Paper 2019/797

Don't forget your roots: constant-time root finding over $\mathbb{F}_{2^m}$

Douglas Martins and Gustavo Banegas and Ricardo Custodio

Abstract

In the last few years, post-quantum cryptography has received much attention. NIST is running a competition to select some post-quantum schemes as standard. As a consequence, implementations of post-quantum schemes have become important and with them side-channel attacks. In this paper, we show a timing attack on a code-based scheme which was submitted to the NIST competition. This timing attack recovers secret information because of a timing variance in finding roots in a polynomial. We present four algorithms to find roots that are protected against remote timing exploitation.