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 Title
 An algebraic attack on block ciphers.
 Creator
 Matheis, Kenneth., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

The aim of this work is to investigate an algebraic attack on block ciphers called Multiple Right Hand Sides (MRHS). MRHS models a block cipher as a system of n matrix equations Si := Aix = [Li], where each Li can be expressed as a set of its columns bi1, . . . , bisi . The set of solutions Ti of Si is dened as the union of the solutions of Aix = bij , and the set of solutions of the system S1, . . . , Sn is dened as the intersection of T1, . . . , Tn. Our main contribution is a hardware...
Show moreThe aim of this work is to investigate an algebraic attack on block ciphers called Multiple Right Hand Sides (MRHS). MRHS models a block cipher as a system of n matrix equations Si := Aix = [Li], where each Li can be expressed as a set of its columns bi1, . . . , bisi . The set of solutions Ti of Si is dened as the union of the solutions of Aix = bij , and the set of solutions of the system S1, . . . , Sn is dened as the intersection of T1, . . . , Tn. Our main contribution is a hardware platform which implements a particular algorithm that solves MRHS systems (and hence block ciphers). The case is made that the platform performs several thousand orders of magnitude faster than software, it costs less than US$1,000,000, and that actual times of block cipher breakage can be calculated once it is known how the corresponding software behaves. Options in MRHS are also explored with a view to increase its efficiency.
Show less  Date Issued
 2010
 PURL
 http://purl.flvc.org/FAU/2976444
 Subject Headings
 Ciphers, Cryptography, Data encryption (Computer science), Computer security, Coding theory, Integrated circuits, Design and construction
 Format
 Document (PDF)
 Title
 The existence of minimal logarithmic signatures for classical groups.
 Creator
 Singhi, Nikhil., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

A logarithmic signature (LS) for a nite group G is an ordered tuple = [A1;A2; : : : ;An] of subsets Ai of G, such that every element g 2 G can be expressed uniquely as a product g = a1a2 : : : ; an, where ai 2 Ai. Logarithmic signatures were dened by Magliveras in the late 1970's for arbitrary nite groups in the context of cryptography. They were also studied for abelian groups by Hajos in the 1930's. The length of an LS is defined to be `() = Pn i=1 jAij. It can be easily seen that for a...
Show moreA logarithmic signature (LS) for a nite group G is an ordered tuple = [A1;A2; : : : ;An] of subsets Ai of G, such that every element g 2 G can be expressed uniquely as a product g = a1a2 : : : ; an, where ai 2 Ai. Logarithmic signatures were dened by Magliveras in the late 1970's for arbitrary nite groups in the context of cryptography. They were also studied for abelian groups by Hajos in the 1930's. The length of an LS is defined to be `() = Pn i=1 jAij. It can be easily seen that for a group G of order Qk j=1 pj mj , the length of any LS for G satises `() Pk j=1mjpj . An LS for which this lower bound is achieved is called a minimal logarithmic signature (MLS). The MLS conjecture states that every finite simple group has an MLS. If the conjecture is true then every finite group will have an MLS. The conjecture was shown to be true by a number of researchers for a few classes of finite simple groups. However, the problem is still wide open. This dissertation addresses the MLS conjecture for the classical simple groups. In particular, it is shown that MLS's exist for the symplectic groups Sp2n(q), the orthogonal groups O 2n(q0) and the corresponding simple groups PSp2n(q) and 2n(q0) for all n 2 N, prime power q and even prime power q0. The existence of an MLS is also shown for all unitary groups GUn(q) for all odd n and q = 2s under the assumption that an MLS exists for GUn 1(q). The methods used are very general and algorithmic in nature and may be useful for studying all nite simple groups of Lie type and possibly also the sporadic groups. The blocks of logarithmic signatures constructed in this dissertation have cyclic structure and provide a sort of cyclic decomposition for these classical groups.
Show less  Date Issued
 2011
 PURL
 http://purl.flvc.org/FAU/3172943
 Subject Headings
 Finite groups, Abelian groups, Number theory, Combinatorial group theory, Mathematical recreations, Linear algebraic groups, Lie groups
 Format
 Document (PDF)
 Title
 On the minimal logarithmic signature conjecture.
 Creator
 Singhi, Nidhi., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

