Séminaire de Cryptographie

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Tanja Lange

Binary Edwards curves

The curve shape suggested by Edwards does not define elliptic curves over fields of characteristic 2. We recently generalized the concept of Edwards curves and defined binary Edwards curves. These curves offer complete addition formulas and are the first binary curves with this property. Doubling and differential addition (addition of two points with known difference, like in the Montgomery ladder) are very fast on these curves. We present the design principles behind this choice of curve shape, present the birational equivalence with Weierstrass elliptic curves and explain how to obtain fast doubling and differential addition.

This is joint work with Daniel J. Bernstein and Reza Rezaeian Farashahi.