Compression on the Twisted Jacobi Intersection
Robert Dryło · Fundamenta Informaticae · 2021
Formulas for doubling, differential addition and point recovery after compression were given for many standard models of elliptic curves, and allow for scalar multiplication after compression using the Montgomery ladder algorithm and point recovery on a curve after this multiplication. In this paper we give such formulas for the twisted Jacobi intersection au 2 + v 2 = 1, bu 2 + w 2 = 1. To our knowledge such formulas were not given for this model or for the Jacobi intersection. In projective coordinates these formulas have cost 2 M +2 S +6 D for doubling and 5 M + 2 S + 6 D for differential addition, where M; S; D are multiplication, squaring and multiplication by constants in a field, respectively, choosing suitable curve parameters cost of D may be small.