The minimal logarithmic signature conjecture states that in any finite simple group there are subsets Ai, 1 i s such that the size jAij of each Ai is a prime or 4 and each element of the group has a unique expression as a product Qs i=1 ai of elements ai 2 Ai. Logarithmic signatures have been used in the construction of several cryptographic primitives since the late 1970's [3, 15, 17, 19, 16]. The conjecture is shown to be true for various families of simple groups including cyclic groups,...
Show moreThe minimal logarithmic signature conjecture states that in any finite simple group there are subsets Ai, 1 i s such that the size jAij of each Ai is a prime or 4 and each element of the group has a unique expression as a product Qs i=1 ai of elements ai 2 Ai. Logarithmic signatures have been used in the construction of several cryptographic primitives since the late 1970's [3, 15, 17, 19, 16]. The conjecture is shown to be true for various families of simple groups including cyclic groups, An, PSLn(q) when gcd(n; q 1) is 1, 4 or a prime and several sporadic groups [10, 9, 12, 14, 18]. This dissertation is devoted to proving that the conjecture is true for a large class of simple groups of Lie type called classical groups. The methods developed use the structure of these groups as isometry groups of bilinear or quadratic forms. A large part of the construction is also based on the Bruhat and Levi decompositions of parabolic subgroups of these groups. In this dissertation the conjecture is shown to be true for the following families of simple groups: the projective special linear groups PSLn(q), the projective symplectic groups PSp2n(q) for all n and q a prime power, and the projective orthogonal groups of positive type + 2n(q) for all n and q an even prime power. During the process, the existence of minimal logarithmic signatures (MLS's) is also proven for the linear groups: GLn(q), PGLn(q), SLn(q), the symplectic groups: Sp2n(q) for all n and q a prime power, and for the orthogonal groups of plus type O+ 2n(q) for all n and q an even prime power. The constructions in most of these cases provide cyclic MLS's. Using the relationship between nite groups of Lie type and groups with a split BNpair, it is also shown that every nite group of Lie type can be expressed as a disjoint union of sets, each of which has an MLS.
Show less  Date Issued
 2011
 PURL
 http://purl.flvc.org/FAU/3172946
 Subject Headings
 Finite groups, Abelian groups, Number theory, Combinatorial group theory, Mathematical recreations, Linear algebraic groups, Lie groups
 Format
 Document (PDF)
 Title
 Weakly integrally closed domains and forbidden patterns.
 Creator
 Hopkins, Mary E., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

An integral domain D is weakly integrally closed if whenever there is an element x in the quotient field of D and a nonzero finitely generated ideal J of D such that xJ J2, then x is in D. We define weakly integrally closed numerical monoids similarly. If a monoid algebra is weakly integrally closed, then so is the monoid. A pattern F of finitely many 0's and 1's is forbidden if whenever the characteristic binary string of a numerical monoid M contains F, then M is not weakly integrally...
Show moreAn integral domain D is weakly integrally closed if whenever there is an element x in the quotient field of D and a nonzero finitely generated ideal J of D such that xJ J2, then x is in D. We define weakly integrally closed numerical monoids similarly. If a monoid algebra is weakly integrally closed, then so is the monoid. A pattern F of finitely many 0's and 1's is forbidden if whenever the characteristic binary string of a numerical monoid M contains F, then M is not weakly integrally closed. Any stretch of the pattern 11011 is forbidden. A numerical monoid M is weakly integrally closed if and only if it has a forbidden pattern. For every finite set S of forbidden patterns, there exists a monoid that is not weakly integrally closed and that contains no stretch of a pattern in S. It is shown that particular monoid algebras are weakly integrally closed.
Show less  Date Issued
 2009
 PURL
 http://purl.flvc.org/FAU/199327
 Subject Headings
 Mathematical analysis, Algebra, Homological, Monoids, Categories (Mathematics), Semigroup algebras
 Format
 Document (PDF)
 Title
 Permutationbased data compression.
 Creator
 Mihnea, Amalya, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

