High Quality Content by WIKIPEDIA articles! Multivariate cryptography is the generic term for asymmetric cryptographic primitives based on multivariate polynomials over finite fields. In certain cases those polynomials could be defined over both a ground and an extension field. If the polynomials have the degree two, we talk about multivariate quadratics. Solving systems of multivariate polynomial equations is proven to be NP-Hard or NP-Complete. That`s why those schemes are often considered to be good candidates for post-quantum cryptography, once quantum computers can break the current schemes. Today multivariate quadratics could be used only to build signatures. All attempts to build a secure encryption scheme have so far failed.