# Public-Key Cryptography Based on Polynomial Equations

One of the challenges public-key cryptography faces is the absence of schemes that are secure as well as practical. Today, there is no provably secure public-key cryptosystem in a realistic model, and it has become difficult to compare different cryptosystems and choose the best tool to solve a given problem. Designing public-key cryptosystems based on multivariate polynomial equations problems seems promising. However, several of these cryposystems were destroyed by ad hoc attacks (e.g., Matsumoto-Imai, Hidden Field Equations, etc.).

This project aims to produce methods for assessing the security of a public-key cryposystem based on multivariate polynomial equation solving. More explicitly, a set of techniques for assessing the complexity of breaking the known-plaintext security of a given crypotsystem, and a toolset for implementing these attacks against given instances. It involves the collaborative effort of Ariel Waissbien from CoreLabs, Guillermo Matera (Universidad Nacional General Sarmiento, and CONICET) and Antonio Cafure (Universidad Nacional General Sarmiento and Universidad de Buenos Aires).