Summary: We present here new multivariate schemes that can be seen as HFE generalization having a property called “Two-Face”. Particularly, we present five such families of algorithms named “Dob”, “Simple Pat”, “General Pat”, “Mac”, and “Super Two-Face”. These families have connections between them, some of them are refinements or generalizations of others. Notably, some of these schemes can be used for public key encryption, and some for public key signature. We introduce also new multivariate quadratic permutations that may have interest beyond cryptography.
For the entire collection see [Zbl 1387.94004].