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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]

Daniel Bernstein and Tanja Lange [9] proved that two given addition formulas on twisted Edwards elliptic curves ax² +y² = 1+dxy are complete (i.e. the sum of any two points on a curve can be computed using one of these formulas). In this paper we give simple verification of completeness of these formulas using a program written in Magma, which is based on the fact that completeness means that some systems of polynomial equations have no solutions. This method may also be useful to verify completeness of additions formulas on other models of elliptic curves. [ABSTRACT FROM AUTHOR]