Leakage from Montgomery Multiplication


  1. 1.
    P. D. Barrett. Implementing the Rivest Shamir Adleman public key encryption algorithm on standard digital signal processor,Advances in Cryptology – crypto ’86, pp. 311–323, Springer, 1987.Google Scholar
  2. 2.
    J.-J. Quisquater. Presentation at the rump session of Eurocrypt ’90.Google Scholar
  3. 3.
    Ç. K. Koç, T. Acar, and B. S. Kaliski, Jr. Analyzing and Comparing Montgomery Multiplication Algorithms, IEEE Micro, 16(3): 26–33, 1996.CrossRefGoogle Scholar
  4. 4.
    P. Kocher. Timing Attack on Implementations of Diffie-Hellman, RSA, DSS, and other systems, Advances in Cryptology – crypto ’96, N. Koblitz (editor), LNCS 1109, pp. 104–113, Springer-Verlag, 1996.Google Scholar
  5. 5.
    P. Kocher, J. Jaffe, and B. Jun, Differential Power Analysis, Advances in Cryptology – crypto ’99, M. Wiener (ed.), LNCS 1666, pp. 388–397, Springer-Verlag, 1999.Google Scholar
  6. 6.
    P. L. Montgomery. Modular Multiplication without Trial Division, Mathematics of Computation, 44 (170): 519–521, 1985.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    NIST/SEMATECH. Cumulative Distribution Function of the Standard Normal Distribution S1. in the “e-Handbook of Statistical Methods” at http://www.itl.nist.gov/div898/handbook/, 2006.
  8. 8.
    NIST. Digital Signature Standard, Appendix 6 (July 1999), Federal Information Processing Standard (FIPS) 186-2, Jan 2000.Google Scholar
  9. 9.
    S. E. Eldridge and C. D. Walter. Hardware Implementation of Montgomery’s Modular Multiplication Algorithm, IEEE Trans. Comp. 42: 693–699, 1993.CrossRefGoogle Scholar
  10. 10.
    C. D. Walter. Systolic Modular Multiplication, IEEE Trans. Comp. 42, 1993, 376–378.CrossRefGoogle Scholar
  11. 11.
    C. D. Walter. Montgomery Exponentiation Needs No Final Subtractions, Electronics Letters, 35 (21): 1831–1832, October 1999.CrossRefGoogle Scholar
  12. 12.
    C. D. Walter and S. Thompson. Distinguishing Exponent Digits by Observing Modular Subtractions, Topics in Cryptology – CT-RSA 2001, D. Naccache (editor), LNCS 2020, pp. 192–207, Springer-Verlag, 2001.Google Scholar
  13. 13.
    C. D. Walter. Precise Bounds for Montgomery Modular Multiplication and Some Potentially Insecure RSA Moduli, Proceedings of CT-RSA 2002, LNCS 2271, pp. 30–39, Springer-Verlag, 2002.Google Scholar
  14. 14.
    C. D. Walter. Longer Keys may facilitate Side Channel Attacks, Selected Areas in Cryptography – SAC 2003, LNCS 3006, pp. 42–57, Springer-Verlag, 2004.Google Scholar
  15. 15.
    C. D. Walter. Simple Power Analysis of Unified Code for ECC Double and Add Proceedings of CHES 2004, LNCS 3156, pp. 191–204, Springer-Verlag, 2002.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Comodo CA LtdAmerica

Personalised recommendations