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Public Key Perturbation of Randomized RSA Implementations

  • Alexandre Berzati
  • Cécile Canovas-Dumas
  • Louis Goubin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6225)

Abstract

Among all countermeasures that have been proposed to thwart side-channel attacks against RSA implementations, the exponent randomization method – also known as exponent blinding – has been very early suggested by P. Kocher in 1996, and formalized by J.-S. Coron at CHES 1999. Although it has been used for a long time, some authors pointed out the fact that it does not intrinsically remove all sources of leakage. At CHES 2003, P.-A. Fouque and F. Valette devised the so-called “Doubling Attack” that can recover the blinded secret exponent from an SPA analysis. In this paper, we consider the case of fault injections. Although it was conjectured by A. Berzati et al. at CT-RSA 2009 that exponent randomization avoids fault attacks, we describe here how to recover the RSA private key under a practical fault model. Our attack belongs to the family of public key perturbations and is the first fault attack against RSA implementations with the exponent randomization countermeasure. In practice, for a 1024-bit RSA signature algorithms, the attack succeeds from about 1000 faulty signatures.

Keywords

RSA fault attacks exponent randomization/blinding public modulus 

References

  1. 1.
    Berzati, A., Canovas, C., Dumas, J.-G., Goubin, L.: Fault Attacks on RSA Public Keys: Left-To-Right Implementations are also Vulnerable. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 414–428. Springer, Heidelberg (2009)Google Scholar
  2. 2.
    Berzati, A., Canovas, C., Goubin, L.: Perturbating RSA Public Keys: an Improved Attack. In: Oswald, E., Rohatgi, P. (eds.) CHES 2008. LNCS, vol. 5154, pp. 380–395. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  3. 3.
    Biehl, I., Meyer, B., Müller, V.: Differential Fault Attacks on Ellitic Curve Cryptosystems. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 131–146. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  4. 4.
    Blömer, J., Otto, M.: Wagner’s Attack on a secure CRT-RSA Algorithm Reconsidered. In: Breveglieri, L., Koren, I., Naccache, D., Seifert, J.-P. (eds.) FDTC 2006. LNCS, vol. 4236, pp. 13–23. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. 5.
    Brier, E., Chevallier-Mames, B., Ciet, M., Clavier, C.: Why One Should Also Secure RSA Public Key Elements. In: Goubin, L., Matsui, M. (eds.) CHES 2006. LNCS, vol. 4249, pp. 324–338. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Clavier, C.: De la sécurité physique des crypto-systèmes embarqués. PhD thesis, Université de Versailles Saint-Quentin (2007)Google Scholar
  7. 7.
    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
  8. 8.
    Fouque, P.-A., Kunz-Jacques, S., Martinet, G., Muller, F., Valette, F.: Power Attack on Small RSA Public Exponent. In: Goubin, L., Matsui, M. (eds.) CHES 2006. LNCS, vol. 4249, pp. 339–353. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  9. 9.
    Fouque, P.-A., Réal, D., Valette, F., Drissi, M.: The Carry Leakage on the Randomized Exponent Countermeasure. In: Oswald, E., Rohatgi, P.P. (eds.) CHES 2008. LNCS, vol. 5154, pp. 198–213. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    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
  11. 11.
    Kocher, P.: 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
  12. 12.
    Seifert, J.-P.: On Authenticated Computing and RSA-Based Authentication. In: ACM Conference on Computer and Communications Security (CCS 2005), pp. 122–127. ACM Press, New York (2005)CrossRefGoogle Scholar
  13. 13.
    Wagner, D.: Cryptanalysis of a provably secure CRT-RSA algorithm. In: Proceedings of the 11th ACM Conference on Computer Security (CCS 2004), pp. 92–97. ACM, New York (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Alexandre Berzati
    • 1
    • 2
  • Cécile Canovas-Dumas
    • 1
  • Louis Goubin
    • 2
  1. 1.CEA-LETI/MINATECGrenoble Cedex 9France
  2. 2.Versailles Saint-Quentin-en-Yvelines UniversityVersailles CedexFrance

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