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Section A

An improvement of the Barrett modular reduction algorithm

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Pages 1874-1879 | Received 04 Aug 2013, Accepted 28 Oct 2013, Published online: 24 Jan 2014

References

  • P. Barrett, Implementing the Rivest Shamir and Adleman public key encryption algorithm on a standard digital signal processor, Advances in Cryptology – CRYPTO’86, Santa Barbara, CA, 11–15 August 1986, Lecture Notes in Computer Science, Vol. 263, Springer-Verlag, Heidelberg, 1987, pp. 311–323.
  • J. Carvalho, Comparative analysis of authentication schemes on a Java Card smart card, Master's diss., in the Instituto Superior Técnico of the Universidade Téchnica de Lisboa, 2011. Available at https://dspace.ist.utl.pt/bitstream/2295/1039598/1/dissertacao.pdf.
  • V. Dupaquis and A. Venelli, Redundant modular reduction algorithms, Smart Card Research and Advanced Applications – 10th IFIP WG 8.8/11.2 International Conference, CARDIS’11, Leuven, Belgium, 14–16 September 2011, Lecture Notes in Computer Science, Vol. 7079, Springer-Verlag, Heidelberg, 2011, pp. 102–114.
  • D. Hanerson, A. Menezes, and S. Vanstone, Guide to Elliptic Curve Cryptography, Springer-Verlag, New York, 2004.
  • P. Montgomery, Modular multiplication without trial division, Math. Comput. 44 (1985), pp. 519–521. doi: 10.1090/S0025-5718-1985-0777282-X
  • V. Shoup, A Computational Introduction to Number Theory and Algebra, Cambridge University Press, Cambridge, 2005.
  • E. Win, S. Mister, B. Preneel, and M. Wiener, On the performance of signature schemes based on elliptic curves, Algorithmic Number Theory, Third International Symposium, ANTS-III, Portland, Oregon, 21–25 June 1998, ecture Notes in Computer Science, Vol. 1423, Springer-Verlag, Heidelberg, 1998, pp. 252–266.

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