View All Items

Title: Solving approximate SVP in an Ideal Lattice using a cluster.
Creator: Khadka, Bal K., Magliveras, Spyros S., Graduate College
Abstract/Description: The shortest vector problem SVP is de ned as follows: For a given basis B of an integral lattice L fi nd a vector v in L whose length is minimal. Here we present the result of our experiments based on a hill climbing algorithm using a computer cluster and a number of parallel executions of a standard basis reduction technique, such as LLL, to successfully reduce an initial basis of L. We begin by reducing ideal lattices of relatively small dimension and progressively reduce ideal lattices of...
Show moreThe shortest vector problem SVP is de ned as follows: For a given basis B of an integral lattice L fi nd a vector v in L whose length is minimal. Here we present the result of our experiments based on a hill climbing algorithm using a computer cluster and a number of parallel executions of a standard basis reduction technique, such as LLL, to successfully reduce an initial basis of L. We begin by reducing ideal lattices of relatively small dimension and progressively reduce ideal lattices of higher dimension, beating several earlier published solutions to the approximate SVP problem.
Show less
Date Issued: 2014
PURL: http://purl.flvc.org/fau/fd/FA00005827
Format: Document (PDF)

Title: Defeating p-attack in non-abelian discrete logarithm problem.
Creator: Magar, Krishna Thapa, Ilic, Ivana, Magliveras, Spyros S., Graduate College
Date Issued: 2013-04-12
PURL: http://purl.flvc.org/fcla/dt/3361325
Subject Headings: Non-Abelian groups, Logarithms
Format: Document (PDF)

Title: New LS[3][2,3,2^8] Geometric Large Sets.
Creator: Hurley, Michael Robert, Khadka, Bal K., Magliveras, Spyros S., Graduate College
Abstract/Description: Let V be an n-dimensional vector space over the field of q elements. By a geometric t-[qn,k,λ] design we mean a collection D of k-dimensional subspaces if V, called blocks, such that every tdimensional subspace T of V appears in exactly λ blocks in D. In a recent paper Braun, Kohnert, Ӧstergård, and Wassermann constructed the first ever known large set LS[N][2,k,qn], namely an LS[3][2,3,28] under a cyclic group G of order 255. In this work we construct an additional 8 large sets with the same...
Show moreLet V be an n-dimensional vector space over the field of q elements. By a geometric t-[qn,k,λ] design we mean a collection D of k-dimensional subspaces if V, called blocks, such that every tdimensional subspace T of V appears in exactly λ blocks in D. In a recent paper Braun, Kohnert, Ӧstergård, and Wassermann constructed the first ever known large set LS[N][2,k,qn], namely an LS[3][2,3,28] under a cyclic group G of order 255. In this work we construct an additional 8 large sets with the same parameters, using the L3 algorithm for lattice basis-reduction.
Show less
Date Issued: 2015
PURL: http://purl.flvc.org/fau/fd/FA00005885
Format: Document (PDF)

Title: Enhanced 1-D chaotic key-based algorithm for image encryption.
Creator: Furht, Borko, Socek, Daniel, Magliveras, Spyros S.
Abstract/Description: A recently proposed Chaotic-Key Based Algorithm (CKBA) has been shown to be unavoidably susceptible to chosen/known-plaintext attacks and ciphertext-only attacks. In this paper we enhance the CKBA algorithm three-fold: 1) we change the 1-D chaotic Logistic map to a piecewise linear chaotic map (PWLCM) to improve the balance property, 2) we increase the key size to 128 bits, and 3) we add two more cryptographic primitives and extend the scheme to operate on multiple rounds so that the chosen...
Show moreA recently proposed Chaotic-Key Based Algorithm (CKBA) has been shown to be unavoidably susceptible to chosen/known-plaintext attacks and ciphertext-only attacks. In this paper we enhance the CKBA algorithm three-fold: 1) we change the 1-D chaotic Logistic map to a piecewise linear chaotic map (PWLCM) to improve the balance property, 2) we increase the key size to 128 bits, and 3) we add two more cryptographic primitives and extend the scheme to operate on multiple rounds so that the chosen/knownplaintext attacks are no longer possible. The new cipher has much stronger security and its performance characteristics remain very good.
Show less
Date Issued: 2004-11-22
PURL: http://purl.flvc.org/fcla/dt/358402
Subject Headings: Data encryption (Computer science), Computer algorithm, Mulitmedia systems --Security measures.
Format: Document (PDF)

