Elliptic curves and their cryptographic applications

This thesis is a basic overview of elliptic curves and their applications to Cryptography. We begin with basic definitions and a demonstration that, given an elliptic curve addition, the points of an elliptic curve form a mathematical group. We then proceed to delve further into the mathematics, discussing torsion points on the group of elliptic curves before investigating the behavior of elliptic curves over finite fields wherein is given a proof of Hasse\u27s Theorem on elliptic curves. With these tools, we discuss the discrete log problem, and the connection between elliptic curves and the field of cryptography. Finally, we look at elliptic curves over C and establish a trapdoor isomorphism between elliptic curves, and a topological torus --Document

Finite semifields and nonsingular tensors

In this article, we give an overview of the classification results in the theory of finite semifields (note that this is not intended as a survey of finite semifields including a complete state of the art (see also Remark 1.10)) and elaborate on the approach using nonsingular tensors based on Liebler (Geom Dedicata 11(4):455-464, 1981)