Lattice-Based Cryptography and the Shortest Vector Problem

Abstract

Record ID: 243

Award(s): Excellence in Research Communication

Program Affiliation: McNair Scholars Program

Presentation Type: Podium

Abstract: Cryptography is the practice of writing and solving codes that are used to protect private information, including banking information, sensitive messages, and passwords. Due to the constant improvements to technology, cryptography is also one of the fastest improving fields in mathematics. However, for as fast as the field is changing, there is always someone capable of breaking the newly formed codes and invading the privacy of millions. Lattice-Based Cryptography has been argued as the most promising form of encryption, using the Shortest Vector Problem (SVP) as a main source of encryption. The SVP is so valuable in cryptography because it is simple to understand, yet hard to calculate. In our research, we will attempt to alter a graph from the research paper, "HAWK: Module LIP makes Lattice Signatures Fast, Compact and Simple" by Léo Ducas et al., which discusses the Shortest Vector Problem. Making alterations to the graph would increase the efficiency and running time of a contract system that calculates the shortest vector in a lattice up to 300 dimensions. Improving the efficiency of the computer program could ensure security for everyone that would be nearly impossible to crack, even in a world with quantum computers.