Title: Covering Small Alternating Groups with Proper Subgroups.
Creator: Epstein, Michael, Kappe, Luise-Charlotte, Magliveras, Spyros S., Graduate College, Popova, Daniela
Abstract/Description: Any group with a finite noncyclic homomorphic image is a finite union of proper subgroups. Given such a group G, we define the covering number of G to be the least positive integer m such that G is the union of m proper subgroups. We present recent results on the determination of the covering numbers of the alternating groups on nine and eleven letters.
Date Issued: 2015
PURL: http://purl.flvc.org/fau/fd/FA00005874
Format: Document (PDF)

Title: Deterministic and non-deterministic basis reduction techniques for NTRU lattices.
Creator: Socek, Daniel, Florida Atlantic University, Magliveras, Spyros S.
Abstract/Description: Finding the shortest or a "short enough" vector in an integral lattice of substantial dimension is a difficult problem. The problem is not known to be but most people believe it is [7]. The security of the newly proposed NTRU cryptosystem depends solely on this fact. However, by the definition NTRU lattices possess a certain symmetry. This suggests that there may be a way of taking advantage of this symmetry to enable a new cryptanalytical approach in combination with existing good lattice...
Show moreFinding the shortest or a "short enough" vector in an integral lattice of substantial dimension is a difficult problem. The problem is not known to be but most people believe it is [7]. The security of the newly proposed NTRU cryptosystem depends solely on this fact. However, by the definition NTRU lattices possess a certain symmetry. This suggests that there may be a way of taking advantage of this symmetry to enable a new cryptanalytical approach in combination with existing good lattice reduction algorithms. The aim of this work is to exploit the symmetry inherent in NTRU lattices to design a non-deterministic algorithm for improving basis reduction techniques for NTRU lattices. We show how the non-trivial cyclic automorphism of an NTRU lattice enables further reduction. Our approach combines the recently published versions of the famous LLL algorithm for lattice basis reduction with our automorphism utilization techniques.
Show less
Date Issued: 2002
PURL: http://purl.flvc.org/fcla/dt/12933
Subject Headings: Cryptography, Lattice theory, Algorithms
Format: Document (PDF)

Title: New approaches to encryption and steganography for digital videos.
Creator: Furht, Borko, Socek, Daniel, Kalva, Hari, Magliveras, Spyros S., Marques, Oge, Culibrk, Dubravko
Date Issued: 2007
PURL: http://purl.flvc.org/fcla/dt/337435
Subject Headings: Multimedia systems --Security measures., Digital video., Digital watermarking., Data encryption (Computer science) --Technological innovations., Cryptography.
Format: Document (PDF)

Title: Computing automorphism groups of projective planes.
Creator: Adamski, Jesse Victor, Magliveras, Spyros S., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: The main objective of this thesis was to find the full automorphism groups of finite Desarguesian planes. A set of homologies were used to generate the automorphism group when the order of the plane was prime. When the order was a prime power Pa,a ≠ 1 the Frobenius automorphism was added to the set of homologies, and then the full automorphism group was generated. The Frobenius automorphism was found by using the planar ternary ring derived from a coordinatization of the plane.
Date Issued: 2013
PURL: http://purl.flvc.org/fau/fd/FA0004000
Subject Headings: Combinatorial group theory, Finite geometrics, Geometry, Projective
Format: Document (PDF)

Title: The Finite Abelian Hidden Subgroup Problem.
Creator: Losert, Bernd, Magliveras, Spyros S., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: The hidden subgroup problem has been an active topic of research in quantum computing for over the past 10 years. Out of all the literature that is out there on this topic, there are very few survey articles which discuss most or all of the details concerning the Abelian hidden subgroup problem. As a matter of fact , many articles [17, 26 , 22, 45] claim that an eff-icient quantum algorithm for the Abelian hidden subgroup problem is folklore. To quote Jozsa [21]: " ... the detailed...
Show moreThe hidden subgroup problem has been an active topic of research in quantum computing for over the past 10 years. Out of all the literature that is out there on this topic, there are very few survey articles which discuss most or all of the details concerning the Abelian hidden subgroup problem. As a matter of fact , many articles [17, 26 , 22, 45] claim that an eff-icient quantum algorithm for the Abelian hidden subgroup problem is folklore. To quote Jozsa [21]: " ... the detailed description of an efficient quantum algorithm for the general abelian hidden subgroup problem seems not to have been described in the literature." Apart from banishing this folklore, the aim of this work is to serve as a monograph about the Abelian hidden subgroup, discussing many of the finer points that are ignored in the literature so as to make it accessible and comprehensible to the mathematically mature reader.
Show less
Date Issued: 2010
PURL: http://purl.flvc.org/fau/fd/FA00000790
Format: Document (PDF)

