Welcome to the resource topic for 2008/439
Title:
Linear equivalence between elliptic curves in Weierstrass and Hesse form
Authors: Alexander Rostovtsev
Abstract:Elliptic curves in Hesse form admit more suitable arithmetic than ones in Weierstrass form. But elliptic curve cryptosystems usually use Weierstrass form. It is known that both those forms are birationally equivalent. Birational equivalence is relatively hard to compute. We prove that elliptic curves in Hesse form and in Weierstrass form are linearly equivalent over initial field or its small extension and this equivalence is easy to compute. If cardinality of finite field q = 2 (mod 3) and Frobenius trace T = 0 (mod 3), then equivalence is defined over initial finite field. This linear equivalence allows multiplying of an elliptic curve point in Weierstrass form by passing to Hessian curve, computing product point for this curve and passing back. This speeds up the rate of point multiplication about 1,37 times.
ePrint: https://eprint.iacr.org/2008/439
See all topics related to this paper.
Feel free to post resources that are related to this paper below.
Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.
For more information, see the rules for Resource Topics .