Differential Addition in Edwards Coordinates Revisited and a Short Note on Doubling in Twisted Edwards Form
Srinivasa Rao Subramanya Rao · 2016
Cryptographic algorithms in smart cards and other constrained environments increasingly rely on Elliptic Curves and thus it is desirable to have fast algorithms for elliptic curve arithmetic. In this paper, we provide (i) faster differential addition formulae for elliptic curve arithmetic on Generalized Edwards’ Curves improving upon the currently known formulae in the literature, proposed by Justus and Loebenberger at IWSEC 2010, (ii) more efficient affine differential addition formulae for a new model of Binary Edwards Curves proposed by Wu, Tang and Feng at INDOCRYPT 2012 and (iii) an algorithm for point doubling on Twisted Edwards Curves with a smaller footprint when the implementation is desired to work across Homogeneous Projective, Inverted and Extended Homogeneous Projective Coordinates.