Formal Analysis of CRT-RSA Vigilant's Countermeasure Against the BellCoRe Attack: A Pledge for Formal Methods in the Field of Implementation Security

TL;DR

This paper formally analyzes Vigilant's CRT-RSA countermeasure against BellCoRe attacks, revealing flaws in the original and simplifying the repaired version, thereby demonstrating the importance of formal methods in implementation security.

Contribution

It provides the first formal analysis of Vigilant's countermeasure and its repair, identifying flaws and simplifying the solution while proving its resistance to attacks.

Findings

Original Vigilant's countermeasure is flawed.

Repaired version can be simplified further.

Formal proof confirms resistance to BellCoRe attack.

Abstract

In our paper at PROOFS 2013, we formally studied a few known countermeasures to protect CRT-RSA against the BellCoRe fault injection attack. However, we left Vigilant's countermeasure and its alleged repaired version by Coron et al. as future work, because the arithmetical framework of our tool was not sufficiently powerful. In this paper we bridge this gap and then use the same methodology to formally study both versions of the countermeasure. We obtain surprising results, which we believe demonstrate the importance of formal analysis in the field of implementation security. Indeed, the original version of Vigilant's countermeasure is actually broken, but not as much as Coron et al. thought it was. As a consequence, the repaired version they proposed can be simplified. It can actually be simplified even further as two of the nine modular verifications happen to be unnecessary. Fortunately, we could formally prove the simplified repaired version to be resistant to the BellCoRe attack, which was considered a "challenging issue" by the authors of the countermeasure themselves.