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Pages
 Title
 A Constructive Theory of Ordered Sets and their Completions.
 Creator
 Joseph, Jean S., Richman, Fred, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

The context for the development of this work is constructive mathematics without the axiom of countable choice. By constructive mathematics, we mean mathematics done without the law of excluded middle. Our original goal was to give a list of axioms for the real numbers R by only considering the order on R. We instead develop a theory of ordered sets and their completions and a theory of ordered abelian groups.
 Date Issued
 2018
 PURL
 http://purl.flvc.org/fau/fd/FA00013007
 Subject Headings
 Constructive mathematics, Ordered sets, Abelian groups
 Format
 Document (PDF)
 Title
 A Study on Partially Homomorphic Encryption Schemes.
 Creator
 Mithila, Shifat P., Karabina, Koray, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

High processing time and implementation complexity of the fully homomorphic encryption schemes intrigued cryptographers to extend partially homomorphic encryption schemes to allow homomorphic computation for larger classes of polynomials. In this thesis, we study several public key and partially homomorphic schemes and discuss a recent technique for boosting linearly homomorphic encryption schemes. Further, we implement this boosting technique on CGS linearly homomorphic encryption scheme to...
Show moreHigh processing time and implementation complexity of the fully homomorphic encryption schemes intrigued cryptographers to extend partially homomorphic encryption schemes to allow homomorphic computation for larger classes of polynomials. In this thesis, we study several public key and partially homomorphic schemes and discuss a recent technique for boosting linearly homomorphic encryption schemes. Further, we implement this boosting technique on CGS linearly homomorphic encryption scheme to allow one single multiplication as well as arbitrary number of additions on encrypted plaintexts. We provide MAGMA source codes for the implementation of the CGS scheme along with the boosted CGS scheme.
Show less  Date Issued
 2017
 PURL
 http://purl.flvc.org/fau/fd/FA00004840, http://purl.flvc.org/fau/fd/FA00004840
 Subject Headings
 Computer networksSecurity measures., Computer security., ComputersAccess controlCode words., Cyberinfrastructure., Computer network architectures., Cryptography., Number theoryData processing.
 Format
 Document (PDF)
 Title
 Algebraic and combinatorial aspects of group factorizations.
 Creator
 Bozovic, Vladimir., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

The aim of this work is to investigate some algebraic and combinatorial aspects of group factorizations. The main contribution of this dissertation is a set of new results regarding factorization of groups, with emphasis on the nonabelian case. We introduce a novel technique for factorization of groups, the socalled free mappings, a powerful tool for factorization of a wide class of abelian and nonabelian groups. By applying a certain group action on the blocks of a factorization, a number...
Show moreThe aim of this work is to investigate some algebraic and combinatorial aspects of group factorizations. The main contribution of this dissertation is a set of new results regarding factorization of groups, with emphasis on the nonabelian case. We introduce a novel technique for factorization of groups, the socalled free mappings, a powerful tool for factorization of a wide class of abelian and nonabelian groups. By applying a certain group action on the blocks of a factorization, a number of combinatorial and computational problems were noted and studied. In particular, we analyze the case of the group Aut(Zn) acting on blocks of factorization of Zn. We present new theoretical facts that reveal the numerical structure of the stabilizer of a set in Zn, under the action of Aut(Zn). New algorithms for finding the stabilizer of a set and checking whether two sets belong to the same orbit are proposed.
Show less  Date Issued
 2008
 PURL
 http://purl.flvc.org/FAU/107805
 Subject Headings
 Physical measurements, Mapping (Mathematics), Combinatorial enumeration problems, Algebra, Abstract
 Format
 Document (PDF)
 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
 Asymmetric information in fads models in Lâevy markets.
 Creator
 Buckley, Winston S., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

Fads models for stocks under asymmetric information in a purely continuous(GBM) market were first studied by P. Guasoni (2006), where optimal portfolios and maximum expected logarithmic utilities, including asymptotic utilities for the informed and uninformed investors, were presented. We generalized this theory to Lâevy markets, where stock prices and the process modeling the fads are allowed to include a jump component, in addition to the usual continuous component. We employ the methods of...
Show moreFads models for stocks under asymmetric information in a purely continuous(GBM) market were first studied by P. Guasoni (2006), where optimal portfolios and maximum expected logarithmic utilities, including asymptotic utilities for the informed and uninformed investors, were presented. We generalized this theory to Lâevy markets, where stock prices and the process modeling the fads are allowed to include a jump component, in addition to the usual continuous component. We employ the methods of stochastic calculus and optimization to obtain analogous results to those obtained in the purely continuous market. We approximate optimal portfolios and utilities using the instantaneous centralized and quasicentralized moments of the stocks percentage returns. We also link the random portfolios of the investors, under asymmetric information to the purely deterministic optimal portfolio, under symmetric information.
Show less  Date Issued
 2009
 PURL
 http://purl.flvc.org/FAU/3337187
 Subject Headings
 Investments, Mathematical models, Capital market, Mathematical models, Finance, Mathematical models, Information theory in economics, Capital asset pricing model, Lâevy processes
 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
 AuslanderReiten theory for systems of submodule embeddings.
 Creator
 Moore, Audrey., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

