Paper 2022/203

A New Perturbation for Multivariate Public Key Schemes such as HFE and UOV

Jean-Charles Faugère, Gilles macario-Rat, Jacques Patarin, and Ludovic Perret


We present here the analysis of a new perturbation, that seems to strengthen significantly the security of some families of multivariate schemes. Thanks to this new perturbation, we are indeed able to get interestingly efficient signature and encryption public key schemes, in particular when combining this perturbation to the well known trapdoors HFE and UOV. We present here the best attacks that we know against these variant schemes and we give practical examples of parameters for current standard of security.

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Publication info
Preprint. MINOR revision.
public-key cryptographypost-quantum multivariate cryptographyUOVHFEGröbner basisMinRank problemdifferential attacks
Contact author(s)
gilles macariorat @ orange com
jpatarin @ club-internet fr
ludovic perret @ cryptonext-security com
jcf @ cryptonext-security com
2022-03-19: last of 4 revisions
2022-02-20: received
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      author = {Jean-Charles Faugère and Gilles macario-Rat and Jacques Patarin and Ludovic Perret},
      title = {A New Perturbation for Multivariate Public Key Schemes such as HFE and UOV},
      howpublished = {Cryptology ePrint Archive, Paper 2022/203},
      year = {2022},
      note = {\url{}},
      url = {}
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