Séminaire de Cryptographie

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Dan Bernstein

The elliptic-curve zoo

The pursuit of speed in elliptic-curve factoring and in elliptic-curve cryptography has led researchers to consider a remarkable variety of curve shapes and point representations. Tanja Lange and I have built an Explicit-Formulas Database, http://hyperelliptic.org/EFD, collecting (and sometimes correcting and often improving) the addition formulas in the literature; EFD now contains 296 computer-verified explicit addition formulas for 20 representations of points on 8 shapes of elliptic curves over large-characteristic fields. In this talk I will survey the speeds that have been obtained from several interesting curve shapes. If time permits I will also comment on characteristic 2.