On the (in)security of ROS (original) (raw)

Paper 2020/945

On the (in)security of ROS

Tancrède Lepoint

Julian Loss

Michele Orrù

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 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.

Note: 2024-02-01: clarified that our attacks do not extend to [BL13] and [CZMS06] and improved writing

BibTeX

@misc{cryptoeprint:2020/945, author = {Fabrice Benhamouda and Tancrède Lepoint and Julian Loss and Michele Orrù and Mariana Raykova}, title = {On the (in)security of {ROS}}, howpublished = {Cryptology {ePrint} Archive, Paper 2020/945}, year = {2020}, doi = {10.1007/s00145-022-09436-0}, url = {https://eprint.iacr.org/2020/945} }