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Trading Inversions for Multiplications in Elliptic Curve Cryptography

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Abstract

Recently, Eisenträger et al. proposed a very elegant method for speeding up scalar multiplication on elliptic curves. Their method relies on improved formulas for evaluating S=(2P + Q) from given points P and Q on an elliptic curve. Compared to the naive approach, the improved formulas save a field multiplication each time the operation is performed. This paper proposes a variant which is faster whenever a field inversion is more expensive than six field multiplications. We also give an improvement when tripling a point, and present a ternary/binary method to perform efficient scalar multiplication.

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Authors and Affiliations

  1. Gemplus S.A., Card Security Group, La Vigie, Avenue du Jujubier, ZI Athélia IV, 13705, La Ciotat Cedex, France

    Mathieu Ciet

  2. CIM-PACA, Centre de Micro-électronique de Provence – George Charpak, Avenue des Anénomes, Quartier Saint Pierre, 13120, Gardanne, France

    Marc Joye

  3. Microsoft Research, One Microsoft Way, Redmond, WA, 98052, USA

    Kristin Lauter & Peter L. Montgomery

Authors
  1. Mathieu Ciet
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  2. Marc Joye
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  3. Kristin Lauter
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  4. Peter L. Montgomery
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Corresponding author

Correspondence to Mathieu Ciet.

Additional information

Communicated by: A. J. Menezes

Mathieu Ciet - This work was done while the first author was with the UCL Crypto Group, Belgium (see http://www.dice.ucl.ac.be/crypto/), under Walloon region project Milos.

Marc Joye - Seconded from Gemplus.

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Ciet, M., Joye, M., Lauter, K. et al. Trading Inversions for Multiplications in Elliptic Curve Cryptography. Des Codes Crypt 39, 189–206 (2006). https://doi.org/10.1007/s10623-005-3299-y

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  • DOI: https://doi.org/10.1007/s10623-005-3299-y

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