Ecc: Do we need to count?

Abstract

A prohibitive barrier faced by elliptic curve users is the difficulty of computing the curves' cardinalities. Despite recent theoretical breakthroughs, point counting still remains very cumbersome and intensively time consuming. In this paper we show that point counting can be avoided at the cost of a protocol slow-down. This slow-down factor is quite important (typically ≅ 500) but proves that the existence of secure elliptic-curve signatures is not necessarily conditioned by point counting.