Taxonomy of Public Key Schemes based on the problem of Multivariate Quadratic equations

Multivariate quadratic systems can be used to construct both secure and efficient public key schemes. In this article, we introduce the necessary mathematical tools to deal with multivariate quadratic systems, present an overview of important schemes known so far and outline how they fit into a taxonomy of only four basic schemes and some generic modifiers. Moreover, we suggest new constructions not previously considered. In this context, we propose some open problems and new research directions in the field of multivariate quadratic schemes. Cryptology ePrint Archive, Report 2005/077 http://eprint.iacr.org/ Current Version: 2005-12-15 First Revision: 2005-05-12 First Version: 2005-03-12