International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Improved cryptanalysis of UOV and Rainbow

Ward Beullens , imec-COSIC KU Leuven
DOI: 10.1007/978-3-030-77870-5_13 (login may be required)
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Presentation: Slides
Conference: EUROCRYPT 2021
Abstract: The contributions of this paper are twofold. First, we simplify the description of the Unbalanced Oil and Vinegar scheme (UOV) and its Rainbow variant, which makes it easier to understand the scheme and the existing attacks. We hope that this will make UOV and Rainbow more approachable for cryptanalysts. Secondly, we give two new attacks against the UOV and Rainbow signature schemes; the intersection attack that applies to both UOV and Rainbow and the rectangular MinRank attack that applies only to Rainbow. Our attacks are more powerful than existing attacks. In particular, we estimate that compared to previously known attacks, our new attacks reduce the cost of a key recovery by a factor of 2^17, 2^53, and 2^73 for the parameter sets submitted to the second round of the NIST PQC standardization project targeting the security levels I, III, and V respectively. For the third round parameters, the cost is reduced by a factor of 2^20, 2^40, and 2^55 respectively. This means all these parameter sets fall short of the security requirements set out by NIST.
Video from EUROCRYPT 2021
  title={Improved cryptanalysis of UOV and Rainbow},
  author={Ward Beullens},