Paper 2012/122

Efficient Arithmetic on Elliptic Curves over Fields of Characteristic Three

Reza R. Farashahi, Hongfeng Wu, and Chang-An Zhao


This paper presents new explicit formulas for the point doubling, tripling and addition for Hessian curves and their equivalent Weierstrass curves over finite fields of characteristic three. The cost of basic point operations is lower than that of all previously proposed ones. The new doubling, mixed addition and tripling formulas in projective coordinates require 3M+2C, 8M+1C+1D and 4M+4C+1D respectively, where M, C and D is the cost of a field multiplication, a cubing and a multiplication by a constant. Finally, we present several examples of ordinary elliptic curves in characteristic three for high security levels.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Elliptic curveHessian curvescalar multiplicationcryptography
Contact author(s)
whfmath @ gmail com
2012-05-09: revised
2012-03-13: received
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      author = {Reza R.  Farashahi and Hongfeng Wu and Chang-An Zhao},
      title = {Efficient Arithmetic on Elliptic Curves over Fields of Characteristic Three},
      howpublished = {Cryptology ePrint Archive, Paper 2012/122},
      year = {2012},
      note = {\url{}},
      url = {}
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