Submitted Contributions

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Volume 948 of the series Lecture Notes in Computer Science pp 146-157

Date:

Fast exponentation in cryptography

  • Irina. E. BocharovaAffiliated withSt.-Petersburg Academy of Airspace Instrumentation
  • , Boris. D. KudryashovAffiliated withSt.-Petersburg Academy of Airspace Instrumentation

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Abstract

We consider the problem of minimizing the number of multiplications in computing f(x)=x n , 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.