Author Type

Graduate Student

Date of Award

2006

Document Type

Dissertation

Publication Status

Version of Record

Submission Date

October 2026

Thesis/Dissertation Advisor [Chair]

Magliveras, Spyros S.

Abstract

With the publication of Shor's quantum algorithm for solving discrete logarithms in finite cyclic groups, a need for new cryptographic primitives arose; namely, for more secure primitives that would prevail in the post-quantum era. The aim of this dissertation is to exploit some hard problems arising from group theory for use in cryptography. Over the years, there have been many such proposals. We first look at two recently proposed schemes based on some form of a generalization of the discrete logari thm problem (DLP), identify their weaknesses, and cryptanalyze them. By applying the exper tise gained from the above cryptanalyses, we define our own generalization of the DLP to arbitrary finite groups. We show that such a definition leads to the design of signature schemes and pseudo-random number generators with provable security under a security assumption based on a group theoretic problem. In particular, our security assumption is based on the hardness of factorizing elements of the projective special linear group over a finite field in some representations. We construct a one-way function based on this group theoretic assumption and provide a security proof.

Extent

78 p.

Comments

Includes bibliography.|Dissertation (Ph.D.)--Florida Atlantic University, 2006.|FAU Electronic Theses and Dissertations Collection|Charles E. Schmidt College of Science|Includes bibliography.

Identifier

FA00000878

Format

pdf

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