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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 au2 + v2 = 1, bu2 + w2 = 1. To our knowledge such formulas were not given for this model or for the Jacobi intersection. In projective coordinates these formulas have cost 2M +2S +6D for doubling and 5M + 2S + 6D 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. [ABSTRACT FROM AUTHOR]

In this paper for elliptic curves provided by Huff's equation Ha,b: ax(y²-1 = by (x² -1) and general Huff's equation ... and degree 2 compression function f(x, y) = xy on these curves, herein we provide formulas for doubling and differential addition after compression, which for Huff's curves are as efficient as Montgomery's formulas for Montgomery's curves B y² = x³ + Ax² + x. For these curves we also provided point recovery formulas after compression, which for a point P on these curves allows to compute [n] f(P) after compression using the Montgomery ladder algorithm, and then recover [n] P. Using formulas of Moody and Shumow for computing odd degree isogenies on general Huff's curves, we have also provide formulas for computing odd degree isogenies after compression for these curves. Moreover, it is shown herein how to apply obtained formulas using compression to the ECM algorithm. [ABSTRACT FROM AUTHOR]