ECC Challenges

Related Concepts

Elliptic Curve Discrete Logarithm Problem

Definition

For this section, challenges are computational problems posed to stimulate research on problems of interest. The challenges of interest here are related to the security of mechanisms based on elliptic curves.

Background

In 1997 Certicom [1] issued a series of elliptic curve discrete logarithm problem (ECDLP) challenges. Each challenge asks for the solution of an ECDLP instance in $\langle P\rangle$, where P is a point of prime order n on an elliptic curve E defined over a finite field ${\mathbb{F}}_{q}$. The difficulty of the challenge is measured by the bit length of the order n.

Applications

The challenges are of three kinds. In the following, ECCp-k denotes a randomly selected elliptic curve over a prime field; ECC2-k denotes a randomly selected elliptic curve over a characteristic two finite field ${\mathbb F}_{2^m}$, where m is prime; and ECC2K-k denotes a Koblitz curve(i.e., an elliptic curve whose...