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Efficient Parallel Modular Exponentiation Algorithm

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2457))

Abstract

Modular exponentiation is fundamental to several public-key cryptography systems such as the RSA encryption system, as well as the most dominant part of the computation performed. The operation is time consuming for large operands. This paper analyses and compares the complexity of a variety of algorithms proposed to compute the modular exponentiation of a relatively large binary number, and proposes a new parallel modular exponentiation method.

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References

  1. J. Bos and M. Coster, Addition chain heuristics, Proceedings of CRYPTO’89, Lecture Notes in Computer Science 435:400–407, Springer-Verlag, 1989.

    Google Scholar 

  2. P. Downey, B. Leony and R. Sethi, Computing sequences with addition chains, SIAM Journal on Computing, 3:638–696, 1981.

    Article  Google Scholar 

  3. B.S. Kaliski Jr., The Z80180 and big-number arithmetic, Dr. Dobb’s Journal, 50:58, September 1993.

    Google Scholar 

  4. D.E. Knuth, The art of programming: seminumerical algorithms, volume 2. Reading, MA: Addison-Wesley, Second edition, 1981.

    MATH  Google Scholar 

  5. Ç.K. Koç, Analysis of sliding window techniques for exponentiation, Computers and Mathematics with Applications, 30(10):17–24, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  6. Ç.K. Koç, High speed RSA implementation, Research Report, RSA Laboratories, Version 2, California, United States of America, 1994.

    Google Scholar 

  7. Ç.K. Koç and C.Y. Hung, Adaptive m-ary segmentation and canonical recoding algorithms for multiplication of large binary numbers, Computers and Mathematics with Applications, 24(3):3–12,1992.

    Article  MATH  MathSciNet  Google Scholar 

  8. Ç.K. Koç, High-radix and bit recoding techniques for modular exponentiation, International Journal of Computer Mathematics, 40(3&4):139–156, 1991.

    Article  MATH  Google Scholar 

  9. N. Kunihiro and H. Yamamoto, Window and extended window methods for addition chain and addition-subtraction chain, IEICE Transactions, E81-A(1):72–81, January 1998.

    Google Scholar 

  10. N. Kunihiro and H. Yamamoto, New methods for generating short addition chain, IEICE Transactions, E83-A(1):60–67, January 2000.

    Google Scholar 

  11. A. Menezes, P. van Oorschot and S. Vanstone, Handbook of applied cryptography, CRC Press, 1996.

    Google Scholar 

  12. National Institute of Standards and Technology, Digital signature standard—DSS, Federal Register, 56:169, 1991.

    Google Scholar 

  13. R.L. Rivest, A. Shamir and L. Adleman, A method for obtaining digital signatures and public-key cryptosystems, Communications of the ACM, 21(2):120–126, 1978.

    Article  MATH  MathSciNet  Google Scholar 

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© 2002 Springer-Verlag Berlin Heidelberg

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Nedjah, N., de Macedo Mourelle, L. (2002). Efficient Parallel Modular Exponentiation Algorithm. In: Yakhno, T. (eds) Advances in Information Systems. ADVIS 2002. Lecture Notes in Computer Science, vol 2457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36077-8_43

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  • DOI: https://doi.org/10.1007/3-540-36077-8_43

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00009-9

  • Online ISBN: 978-3-540-36077-3

  • eBook Packages: Springer Book Archive

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