values Power Analysis Using Special Points on Elliptic Curves

  • Cédric Murdica
  • Sylvain Guilley
  • Jean-Luc Danger
  • Philippe Hoogvorst
  • David Naccache
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7275)

Abstract

Elliptic Curve Cryptosystems (ECC) on Smart-Cards can be vulnerable to Side Channel Attacks such as the Simple Power Analysis (SPA) or the Differential Power Analysis (DPA) if they are not carefully implemented. Goubin proposed a variant of the DPA using the point (0, y). This point is randomized neither by projective coordinates nor by isomorphic class. Akishita and Takagi extended this attack by considering not only points with a zero coordinate, but also points containing a zero value on intermediate registers during doubling and addition formulas. This attack increases the number of possible special points on elliptic curve that need a particular attention. In this paper, we introduce a new attack based on special points that show up internal collision power analysis. This attack increases more the number of possible special points on elliptic curve that need a particular attention. Like Goubin’s attack and Akishita and Takagi’s attack, our attack works if a fixed scalar is used and the attacker can chose the base point.

Keywords

Elliptic Curve Cryptosystem Differential Power Analysis Zero Value Point Attack Collision Power Analysis 

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References

  1. 1.
    Standard for Efficient Cryptography (SECG), http://www.secg.org/
  2. 2.
    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)CrossRefGoogle Scholar
  3. 3.
    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)CrossRefGoogle Scholar
  4. 4.
    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)CrossRefGoogle Scholar
  5. 5.
    Clavier, C., Feix, B., Gagnerot, G., Roussellet, M., Verneuil, V.: Improved Collision-Correlation Power Analysis on First Order Protected AES. In: Preneel, B., Takagi, T. (eds.) CHES 2011. LNCS, vol. 6917, pp. 49–62. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  6. 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)CrossRefGoogle Scholar
  7. 7.
    Fan, J., Gierlichs, B., Vercauteren, F.: To Infinity and Beyond: Combined Attack on ECC Using Points of Low Order. In: Preneel, B., Takagi, T. (eds.) CHES 2011. LNCS, vol. 6917, pp. 143–159. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  8. 8.
    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)CrossRefGoogle Scholar
  9. 9.
    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)CrossRefGoogle Scholar
  10. 10.
    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)CrossRefGoogle Scholar
  11. 11.
    Schramm, K., Wollinger, T., Paar, C.: A New Class of Collision Attacks and Its Application to DES. In: Johansson, T. (ed.) FSE 2003. LNCS, vol. 2887, pp. 206–222. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  12. 12.
    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)CrossRefGoogle Scholar
  13. 13.
    Yen, S.-M., Lien, W.-C., Moon, S.-J., Ha, J.C.: 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)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Cédric Murdica
    • 1
    • 2
  • Sylvain Guilley
    • 1
    • 2
  • Jean-Luc Danger
    • 1
    • 2
  • Philippe Hoogvorst
    • 2
  • David Naccache
    • 3
  1. 1.Secure-IC S.A.S.RennesFrance
  2. 2.Département COMELECInstitut TELECOM, TELECOM ParisTech, CNRS LTCIParisFrance
  3. 3.Ecole normale supérieure, Equipe de cryptographieParis cedex 05France

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