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

We present here the analysis of a new perturbation noted +̂, 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 ([12]) and UOV ([9]). We present here the best attacks that we know against these variant schemes HFE+̂− and UOV and we give practical examples of parameters for current standard of security.