Fast Exponentiation with Precomputation

Extended Abstract
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 658)


In several cryptographic systems, a fixed element g of a group (generally \( \mathbb{Z}/q\mathbb{Z} \) ) is repeatedly raised to many different powers. In this paper we present a practical method of speeding up such systems, using precomputed values to reduce the number of multiplications needed. In practice this provides a substantial improvement over the level of performance that can be obtained using addition chains, and allows the computation of g n for n < N in O(log N/log log N) group multiplications. We also show how these methods can be parallelized, to compute powers in O(log log N) group multiplications with O(log N/log log N) processors.


Smart Card Modular Multiplication Binary Method Defense Advance Research Project Agency Modular Exponentiation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  1. 1.Division 1423Sandia National LaboratoriesAlbuquerque
  2. 2.Department of Computer ScienceUniversity of GeorgiaAthens
  3. 3.Department of MathematicsM.I.T.Cambridge

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