Constructing Isogenies between Elliptic Curves over Finite Fields
نویسنده
چکیده
Let E1 and E2 be ordinary elliptic curves over a finite field Fp such that #E1(Fp) = #E2(Fp). Tate’s isogeny theorem states that there is an isogeny from E1 to E2 which is defined over Fp. The goal of this paper is to describe a probabilistic algorithm for constructing such an isogeny. The algorithm proposed in this paper has exponential complexity in the worst case. Nevertheless, it is efficient in certain situations (i.e., when the class number of the endomorphism ring is small). The significance of these results to elliptic curve cryptography is discussed.
منابع مشابه
Isogenies on Edwards and Huff curves
Isogenies of elliptic curves over finite fields have been well-studied, in part because there are several cryptographic applications. Using Vélu’s formula, isogenies can be constructed explicitly given their kernel. Vélu’s formula applies to elliptic curves given by a Weierstrass equation. In this paper we show how to similarly construct isogenies on Edwards curves and Huff curves. Edwards and ...
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