A Secure and Practical CRT-Based RSA to Resist Side Channel Attacks

  • ChangKyun Kim
  • JaeCheol Ha
  • Sung-Hyun Kim
  • Seokyu Kim
  • Sung-Ming Yen
  • SangJae Moon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3043)


A secure and practical CRT-based RSA signature scheme is proposed against side channel attacks, including power analysis attack, timing attack, and fault analysis attack. The performance advantage obtained over other existing countermeasures is demonstrated. To prevent from fault attack, the proposed countermeasure employs a fault diffusion concept which is to spread the fault into the correct term during the recombination process by using CRT. This new countermeasure is also secure against differential power attack by using the message random blinding technique on RSA with CRT.


CRT DPA Fault attack RSA Side channel attack Smart card 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    den Boer, B., Lemke, K., Wieke, G.: A DPA attack against the modular reduction within a CRT implementation of RSA. In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 228–243. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  2. 2.
    Boneh, D., DeMillo, R.A., Liption, R.J.: One the important of checking cryptographic protocols for faults. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 37–51. Springer, Heidelberg (1997)Google Scholar
  3. 3.
    Coron, J.: 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
  4. 4.
    Joye, M., Lenstra, A.K., Quisquater, J.-J.: Chinese remaindering based cryptosystems in the presence of faults. Journal of Cryptology 12(4), 241–245 (1999)zbMATHCrossRefGoogle Scholar
  5. 5.
    Joye, M., Quisquater, J.-J., Bao, F., Deng, R.H.: RSA-type signatures in the presence of transient faults. In: Darnell, M.J. (ed.) Cryptography and Coding 1997. LNCS, vol. 1355, pp. 155–160. Springer, Heidelberg (1997)Google Scholar
  6. 6.
    Lenstra, A.K.: Memo on RSA signature generation in the presence of faults (September 1996) Google Scholar
  7. 7.
    Menezes, A.J., van Oorchot, P.C., Vanstone, S.A.: Handbook of applied cryptography. CRC Press, Boca Raton (1997)zbMATHGoogle Scholar
  8. 8.
    Quisquater, J.-J., Couvreur, C.: Fast decipherment algorithm for RSA public key cryptosystem. Electronics Letters 18(21), 905–907 (1982)CrossRefGoogle Scholar
  9. 9.
    Rivest, R.L., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystem. Commun. of ACM 21(2), 120–126 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    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
  11. 11.
    Shamir, A.: How to check modular exponentiation. Presented at the rump session of EUROCRYPT 1997, Konstanz, Germany (May 1997)Google Scholar
  12. 12.
    Shamir, A.: Method and apparatus for protecting public key schemes from timing and fault attacks, United States Patent 5991415, November 23 (1999) Google Scholar
  13. 13.
    Yen, S.M., Kim, S.J., Lim, S.G., Moon, S.J.: RSA speedup with residue number system immune against hardware fault cryptanalysis. In: Kim, K.-c. (ed.) ICISC 2001. LNCS, vol. 2288, pp. 397–413. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  14. 14.
    Yen, S.M., Moon, S.J., Ha, J.C.: Permanent fault attack on the parameters of RSA with CRT. In: Safavi-Naini, R., Seberry, J. (eds.) ACISP 2003. LNCS, vol. 2727, pp. 285–296. Springer, Heidelberg (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • ChangKyun Kim
    • 1
  • JaeCheol Ha
    • 2
  • Sung-Hyun Kim
    • 3
  • Seokyu Kim
    • 3
  • Sung-Ming Yen
    • 4
  • SangJae Moon
    • 1
  1. 1.School of Electrical Engineering and Computer ScienceKyungpook National Univ.DaeguKorea
  2. 2.Division of Information ScienceKorea Nazarene Univ.Cheonan, ChoongnamKorea
  3. 3.System LSI DivisionSamsung Electronics Co., Ltd.Korea
  4. 4.Dept of Computer Science and InformationEngineering National Central Univ.Chung-LiTaiwan, R.O.C.

Personalised recommendations