Paper 2015/659

Diversity and Transparency for ECC

Jean-Pierre Flori and Jérôme Plût and Jean-René Reinhard and Martin Ekerå

Abstract

Generating and standardizing elliptic curves to use them in a cryptographic context is a hard task. In this note, we don’t make an explicit proposal for an elliptic curve, but we deal with the following issues. Security: We give a list of criteria that should be satisfied by a secure elliptic curve. Although a few of these criteria are incompatible, we detail what we think are the best choices for optimal security. Transparency: We sketch a way to generate a curve in a fully transparent way so that it can be trusted and not suspected to belong to a (not publicly known to be) vulnerable class. In particular, since the computational cost of verifying the output of such a process may be quite high, we sketch out the format of a certificate that eases the computations. We think that this format might deserve being standardized.