Cryptology ePrint Archive: Report 2007/310

A Note on Point Multiplication on Supersingular Elliptic Curves over Ternary Fields

Kwang Ho Kim

Abstract: Recently, the supersingular elliptic curves over ternary fields are widely used in pairing based crypto-applications since they achieve the best possible ratio between security level and space requirement. We propose new algorithms for projective arithmetic on the curves, where the point tripling is field multiplication free, and point addition and point doubling requires one field multiplication less than the known best algorithms, respectively. The algorithms combined with DBNS can lead to apparently speed up scalar multiplications on the curves.

Category / Keywords: implementation / elliptic curve cryptosystem, implementation, characteristic three, supersingular elliptic curve, point tripling, point doubling, point addition, ternary field, scalar multiplication, pairing based cryptosystem

Date: received 10 Aug 2007

Contact author: kimkhhj1980 at yahoo com cn

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Version: 20070816:120404 (All versions of this report)

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