Abstract. In this talk, based on work appearing at PQCrypto 2022, I present a new generic construction for building efficient multivariate encryption schemes. These constructions add a nonlinear modifier to multivariate schemes. This modifier disrupts the algebraic properties that are traditionally used to break multivariate schemes; however, the schemes are susceptible to an attack based on finding short vectors in a lattice related to the private key. Adding to the work presented at PQCrypto 2022 , I show how keys can be generated that appear immune from the lattice attacks due to the fact that the vectors in the related lattice are not among the shortest.