Paper 2020/945

On the (in)security of ROS

Fabrice Benhamouda
Tancrède Lepoint
Julian Loss
Michele Orrù
Mariana Raykova

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

Available format(s)
Cryptographic protocols
Publication info
A minor revision of an IACR publication in JOC 2022
digital signaturescryptanalysis
Contact author(s)
fabrice benhamouda @ gmail com
crypto @ tancre de
lossjulian @ gmail com
michele @ tumbolandia net
marianar @ google com
2024-02-01: last of 5 revisions
2020-07-31: received
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Creative Commons Attribution


      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},
      note = {\url{}},
      url = {}
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