Quantum-resilient cryptographic schemes using multivariate polynomial lattices

In the changing field of post-quantum cryptography, making digital communications immune to quantum attacks is a footstone. This paper proposes a new cryptographic platform called Multivariate Polynomial Lattices (MPL) which combines the structural hardness of lattice-based cryptography with the algebraic hardness of multivariate polynomial systems. MPL uses discrete mathematics to develop strong cryptographic primitives that are secure against classical and quantum attacks. The introduced scheme extends (beyond) currently Multivariate Polynomial Cryptography (MPC3 (d) where it involves lattice into polynomial forms, thus making attacks more difficult if not impossible for anybody but the parities of the scheme. Our method is not only immune to attacks based on algebraic and Grobner basis but also has practical performance so that it can be practically deployed and used in the real world. A full proof that MPL is secure and a full analysis of its performance are presented to show the viability and security of MPL for post-quantum cryptographic schemes. This paper emphasizes the essential nature of lattice structures based polynomial cryptography for the development of this field for securing the digital communications in the future.