Date of Award

2025

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

Kottke, Christopher

Second Advisor

Serban, Vlad

Area of Concentration

Mathematics with Computer Science minor

Abstract

This paper surveys homomorphic encryption, a new field with the goal of making a practical encryption scheme in which it is possible to perform functions on data while it remains encrypted. It examines the defining algorithms and requirements of homomorphic encryption schemes, as well as types of schemes with examples, including the ElGamal and Gentry, Sahai, and Waters schemes. This survey also overviews lattices, hard problems on lattices, and hard problems based on lattice problems, upon which many homomorphic schemes base their security. It explores the shortest vector problem, the bounded-distance decoding problem, and the learning with errors problem, among others. This survey also presents a coded implementation of the Gentry, Sahai, and Waters scheme, which allows us to test the number of computations after which decryption fails for various parameters. This survey also discusses the ring learning with errors problem and fully homomorphic encryption by bootstrapping.

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