How to manipulate curve standards: a white paper for the black hat.

This paper analyzes the cost of breaking ECC under the following assumptions: (1) ECC is using a standardized elliptic curve that was actually chosen by an attacker; (2) the attacker is aware of a vulnerability in some curves that are not publicly known to be vulnerable. This cost includes the cost of exploiting the vulnerability, but also the initial cost of computing a curve suitable for sabotaging the standard. This initial cost depends upon the acceptability used by the public to decide whether to allow a curve as a standard, and (in most cases) also upon the chance of a curve being vulnerable. This paper shows the importance of accurately modeling the actual acceptability criteria: i.e., figuring out what the public can be fooled into accepting. For example, this paper shows that plausible models of the Brainpool acceptability criteria allow the attacker to target a one-in-a-million vulnerability. Keywords: Elliptic-curve cryptography, verifiably random curves, verifiably pseudorandom curves, nothing- up-my-sleeve numbers, sabotaging standards, fighting terrorism, protecting the children