Fast exponentation in cryptography

  • Irina. E. Bocharova
  • Boris. D. Kudryashov
Submitted Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 948)

Abstract

We consider the problem of minimizing the number of multiplications in computing f(x)=xn, where n is an integer and x is an element of any ring. We present new methods which reduce the average number of multiplications comparing with well-known methods, such as the binary method and the q-ary method. We do not compare our approach with algorithms based on addition chains since our approach is intended for cryptosystems with large exponent n and the complexity of constructing the optimal addition chain for such n is too high. We consider the binary representation for the number n and simplify exponentiation by applying ideas close to ideas exploited in data compression. Asymptotical efficiency of the new algorithms is estimated and numerical results are given.

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Irina. E. Bocharova
    • 1
  • Boris. D. Kudryashov
    • 1
  1. 1.St.-Petersburg Academy of Airspace InstrumentationSt.-PetersburgRussia

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