Canonical liftings of Edwards curves
Tom 222 / 2026
Acta Arithmetica 222 (2026), 351-370
MSC: Primary 11G07; Secondary 11Y99
DOI: 10.4064/aa250428-5-1
Opublikowany online: 12 March 2026
Streszczenie
Twisted Edwards curves are genus $1$ curves given by equations of the form $bx^2 + y^2 = 1 + ax^2y^2$. Due to their simplified formulas for point arithmetic, they most often offer better performance in concrete applications, such as cryptography. Here we study the canonical liftings of such curves and their associated elliptic Teichmüller lifts. The coordinate functions of the latter are proved to be polynomials, and their degrees and derivatives are given. Moreover, an algorithm is described for explicit computations, and some properties of the general formulas are given.