The use of permutations in data compression is an aspect that is worthy of further exploration. The work that has been done in video compression based on permutations was primarily oriented towards lossless algorithms. The study of previous algorithms has led to a new algorithm that could be either lossless or lossy, for which the amount of compression and the quality of the output can be controlled. The lossless version of our algorithm performs close to lossy versions of H.264 and it...
Show moreThe use of permutations in data compression is an aspect that is worthy of further exploration. The work that has been done in video compression based on permutations was primarily oriented towards lossless algorithms. The study of previous algorithms has led to a new algorithm that could be either lossless or lossy, for which the amount of compression and the quality of the output can be controlled. The lossless version of our algorithm performs close to lossy versions of H.264 and it improves on them for the majority of the videos that we analyzed. Our algorithm could be used in situations where there is a need for lossless compression and the video sequences are part of a single scene, e.g., medical videos, where loss of information could be risky or expensive. Some results on permutations, which may be of independent interest, arose in developing this algorithm. We report on these as well.
Show less  Date Issued
 2011
 PURL
 http://purl.flvc.org/FAU/3333054
 Subject Headings
 Data compression (Telecommunication), Combinatorics, Network architecture and design, Computer network architectures, Mathematical optimization
 Format
 Document (PDF)
 Title
 A class of rational surfaces with a nonrational singularity explicitly given by a single equation.
 Creator
 Harmon, Drake., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

The family of algebraic surfaces X dened by the single equation zn = (y a1x) (y anx)(x 1) over an algebraically closed eld k of characteristic zero, where a1; : : : ; an 2 k are distinct, is studied. It is shown that this is a rational surface with a nonrational singularity at the origin. The ideal class group of the surface is computed. The terms of the ChaseHarrisonRosenberg seven term exact sequence on the open complement of the ramication locus of X ! A2 are computed; the Brauer group...
Show moreThe family of algebraic surfaces X dened by the single equation zn = (y a1x) (y anx)(x 1) over an algebraically closed eld k of characteristic zero, where a1; : : : ; an 2 k are distinct, is studied. It is shown that this is a rational surface with a nonrational singularity at the origin. The ideal class group of the surface is computed. The terms of the ChaseHarrisonRosenberg seven term exact sequence on the open complement of the ramication locus of X ! A2 are computed; the Brauer group is also studied in this unramied setting. The analysis is extended to the surface eX obtained by blowing up X at the origin. The interplay between properties of eX , determined in part by the exceptional curve E lying over the origin, and the properties of X is explored. In particular, the implications that these properties have on the Picard group of the surface X are studied.
Show less  Date Issued
 2013
 PURL
 http://purl.flvc.org/fcla/dt/3360782
 Subject Headings
 Mathematics, Galois modules (Algebra), Class field theory, Algebraic varieties, Integral equations
 Format
 Document (PDF)
 Title
 Design and analysis of key establishment protocols.
 Creator
 Neupane, Kashi., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