Title: An Algorithmic Approach to Tran Van Trung's Basic Recursive Construction of t-Designs.
Creator: Lopez, Oscar A., Magliveras, Spyros S., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: It was not until the 20th century that combinatorial design theory was studied as a formal subject. This field has many applications, for example in statistical experimental design, coding theory, authentication codes, and cryptography. Major approaches to the problem of discovering new t-designs rely on (i) the construction of large sets of t designs, (ii) using prescribed automorphism groups, (iii) recursive construction methods. In 2017 and 2018, Tran Van Trung introduced new recursive...
Show moreIt was not until the 20th century that combinatorial design theory was studied as a formal subject. This field has many applications, for example in statistical experimental design, coding theory, authentication codes, and cryptography. Major approaches to the problem of discovering new t-designs rely on (i) the construction of large sets of t designs, (ii) using prescribed automorphism groups, (iii) recursive construction methods. In 2017 and 2018, Tran Van Trung introduced new recursive techniques to construct t – (v, k, λ) designs. These methods are of purely combinatorial nature and require using "ingredient" t-designs or resolutions whose parameters satisfy a system of non-linear equations. Even after restricting the range of parameters in this new method, the task is computationally intractable. In this work, we enhance Tran Van Trung's "Basic Construction" by a robust and efficient hybrid computational apparatus which enables us to construct hundreds of thousands of new t – (v, k, Λ) designs from previously known ingredient designs. Towards the end of the dissertation we also create a new family of 2-resolutions, which will be infinite if there are infinitely many Sophie Germain primes.
Show less
Date Issued: 2019
PURL: http://purl.flvc.org/fau/fd/FA00013233
Subject Headings: Combinatorial designs and configurations, Algorithms, t-designs
Format: Document (PDF)

Title: The Covering Numbers of Some Finite Simple Groups.
Creator: Epstein, Michael, Magliveras, Spyros S., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: A finite cover C of a group G is a finite collection of proper subgroups of G such that G is equal to the union of all of the members of C. Such a cover is called minimal if it has the smallest cardinality among all finite covers of G. The covering number of G, denoted by σ(G), is the number of subgroups in a minimal cover of G. Here we determine the covering numbers of the projective special unitary groups U3(q) for q ≤ 5, and give upper and lower bounds for the covering number of U3(q) when...
Show moreA finite cover C of a group G is a finite collection of proper subgroups of G such that G is equal to the union of all of the members of C. Such a cover is called minimal if it has the smallest cardinality among all finite covers of G. The covering number of G, denoted by σ(G), is the number of subgroups in a minimal cover of G. Here we determine the covering numbers of the projective special unitary groups U3(q) for q ≤ 5, and give upper and lower bounds for the covering number of U3(q) when q > 5. We also determine the covering number of the McLaughlin sporadic simple group, and verify previously known results on the covering numbers of the Higman-Sims and Held groups.
Show less
Date Issued: 2019
PURL: http://purl.flvc.org/fau/fd/FA00013203
Subject Headings: Finite simple groups, Covering numbers
Format: Document (PDF)

Title: Low rank transitive representations, primitive extensions, and the collision problem in PSL (2, q).
Creator: Thapa Magar, Krishna B., Magliveras, Spyros S., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: Every transitive permutation representation of a finite group is the representation of the group in its action on the cosets of a particular subgroup of the group. The group has a certain rank for each of these representations. We first find almost all rank-3 and rank-4 transitive representations of the projective special linear group P SL(2, q) where q = pm and p is an odd prime. We also determine the rank of P SL (2, p) in terms of p on the cosets of particular given subgroups. We then...
Show moreEvery transitive permutation representation of a finite group is the representation of the group in its action on the cosets of a particular subgroup of the group. The group has a certain rank for each of these representations. We first find almost all rank-3 and rank-4 transitive representations of the projective special linear group P SL(2, q) where q = pm and p is an odd prime. We also determine the rank of P SL (2, p) in terms of p on the cosets of particular given subgroups. We then investigate the construction of rank-3 transitive and primitive extensions of a simple group, such that the extension group formed is also simple. In the latter context we present a new, group theoretic construction of the famous Hoffman-Singleton graph as a rank-3 graph.
Show less
Date Issued: 2015
PURL: http://purl.flvc.org/fau/fd/FA00004471, http://purl.flvc.org/fau/fd/FA00004471
Subject Headings: Combinatorial designs and configurations, Cryptography, Data encryption (Computer science), Finite geometries, Finite groups, Group theory, Permutation groups
Format: Document (PDF)

