On the (in)security of ROS

We present an algorithm solving the ROS (Random inhomogeneities in a Overdetermined Solvable system of linear equations) problem in polynomial time for l > log p dimensions. Our algorithm can be combined with Wagner’s attack, and leads to a sub-exponential solution for any dimension l with best complexity known so far. When concurrent executions are allowed, our algorithm leads to practical attacks against unforgeability of blind signature schemes such as Schnorr and Okamoto--Schnorr blind signatures, threshold signatures such as GJKR and the original version of FROST, multisignatures such as CoSI and the two-round version of MuSig, partially blind signatures such as Abe-Okamoto, and conditional blind signatures such as ZGP17.