Consider a scenario where a server S shares a symmetric key kU with each user U. Building on a 2party solution of Bohli et al., we describe an authenticated 3party key establishment which remains secure if a computational Bilinear Diffie Hellman problem is hard or the server is uncorrupted. If the BDH assumption holds during a protocol execution, but is invalidated later, entity authentication and integrity of the protocol are still guaranteed. Key establishment protocols based on hardness...
Show moreConsider a scenario where a server S shares a symmetric key kU with each user U. Building on a 2party solution of Bohli et al., we describe an authenticated 3party key establishment which remains secure if a computational Bilinear Diffie Hellman problem is hard or the server is uncorrupted. If the BDH assumption holds during a protocol execution, but is invalidated later, entity authentication and integrity of the protocol are still guaranteed. Key establishment protocols based on hardness assumptions, such as discrete logarithm problem (DLP) and integer factorization problem (IFP) are vulnerable to quantum computer attacks, whereas the protocols based on other hardness assumptions, such as conjugacy search problem and decomposition search problem can resist such attacks. The existing protocols based on the hardness assumptions which can resist quantum computer attacks are only passively secure. Compilers are used to convert a passively secure protocol to an actively secure protoc ol. Compilers involve some tools such as, signature scheme and a collisionresistant hash function. If there are only passively secure protocols but not a signature scheme based on same assumption then the application of existing compilers requires the use of such tools based on different assumptions. But the introduction of new tools, based on different assumptions, makes the new actively secure protocol rely on more than one hardness assumptions. We offer an approach to derive an actively secure twoparty protocol from a passively secure twoparty protocol without introducing further hardness assumptions. This serves as a useful formal tool to transform any basic algebric method of public key cryptography to the real world applicaticable cryptographic scheme. In a recent preprint, Vivek et al. propose a compiler to transform a passively secure 3party key establishment to a passively secure group key establishment. To achieve active security, they apply this compiler to Joux's, protoc ol and apply a construction by Katz and Yung, resulting in a 3round group key establishment. In this reserach, we show how Joux's protocol can be extended to an actively secure group key establishment with two rounds. The resulting solution is in the standard model, builds on a bilinear DiffieHellman assumption and offers forward security as well as strong entity authentication. If strong entity authentication is not required, then one half of the participants does not have to send any message in the second round, which may be of interest for scenarios where communication efficiency is a main concern.
Show less  Date Issued
 2012
 PURL
 http://purl.flvc.org/FAU/3342239
 Subject Headings
 Computer networks, Security measures, Computer network protocols, Data encryption (Computer science), Public key infrastructure (Computer security)
 Format
 Document (PDF)
 Title
 Cryptography in the presence of keydependent messages.
 Creator
 Gonzalez, Madeline., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

The aim of this work is to investigate a security model in which we allow an adversary to have access to functions of the secret key. In recent years, significant progress has been made in understanding the security of encryption schemes in the presence of keydependent plaintexts or messages (known as KDM). Here, we motivate and explore the security of a setting, where an adversary against a message authentication code (MAC) or signature scheme can access signatures on keydependent messages...
Show moreThe aim of this work is to investigate a security model in which we allow an adversary to have access to functions of the secret key. In recent years, significant progress has been made in understanding the security of encryption schemes in the presence of keydependent plaintexts or messages (known as KDM). Here, we motivate and explore the security of a setting, where an adversary against a message authentication code (MAC) or signature scheme can access signatures on keydependent messages. We propose a way to formalize the security of message authentication schemes in the presence of keydependent MACs (KDEUF) and of signature schemes in the presence of keydependent signatures (KDS). An attack on a message recognition protocol involving a MAC is presented. It turns out that the situation is quite different from keydependent encryption: To achieve KDEUFsecurity or KDSsecurity under nonadaptive chosen message attacks, the use of a stateful signing algorithm is inevitable even in the random oracle model. After discussing the connection between keydependent signing and forward security, we describe a compiler which lifts any EUFCMA secure onetime signature scheme to a forward secure signature scheme offering KDSCMA security. Then, we discuss how aggregate signatures can be used to combine the signatures in the certificate chain used in the compiler. A natural question arises about how to combine the security definitions of KDM and KDS to come up with a signcryption scheme that is secure. We also offer a connection with LeakageResilient Signatures, which take into account sidechannel attacks. Lastly, we present some open problems for future research.
Show less  Date Issued
 2009
 PURL
 http://purl.flvc.org/FAU/2182087
 Subject Headings
 Cryptography, Data processing, Digital signatures, Computer security, Data encryption (Computer science), Software protection
 Format
 Document (PDF)
 Title
 Empirical likelihood method for segmented linear regression.
 Creator
 Liu, Zhihua., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

