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Computing isogenies between Montgomery curves using the action of (0,0)
Velu's formulas Montgomery form 2-isogenies
2017/12/19
A recent paper by Costello and Hisil at Asiacrypt'17 presents efficient formulas for computing isogenies with odd-degree cyclic kernels on Montgomery curves. We provide a constructive proof of a gener...
Montgomery curves and the Montgomery ladder
Montgomery curves Montgomery ladder Edwards curves
2017/4/5
The Montgomery ladder is a remarkably simple method of computing scalar multiples of points on a broad class of elliptic curves. This article surveys a wide range of topics related to the Montgomery l...
Montgomery curves and their arithmetic: The case of large characteristic fields
Montgomery curve Montgomery ladder elliptic curve cryptography
2017/3/6
Three decades ago, Montgomery introduced a new elliptic curve model for use in Lenstra's ECM factorization algorithm. Since then, his curves and the algorithms associated with them have become foundat...