The project is concerned with the creation and the study of new one-way trapdoor functions. This would ultimately lead to the construction of new public-key cryptosystems. The study of one-way trapdoor functions is interesting both from a theoretical and from a practical point of view. From a theoretical point of view, the research involves techniques from different parts of algebra and geometry, such as the theory of finite rings, the theory of semigroups and loops, and arithmetic algebraic geometry.
From the point of view of applications, this research could lead to new cryptographic protocols of potential interest to industry and government.
The two main research directions of the proposal are:
1) Creation and study of new public key cryptosystems
based on semigroup actions.
2) Creation and study of new algebraic geometry (AG) based