For a segmented regression system with an unknown changepoint over two domains of a predictor, a new empirical likelihood ratio test statistic is proposed to test the null hypothesis of no change. The proposed method is a nonparametric method which releases the assumption of the error distribution. Under the null hypothesis of no change, the proposed test statistic is shown empirically Gumbel distributed with robust location and scale parameters under various parameter settings and error...
Show moreFor a segmented regression system with an unknown changepoint over two domains of a predictor, a new empirical likelihood ratio test statistic is proposed to test the null hypothesis of no change. The proposed method is a nonparametric method which releases the assumption of the error distribution. Under the null hypothesis of no change, the proposed test statistic is shown empirically Gumbel distributed with robust location and scale parameters under various parameter settings and error distributions. Under the alternative hypothesis with a changepoint, the comparisons with two other methods (Chen's SIC method and Muggeo's SEG method) show that the proposed method performs better when the slope change is small. A power analysis is conducted to illustrate the performance of the test. The proposed method is also applied to analyze two real datasets: the plasma osmolality dataset and the gasoline price dataset.
Show less  Date Issued
 2011
 PURL
 http://purl.flvc.org/FAU/3332719
 Subject Headings
 Changepoint problems, Regression analysis, Econometrics, Limit theory (Probability theory)
 Format
 Document (PDF)
 Title
 The enumeration of lattice paths and walks.
 Creator
 Gao, Shanzhen., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

A wellknown long standing problem in combinatorics and statistical mechanics is to find the generating function for selfavoiding walks (SAW) on a twodimensional lattice, enumerated by perimeter. A SAW is a sequence of moves on a square lattice which does not visit the same point more than once. It has been considered by more than one hundred researchers in the pass one hundred years, including George Polya, Tony Guttmann, Laszlo Lovasz, Donald Knuth, Richard Stanley, Doron Zeilberger,...
Show moreA wellknown long standing problem in combinatorics and statistical mechanics is to find the generating function for selfavoiding walks (SAW) on a twodimensional lattice, enumerated by perimeter. A SAW is a sequence of moves on a square lattice which does not visit the same point more than once. It has been considered by more than one hundred researchers in the pass one hundred years, including George Polya, Tony Guttmann, Laszlo Lovasz, Donald Knuth, Richard Stanley, Doron Zeilberger, Mireille BousquetMlou, Thomas Prellberg, Neal Madras, Gordon Slade, Agnes Dit tel, E.J. Janse van Rensburg, Harry Kesten, Stuart G. Whittington, Lincoln Chayes, Iwan Jensen, Arthur T. Benjamin, and many others. More than three hundred papers and a few volumes of books were published in this area. A SAW is interesting for simulations because its properties cannot be calculated analytically. Calculating the number of selfavoiding walks is a common computational problem. A recently proposed model called prudent selfavoiding walks (PSAW) was first introduced to the mathematics community in an unpublished manuscript of Pra, who called them exterior walks. A prudent walk is a connected path on square lattice such that, at each step, the extension of that step along its current trajectory will never intersect any previously occupied vertex. A lattice path composed of connected horizontal and vertical line segments, each passing between adjacent lattice points. We will discuss some enumerative problems in selfavoiding walks, lattice paths and walks with several step vectors. Many open problems are posted.
Show less  Date Issued
 2011
 PURL
 http://purl.flvc.org/FAU/3183129
 Subject Headings
 Combinatorial analysis, Approximation theory, Mathematical statistics, Limit theorems (Probabilty theory)
 Format
 Document (PDF)
 Title
 On projected planes.
 Creator
 Caliskan, Cafer., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

