Physical Sciences and Mathematics Commons^™

Exploring Platform (Semi)Groups For Non-Commutative Key-Exchange Protocols, Ha Lam

Dissertations, Theses, and Capstone Projects

In this work, my advisor Delaram Kahrobaei, our collaborator David Garber, and I explore polycyclic groups generated from number fields as platform for the AAG key-exchange protocol. This is done by implementing four different variations of the length-based attack, one of the major attacks for AAG, and submitting polycyclic groups to all four variations with a variety of tests. We note that this is the first time all four variations of the length-based attack are compared side by side. We conclude that high Hirsch length polycyclic groups generated from number fields are suitable for the AAG key-exchange protocol.

Delaram Kahrobaei …

A New Public-Key Cryptosystem, Christopher James Hettinger

Theses and Dissertations

Public key cryptosystems offer important advantages over symmetric methods, but the most important such systems rely on the difficulty of integer factorization (or the related discrete logarithm problem). Advances in quantum computing threaten to render such systems useless. In addition, public-key systems tend to be slower than symmetric systems because of their use of number-theoretic algorithms. I propose a new public key system which may be secure against both classical and quantum attacks, while remaining simple and very fast. The system's action is best described in terms of linear algebra, while its security is more naturally explained in the context …

Defy: A Deniable File System For Flash Memory, Timothy M. Peters

Master's Theses

While solutions for file system encryption can prevent an adversary from determining the contents of files, in situations where a user wishes to hide even the existence of data, encryption alone is not enough. Indeed, encryption may draw attention to those files, as they most likely contain information the user wishes to keep secret, and coercion can be a very strong motivator for the owner of an encrypted file system to surrender their secret key.

Herein we present DEFY, a deniable file system designed to work exclusively with solid-state drives, particularly those found in mobile devices. Solid-state drives have unique …

Pre-Computation In Width-W Τ-Adic Naf Implementations On Koblitz Curves, William Robert Trost

Theses and Dissertations

This paper examines scalar multiplication on Koblitz curves employing the Frobenius endomorphism. We examine simple binary scalar multiplication, binary Non Adjacent Formats or NAF's, followed by τ-NAF methods. We pay particular attention to width-τ-NAF where we focus on pre-computation. We present alternative pre-computation arrangements for α_u for width sizes of 5 and 6 which are better than any previously published results since they: involve a single power of τ are based on least norms; and have a maximum of 2^{w - 2} - 1 elliptic curve operations. We then study widths of 7 and 8 producing efficient arrangements. …