Two is the fastest prime: lambda coordinates for binary elliptic curves

  title={Two is the fastest prime: lambda coordinates for binary elliptic curves},
  author={Thomaz Oliveira and Julio L{\'o}pez Hernandez and Diego F. Aranha and Francisco Rodr{\'i}guez-Henr{\'i}quez},
  journal={Journal of Cryptographic Engineering},
In this work, we present new arithmetic formulas for a projective version of the affine point representation $$(x,x+y/x),$$ ( x , x + y / x ) , for $$x\ne 0,$$ x ≠ 0 , which leads to an efficient computation of the scalar multiplication operation over binary elliptic curves. A software implementation of our formulas applied to a binary Galbraith–Lin–Scott elliptic curve defined over the field $$\mathbb {F}_{2^{254}}$$ F 2 254 allows us to achieve speed records for protected/unprotected single… CONTINUE READING
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