This work was motivated by the wellknown question: "Does there exist a nondesarguesian projective plane of prime order?" For a prime p 1, determine all subplanes of order p up to collineations, and check whether one of these is nondesarguesian." In this manuscript we use a grouptheoretic methodology to determine the subplane structures of some nondesarguesian planes. In particular, we determine orbit representatives of all proper Qsubplanes both of a VeblenWedderburn (VW) plane of...
Show moreThis work was motivated by the wellknown question: "Does there exist a nondesarguesian projective plane of prime order?" For a prime p < 11, there is only the pappian plane of order p. Hence, such planes are indeed desarguesian. Thus, it is of interest to examine whether there are nondesarguesian planes of order 11. A suggestion by Ascher Wagner in 1985 was made to Spyros S. Magliveras: "Begin with a nondesarguesian plane of order pk, k > 1, determine all subplanes of order p up to collineations, and check whether one of these is nondesarguesian." In this manuscript we use a grouptheoretic methodology to determine the subplane structures of some nondesarguesian planes. In particular, we determine orbit representatives of all proper Qsubplanes both of a VeblenWedderburn (VW) plane of order 121 and of the Hughes plane of order 121, under their full collineation groups. In PI, there are 13 orbits of Baer subplanes, all of which are desarguesian, and approximately 3000 orbits of Fano subplanes. In Sigma , there are 8 orbits of Baer subplanes, all of which are desarguesian, 2 orbits of subplanes of order 3, and at most 408; 075 distinct Fano subplanes. In addition to the above results, we also study the subplane structures of some nondesarguesian planes, such as the Hall plane of order 25, the Hughes planes of order 25 and 49, and the Figueora planes of order 27 and 125. A surprising discovery by L. Puccio and M. J. de Resmini was the existence of a plane of order 3 in the Hughes plane of order 25. We generalize this result, showing that there are subplanes of order 3 in the Hughes planes of order q2, where q is a prime power and q 5 (mod 6). Furthermore, we analyze the structure of the full collineation groups of certain Veblen Wedderburn (VW) planes of orders 25, 49 and 121, and discuss how to recover the planes from their collineation groups.
Show less  Date Issued
 2010
 PURL
 http://purl.flvc.org/FAU/1927609
 Subject Headings
 Projected planes, Combinatorial designs and configurations, Surfaces, Algebraic, Manifolds (Mathematics)
 Format
 Document (PDF)
 Title
 Stability analysis for nonlinear systems with timedelays.
 Creator
 Tiwari, Shanaz, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

In this work, we investigate inputtostate stability (ISS) and other related stability properties for control systems with timedelays. To overcome the complexity caused by the presence of the delays, we adopt a Razumikhin approach. The underlying idea of this approach is to treat the delayed variables as system uncertainties. The advantage of this approach is that one works in the more familiar territory of stability analysis for delayfree systems in the context of ISS instead of carrying...
Show moreIn this work, we investigate inputtostate stability (ISS) and other related stability properties for control systems with timedelays. To overcome the complexity caused by the presence of the delays, we adopt a Razumikhin approach. The underlying idea of this approach is to treat the delayed variables as system uncertainties. The advantage of this approach is that one works in the more familiar territory of stability analysis for delayfree systems in the context of ISS instead of carrying out stability analysis on systems of functional differential equations. Our first step is to provide criteria on ISS and inputtoinput stability properties based on the Razumikhin approach. We then turn our attention to largescale interconnected systems. It has been well recognized that the smallgain theory is a powerful tool for stability analysis of interconnected systems. Using the Razumikhin approach, we develop smallgain theorems for interconnected systems consisting of two or more subs ystems with timedelays present either in the interconnection channels or within the subsystems themselves. As an interesting application, we apply our results to an existing model for hematopoesis, a blood cell production process,and improve the previous results derived by linear methods. Another important stability notion in the framework of ISS is the integral ISS (iISS) property. This is a weaker property than ISS, so it supplies to a larger class of systems. As in the case of ISS, we provide Razumikhin criteria on iISS for systems with delays. An example is presented to illustrate that though very useful in practice, the Razumikhin approach only provides sufficient conditions, not equivalent conditions. Finally, we address stability of timevarying systems with delays in the framework of ISS., In particular, we consider LyapunovRazumikhin functions whose decay rates are affected by timevarying functions that can be zero or even negative on some sets of nonzero measure. Our motivation is that it is often less demanding to find or construct such a Lyapunov function than one with a uniform decay rate. We also extend our smallgain theorems to the timevarying case by treating the timevarying system as an auxiliary timeinvariant system.
Show less  Date Issued
 2012
 PURL
 http://purl.flvc.org/FAU/3352880
 Subject Headings
 Nonlinear systems, Simulation methods, Control theory, Stability, Mathematical models, Mathematical optimization
 Format
 Document (PDF)
 Title
 Implementation and comparison of the Golay and first order ReedMuller codes.
 Creator
 Shukina, Olga., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

