Same Value Analysis on Edwards Curves

Recently, several research groups in cryptography have presented new elliptic curve models based on Edwards curves. These new curves were selected for their good performance and security perspectives. Cryptosystems based on elliptic curves in embedded devices can be vulnerable to side-channel attacks (SCA), such as simple power analysis (SPA) or differential power analysis. In this paper, we analyze the existence of special points—whose use in SCA is known as same value analysis (SVA)—in the case of Edwards elliptic curves. These special points can be identified through a power analysis of the scalar multiplication. We show that all Edwards curves recently proposed for standardization contain some of these points and are therefore unsafe against SVA. As a countermeasure, we use the isogeny volcano approach to find SVA-secure isogenous curves to those proposed for standardization. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.