Paper 2020/945

On the (in)security of ROS

Fabrice Benhamouda and Tancrède Lepoint and Michele Orrù and Mariana Raykova

Abstract

We present an algorithm solving the ROS (Random inhomogeneities in a Overdetermined Solvable system of linear equations) problem in polynomial time for large enough dimensions $\ell$. The algorithm implies polynomial-time attacks against blind signatures such as Schnorr and Okamoto--Schnorr blind signatures, threshold signatures such as the one from GJKR (when concurrent executions are allowed), and multisignatures such as CoSI and the two-round version of MuSig.