Title: Techniques in Lattice Basis Reduction.
Creator: Khadka, Bal K., Magliveras, Spyros S., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: The mathematical theory of nding a basis of shortest possible vectors in a given lattice L is known as reduction theory and goes back to the work of Lagrange, Gauss, Hermite, Korkin, Zolotarev, and Minkowski. Modern reduction theory is voluminous and includes the work of A. Lenstra, H. Lenstra and L. Lovasz who created the well known LLL algorithm, and many other researchers such as L. Babai and C. P. Schnorr who created signi cant new variants of basis reduction algorithms. The shortest...
Show moreThe mathematical theory of nding a basis of shortest possible vectors in a given lattice L is known as reduction theory and goes back to the work of Lagrange, Gauss, Hermite, Korkin, Zolotarev, and Minkowski. Modern reduction theory is voluminous and includes the work of A. Lenstra, H. Lenstra and L. Lovasz who created the well known LLL algorithm, and many other researchers such as L. Babai and C. P. Schnorr who created signi cant new variants of basis reduction algorithms. The shortest vector (SVP) and closest vector (CVP) problems, presently considered intractable, are algorithmic tasks that lie at the core of many number theoretic problems, integer programming, nding irreducible factors of polynomials, minimal polynomials of algebraic numbers, and simultaneous diophantine approximation. Lattice basis reduction also has deep and extensive connections with modern cryptography, and cryptanalysis particularly in the post-quantum era. In this dissertation we study and compare current systems LLL and BKZ, and point out their strengths and drawbacks. In addition, we propose and investigate the e cacy of new optimization techniques, to be used along with LLL, such as hill climbing, random walks in groups, our lattice di usion-sub lattice fusion, and multistage hybrid LDSF-HC technique. The rst two methods rely on the sensitivity of LLL to permutations of the input basis B, and optimization ideas over the symmetric group Sm viewed as a metric space. The third technique relies on partitioning the lattice into sublattices, performing basis reduction in the partition sublattice blocks, fusing the sublattices, and repeating. We also point out places where parallel computation can reduce runtimes achieving almost linear speedup. The multistage hybrid technique relies on the lattice di usion and sublattice fusion and hill climbing algorithms. Unlike traditional methods, our approach brings in better results in terms of basis reduction towards nding shortest vectors and minimal weight bases. Using these techniques we have published the competitive lattice vectors of ideal lattice challenge on the lattice hall of fame. Toward the end of the dissertation we also discuss applications to the multidimensional knapsack problem that resulted in the discovery of new large sets of geometric designs still considered very rare. The research introduces innovative techniques in lattice basis reduction theory and provides some space for future researchers to contemplate lattices from a new viewpoint.
Show less
Date Issued: 2016
PURL: http://purl.flvc.org/fau/fd/FA00004678
Subject Headings: Cryptography., Combinatorial analysis., Group theory.
Format: Document (PDF)

Title: New Results in Group Theoretic Cryptology.
Creator: Sramka, Michal, Florida Atlantic University, Magliveras, Spyros S., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: 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...
Show moreWith 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.
Show less
Date Issued: 2006
PURL: http://purl.flvc.org/fau/fd/FA00000878
Subject Headings: Group theory, Mathematical statistics, Cryptography, Combinatorial designs and configurations, Data encryption (Computer science), Coding theory
Format: Document (PDF)

