Trading Inversions for Multiplications in Elliptic Curve Cryptography |
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Authors: | Mathieu Ciet Marc Joye Kristin Lauter Peter L. Montgomery |
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Affiliation: | (1) Gemplus S.A., Card Security Group, La Vigie, Avenue du Jujubier, ZI Athélia IV, 13705 La Ciotat Cedex, France;(2) CIM-PACA, Centre de Micro-électronique de Provence – George Charpak, Avenue des Anénomes, Quartier Saint Pierre, 13120 Gardanne, France;(3) Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA |
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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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Keywords: | elliptic curves cryptography fast arithmetic radix-r decompositions affine coordinates |
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