Abstract

Due to recent advancements in quantum computing, there has been great interest in finding quantum-resistant public key encryption algorithms. Much focus has been given to lattice-based cryptosystems, as certain lattice problems appear difficult even in the quantum setting. In particular, the Learning with Errors (LWE) problem, introduced by Regev, gives a means for constructing numerous public key cryptosystems with very strong proofs of security based on the hardness of finding a short vector in a lattice. We analyze and compare the performance, in terms of memory usage and speed, of four different Learning with Errors cryptosystems: basic LWE, normal-form LWE, amortized LWE, and Ring-LWE. We show that the Ring-LWE cryptosystem obtains the greatest performance in both speed and memory usage, while the amortized LWE obtains similar encryption and decryption speed to the Ring-LWE system, but requires a much larger public key that is slow to generate. We also show that the basic LWE and normal-form LWE cryptosystems have significantly slower encryption times than the amortized LWE and Ring-LWE systems, alongside comparable memory usage to the amortized system. Additionally we analyze the decryption error rates of the four cryptosystems. We find that the basic LWE cryptosystem has a lower rate of decryption errors than the other system, and that all four systems obtain a negligible error rate if the dimension parameter of the systems are chosen to be sufficiently large.

Library of Congress Subject Headings

Cryptography; Lattice theory; Data encryption (Computer science); Quantum computing

Publication Date

6-2025

Document Type

Thesis

Student Type

Graduate

Degree Name

Applied and Computational Mathematics (MS)

Department, Program, or Center

Mathematics and Statistics, School of

College

College of Science

Advisor

Anurag Agarwal

Advisor/Committee Member

Mary Lynn Reed

Advisor/Committee Member

Manuel Lopez

Campus

RIT – Main Campus

Plan Codes

ACMTH-MS

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