Cryptology ePrint Archive: Report 2022/203

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

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

Abstract: 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.

Category / Keywords: public-key cryptography, post-quantum multivariate cryptography, UOV, HFE, Gröbner basis, MinRank problem, differential attacks

Date: received 18 Feb 2022, last revised 19 Mar 2022

Contact author: gilles macariorat at orange com, jpatarin at club-internet fr, ludovic perret at cryptonext-security com, jcf at cryptonext-security com

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Version: 20220319:132426 (All versions of this report)

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