In this project we perform data transmission across noisy channels and recover the message first by using the Golay code, and then by using the firstorder Reed Muller code. The main objective of this thesis is to determine which code among the above two is more efficient for text message transmission by applying the two codes to exactly the same data with the same channel error bit probabilities. We use the comparison of the errorcorrecting capability and the practical speed of the Golay...
Show moreIn this project we perform data transmission across noisy channels and recover the message first by using the Golay code, and then by using the firstorder Reed Muller code. The main objective of this thesis is to determine which code among the above two is more efficient for text message transmission by applying the two codes to exactly the same data with the same channel error bit probabilities. We use the comparison of the errorcorrecting capability and the practical speed of the Golay code and the firstorder ReedMuller code to meet our goal.
Show less  Date Issued
 2013
 PURL
 http://purl.flvc.org/fcla/dt/3362579
 Subject Headings
 Errorcorrecting codes (Information theory), Coding theory, Computer algorithms, Digital modulation
 Format
 Document (PDF)
 Title
 Stochastic optimal impulse control of jump diffusions with application to exchange rate.
 Creator
 Perera, Sandun C., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

We generalize the theory of stochastic impulse control of jump diffusions introduced by Oksendal and Sulem (2004) with milder assumptions. In particular, we assume that the original process is affected by the interventions. We also generalize the optimal central bank intervention problem including market reaction introduced by Moreno (2007), allowing the exchange rate dynamic to follow a jump diffusion process. We furthermore generalize the approximation theory of stochastic impulse control...
Show moreWe generalize the theory of stochastic impulse control of jump diffusions introduced by Oksendal and Sulem (2004) with milder assumptions. In particular, we assume that the original process is affected by the interventions. We also generalize the optimal central bank intervention problem including market reaction introduced by Moreno (2007), allowing the exchange rate dynamic to follow a jump diffusion process. We furthermore generalize the approximation theory of stochastic impulse control problems by a sequence of iterated optimal stopping problems which is also introduced in Oksendal and Sulem (2004). We develop new results which allow us to reduce a given impulse control problem to a sequence of iterated optimal stopping problems even though the original process is affected by interventions.
Show less  Date Issued
 2009
 PURL
 http://purl.flvc.org/FAU/3174308
 Subject Headings
 Management, Mathematical models, Control theory, Stochastic differential equations, Distribution (Probability theory), Optimal stopping (Mathematical statistics), Economics, Mathematical
 Format
 Document (PDF)
 Title
 AUC estimation under various survival models.
 Creator
 Chang, Fazhe., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

In the medical science, the receiving operationg characteristic (ROC) curve is a graphical representation to evaluate the accuracy of a medical diagnostic test for any cutoff point. The area under the ROC curve (AUC) is an overall performance measure for a diagnostic test. There are two parts in this dissertation. In the first part, we study the properties of biExponentiated Weibull models. FIrst, we derive a general moment formula for single Exponentiated Weibull models. Then we move on to...
Show moreIn the medical science, the receiving operationg characteristic (ROC) curve is a graphical representation to evaluate the accuracy of a medical diagnostic test for any cutoff point. The area under the ROC curve (AUC) is an overall performance measure for a diagnostic test. There are two parts in this dissertation. In the first part, we study the properties of biExponentiated Weibull models. FIrst, we derive a general moment formula for single Exponentiated Weibull models. Then we move on to derive the precise formula of AUC and study the maximus likelihood estimation (MLE) of the AUC. Finally, we obtain the asymptotoc distribution of the estimated AUC. Simulation studies are used to check the performance of MLE of AUC under the moderate sample sizes. The second part fo the dissertation is to study the estimation of AUC under the crossing model, which extends the AUC formula in Gonen and Heller (2007).
Show less  Date Issued
 2012
 PURL
 http://purl.flvc.org/FAU/3359287
 Subject Headings
 Receiver operating characteristic curves, Medical screening, Statistical methods, Diagnosis, Statistical methods, Smoothing (Statistics)
 Format
 Document (PDF)
 Title
 Polynomials that are integer valued on the image of an integervalued polynomial.
 Creator
 Marshall, Mario V., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

