A cryptosystem based on algebraic surfaces

Abstract

This thesis discusses a cryptosystem based on algebraic surfaces, which was devised by Akiyama and Goto. At first the basics of cryptography, the P vs. NP problem and algebraic surfaces are discussed. Then the workings of the original version of the cryptosystem are explained, using a toy example to illustrate it. After that, an attack on the cryptosystem is explained, followed by a discussion of ways to resist the attack. The final part of this thesis explains the workings of an improved version of the cryptosystem, that is resistant to the attack. This explanation is also illustrated by a toy example.