Usage of lattices in fully homomorphic encryption

Pudowski, Krzysztof Jan (2023) Usage of lattices in fully homomorphic encryption. Bachelor's Thesis, Mathematics.

Preview	Text bMATH_2023_PudowskiKJ.pdf Download (3MB) | Preview
	Text Toestemming.pdf Restricted to Registered users only Download (142kB)

Abstract

Fully homomorphic encryption (FHE) is a powerful cryptographic primitive that allows computations to be performed on encrypted data without the need to decrypt it. It has numerous applications, ranging from cloud computing and data privacy to secure voting and machine learning. However, FHE is also a computationally intensive task, and efficient implementations are crucial for its practical use. In 2009, Craig Gentry introduced the first FHE scheme based on ideal lattices. The main idea behind lattice-based FHE is to use mathematical structures called lattices to construct encryption schemes that are secure against certain types of attacks. Another compelling reason to consider lattice-based cryptography is the conjured resistance to quantum algorithms, which, unlike previous, number-theoretic approaches, are not “broken”by Shor’s fast integer factorization algorithm. In this bachelor thesis, we present an introduction to lattice-based FHE, focusing on two examples: the Learning With Errors (LWE) scheme and the ring-LWE scheme. We first provide the necessary background in algebraic number theory and complexity theory, and then explain the hardness proofs for LWE and ring-LWE. Finally, we describe the bootstrapping and squashing techniques used to obtain efficient FHE schemes based on LWE and ring-LWE.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Kilicer, P. and Seri, M.
Degree programme:	Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	12 May 2023 13:00
Last Modified:	16 Apr 2025 12:52
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/29746

Actions (login required)

View Item