New Formulae for Efficient Elliptic Curve Arithmetic

  title={New Formulae for Efficient Elliptic Curve Arithmetic},
  author={H{\"u}seyin Hisil and Gary Carter and Ed Dawson},
This paper is on efficient implementation techniques of Elliptic Curve Cryptography. In particular, we improve timings for Jacobiquartic (3M+4S) and Hessian (7M+1S or 3M+6S) doubling operations. We provide a faster mixed-addition (7M+3S+1d) on modified Jacobiquartic coordinates. We introduce tripling formulae for Jacobi-quartic (4M+11S+2d), Jacobi-intersection (4M+10S+5d or 7M+7S+3d), Edwards (9M+4S) and Hessian (8M+6S+1d) forms. We show that Hessian tripling costs 6M+4C+1d for Hessian curves… CONTINUE READING
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  • D. J. Bernstein, T. Lange
  • 2007
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