Let D be an integral domain and f a polynomial that is integervalued on D. We prove that Int(f(D);D) has the Skolem Property and give a description of its spectrum. For certain discrete valuation domains we give a basis for the ring of integervalued even polynomials. For these discrete valuation domains, we also give a series expansion of continuous integervalued functions.
 Date Issued
 2009
 PURL
 http://purl.flvc.org/FAU/216411
 Subject Headings
 Polynomials, Ring of integers, Ideals (Algebra)
 Format
 Document (PDF)
 Title
 A study of divisors and algebras on a double cover of the affine plane.
 Creator
 Bulj, Djordje., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

An algebraic surface defined by an equation of the form z2 = (x+a1y) ... (x + any) (x  1) is studied, from both an algebraic and geometric point of view. It is shown that the surface is rational and contains a singular point which is nonrational. The class group of Weil divisors is computed and the Brauer group of Azumaya algebras is studied. Viewing the surface as a cyclic cover of the affine plane, all of the terms in the cohomology sequence of Chase, Harrison and Roseberg are computed.
 Date Issued
 2012
 PURL
 http://purl.flvc.org/FAU/3355618
 Subject Headings
 Algebraic number theory, Geometry, Data processing, Noncommutative differential geometry, Mathematical physics, Curves, Algebraic, Commutative rings
 Format
 Document (PDF)
 Title
 Construction of combinatorial designs with prescribed automorphism groups.
 Creator
 Kolotoglu, Emre., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

In this dissertation, we study some open problems concerning the existence or nonexistence of some combinatorial designs. We give the construction or proof of nonexistence of some Steiner systems, large sets of designs, and graph designs, with prescribed automorphism groups.
 Date Issued
 2013
 PURL
 http://purl.flvc.org/fcla/dt/3360795
 Subject Headings
 Combinatorial designs and configurations, Finite geometries, Curves, Algebraic, Automorphisms, Mathematical optimization, Steiner systems
 Format
 Document (PDF)
 Title
 Computing topological dynamics from time series.
 Creator
 Wess, Mark., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

The topological entropy of a continuous map quantifies the amount of chaos observed in the map. In this dissertation we present computational methods which enable us to compute topological entropy for given time series data generated from a continuous map with a transitive attractor. A triangulation is constructed in order to approximate the attractor and to construct a multivalued map that approximates the dynamics of the linear interpolant on the triangulation. The methods utilize...
Show moreThe topological entropy of a continuous map quantifies the amount of chaos observed in the map. In this dissertation we present computational methods which enable us to compute topological entropy for given time series data generated from a continuous map with a transitive attractor. A triangulation is constructed in order to approximate the attractor and to construct a multivalued map that approximates the dynamics of the linear interpolant on the triangulation. The methods utilize simplicial homology and in particular the Lefschetz Fixed Point Theorem to establish the existence of periodic orbits for the linear interpolant. A semiconjugacy is formed with a subshift of nite type for which the entropy can be calculated and provides a lower bound for the entropy of the linear interpolant. The dissertation concludes with a discussion of possible applications of this analysis to experimental time series.
Show less  Date Issued
 2008
 PURL
 http://purl.flvc.org/FAU/186294
 Subject Headings
 Algebraic topology, Graph theory, Fixed point theory, Singularities (Mathematics)
 Format
 Document (PDF)
 Title
 Message authentication in an identitybased encryption scheme: 1KeyEncryptThenMAC.
 Creator
 Amento, Brittanney Jaclyn, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

We present an IdentityBased Encryption scheme, 1KeyEncryptThenMAC, in which we are able to verify the authenticity of messages using a MAC. We accomplish this authentication by combining an IdentityBased Encryption scheme given by Boneh and Franklin, with an IdentityBased NonInteractive Key Distribution given by Paterson and Srinivasan, and attaching a MAC. We prove the scheme is chosen plaintext secure and chosen ciphertext secure, and the MAC is existentially unforgeable.
 Date Issued
 2010
 PURL
 http://purl.flvc.org/FAU/2796050
 Subject Headings
 Data encryption (Computer science), Public key cryptopgraphy, Public key infrastructure (Computer security)
 Format
 Document (PDF)