Title: New Geometric Large Sets.
Creator: Hurley, Michael Robert, Magliveras, Spyros S., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: Let V be an n-dimensional vector space over the field of q elements. By a geometric t-[q^n, k, λ] design we mean a collection D of k-dimensional subspaces of V, called blocks, such that every t-dimensional subspace T of V appears in exactly λ blocks in D. A large set, LS [N] [t, k, q^n], of geometric designs is a collection on N disjoint t-[q^n, k, λ] designs that partitions [V K], the collection of k-dimensional subspaces of V. In this work we construct non-isomorphic large sets using...
Show moreLet V be an n-dimensional vector space over the field of q elements. By a geometric t-[q^n, k, λ] design we mean a collection D of k-dimensional subspaces of V, called blocks, such that every t-dimensional subspace T of V appears in exactly λ blocks in D. A large set, LS [N] [t, k, q^n], of geometric designs is a collection on N disjoint t-[q^n, k, λ] designs that partitions [V K], the collection of k-dimensional subspaces of V. In this work we construct non-isomorphic large sets using methods based on incidence structures known as the Kramer-Mesner matrices. These structures are induced by particular group actions on the collection of subspaces of the vector space V. Subsequently, we discuss and use computational techniques for solving certain linear problems of the form AX = B, where A is a large integral matrix and X is a {0,1} solution. These techniques involve (i) lattice basis-reduction, including variants of the LLL algorithm, and (ii) linear programming. Inspiration came from the 2013 work of Braun, Kohnert, Ostergard, and Wassermann, [17], who produced the first nontrivial large set of geometric designs with t ≥ 2. Bal Khadka and Michael Epstein provided the know-how for using the LLL and linear programming algorithms that we implemented to construct the large sets.
Show less
Date Issued: 2016
PURL: http://purl.flvc.org/fau/fd/FA00004732, http://purl.flvc.org/fau/fd/FA00004732
Subject Headings: Group theory., Finite groups., Factorial experiment designs., Irregularities of distribution (Number theory), Combinatorial analysis.
Format: Document (PDF)

Title: Permutation-based transformations for digital multimedia encryption and steganography.
Creator: Socek, Daniel, Florida Atlantic University, Furht, Borko, Magliveras, Spyros S., College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
Abstract/Description: The aim of this work is to explore the utilization of permutation-based transformations to achieve compression, encryption and steganography in the domain of digital videos. The main contribution of this dissertation is a novel type of digital video encryption that has several advantages over other currently available digital video encryption methods. An extended classification of digital video encryption algorithms is presented in order to clarify these advantages. The classification itself...
Show moreThe aim of this work is to explore the utilization of permutation-based transformations to achieve compression, encryption and steganography in the domain of digital videos. The main contribution of this dissertation is a novel type of digital video encryption that has several advantages over other currently available digital video encryption methods. An extended classification of digital video encryption algorithms is presented in order to clarify these advantages. The classification itself represents an original work, since to date, no such comprehensive classification is provided in known scientific literature. Both security and performance aspects of the proposed method are thoroughly analyzed to provide evidence for high security and performance efficiency. Since the basic model is feasible only for a certain class of video sequences and video codecs, several extensions providing broader applicability are described along with the basic algorithm. An additional significant contribution is the proposition of a novel type of digital video steganography based on disguising a given video by another video. Experimental results are generated for a number of video sequences to demonstrate the performance of proposed methods.
Show less
Date Issued: 2006
PURL: http://purl.flvc.org/fcla/dt/12225
Subject Headings: Image processing--Security measures, Data encryption (Computer science), Computer security, Multimedia systems--Security measures
Format: Document (PDF)

FAU Theses and Dissertations (10)	+ -
FAU Graduate Student Research (4)	+ -
FAU College Collections (2)	+ -

Data encryption (Computer science) (4)	+ -
Combinatorial designs and configurations (3)	+ -
Cryptography (3)	+ -
Algorithms (2)	+ -
Combinatorial analysis. (2)	+ -

Cryptography. (2)	+ -
Group theory (2)	+ -
Group theory. (2)	+ -
Coding theory (1)	+ -
Combinatorial group theory (1)	+ -
Computer algorithm (1)	+ -
Computer security (1)	+ -
Covering numbers (1)	+ -
Data encryption (Computer science) --Technological innovations. (1)	+ -
Digital video. (1)	+ -
Digital watermarking. (1)	+ -
Factorial experiment designs. (1)	+ -
Finite geometrics (1)	+ -
Finite geometries (1)	+ -
Finite groups (1)	+ -
Finite groups. (1)	+ -
Finite simple groups (1)	+ -
Geometry, Projective (1)	+ -
Image processing--Security measures (1)	+ -
Irregularities of distribution (Number theory) (1)	+ -
Lattice theory (1)	+ -
Logarithms (1)	+ -
Mathematical statistics (1)	+ -
Mulitmedia systems --Security measures. (1)	+ -
Multimedia systems --Security measures. (1)	+ -

Electronic Thesis or Dissertation (10)	+ -
abstract (2)	+ -
article (2)	+ -
poster (2)	+ -

Magliveras, Spyros S. (16)	+ -
Charles E. Schmidt College of Science (8)	+ -
Department of Mathematical Sciences (8)	+ -
Florida Atlantic University (8)	+ -
Graduate College (4)	+ -

Search In

Sort Results By:

Narrow results by:

Collection

Topical Subject

Genre

Type of Resource

Language

Creator

Format

Owner