In this dissertation, we will investigate aspects of AuslanderReiten theory adapted to the setting of systems of submodule embeddings. Using this theory, we can compute AuslanderReiten quivers of such categories, which among other information, yields valuable information about the indecomposable objects in such a category. A main result of the dissertation is an adaptation to this situation of the Auslander and RingelTachikawa Theorem which states that for an artinian ring R of finite...
Show moreIn this dissertation, we will investigate aspects of AuslanderReiten theory adapted to the setting of systems of submodule embeddings. Using this theory, we can compute AuslanderReiten quivers of such categories, which among other information, yields valuable information about the indecomposable objects in such a category. A main result of the dissertation is an adaptation to this situation of the Auslander and RingelTachikawa Theorem which states that for an artinian ring R of finite representation type, each Rmodule is a direct sum of finitelength indecomposable Rmodules. In cases where this applies, the indecomposable objects obtained in the AuslanderReiten quiver give the building blocks for the objects in the category. We also briefly discuss in which cases systems of submodule embeddings form a Frobenius category, and for a few examples explore pointwise CalabiYau dimension of such a category.
Show less  Date Issued
 2009
 PURL
 http://purl.flvc.org/fcla/dt/210496
 Subject Headings
 Artin algebras, Rings (Algebra), Representation of algebras, Embeddings (Mathematics), Linear algebraic groups
 Format
 Document (PDF)
 Title
 Bayesian approach to an exponential hazard regression model with a change point.
 Creator
 Abraha, Yonas Kidane, Qian, Lianfen, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

This thesis contains two parts. The first part derives the Bayesian estimator of the parameters in a piecewise exponential Cox proportional hazard regression model, with one unknown change point for a right censored survival data. The second part surveys the applications of change point problems to various types of data, such as longterm survival data, longitudinal data and time series data. Furthermore, the proposed method is then used to analyse a real survival data.
 Date Issued
 2014
 PURL
 http://purl.flvc.org/fau/fd/FA00004013
 Subject Headings
 Bayesian statistical decision theory, Mathematical statistics, Multivariate analysis  Data processing
 Format
 Document (PDF)
 Title
 Bijections for partition identities.
 Creator
 Lai, JinMei Jeng, Florida Atlantic University, Meyerowitz, Aaron, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

This paper surveys work of the last few years on construction of bijections for partition identities. We use the more general setting of sieveequivalent families. Suppose A1' ... ,An are subsets of a finite set A and B1' ... ,Bn are subsets of a finite set B. Define AS=∩(i∈S) Ai and BS = ∩ (i∈S) Bi for all S⊆N={1,...,n}. Given explicit bijections fS: AS>BS for each S⊆N, A∪Ai has the same size as B∪Bi. Several authors have given algorithms for producing an explicit bijection between these...
Show moreThis paper surveys work of the last few years on construction of bijections for partition identities. We use the more general setting of sieveequivalent families. Suppose A1' ... ,An are subsets of a finite set A and B1' ... ,Bn are subsets of a finite set B. Define AS=∩(i∈S) Ai and BS = ∩ (i∈S) Bi for all S⊆N={1,...,n}. Given explicit bijections fS: AS>BS for each S⊆N, A∪Ai has the same size as B∪Bi. Several authors have given algorithms for producing an explicit bijection between these two sets. In certain important cases they give the same result. We discuss and compare algorithms, use Graph Theory to illustrate them, and provide PAS CAL programs for them.
Show less  Date Issued
 1992
 PURL
 http://purl.flvc.org/fau/fd/FADT14826
 Subject Headings
 Algorithms, Partitions (Mathematics), Sieves (Mathematics)
 Format
 Document (PDF)
 Title
 The CayleyDickson algebras.
 Creator
 Khalil, Saidah Hasan, Florida Atlantic University, Yiu, Paul Y., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

This thesis studies the various effects of the nonassociativity of the CayleyDickson algebras At, t>3, especially on the structure of their automorphism groups. Beginning with the problem of composition algebra structures on euclidean spaces, we shall explain the origin of the CayleyDickson algebras, and give a selfcontained exposition on some important results on such algebras. These algebras being nonassociative, we focus on the study of the associators of the form (u,w,v) = (uw)v  u(wv...
Show moreThis thesis studies the various effects of the nonassociativity of the CayleyDickson algebras At, t>3, especially on the structure of their automorphism groups. Beginning with the problem of composition algebra structures on euclidean spaces, we shall explain the origin of the CayleyDickson algebras, and give a selfcontained exposition on some important results on such algebras. These algebras being nonassociative, we focus on the study of the associators of the form (u,w,v) = (uw)v  u(wv). The first main result, that if u and v are elements in a CayleyDickson algebra for which (u, w, v) = 0 for all w, then u and v generate a 2dimensional subalgebra isomorphic to C, was conjectured by P. Yiu, and proved by P. Eakin and A. Sathaye. We shall simplify the proof given by these latter authors. This is then used to give a simple proof of R. D. Schafer's theorem on derivations of CayleyDickson algebras, and following also Eakin and Sathaye, a proof of the conjecture by R. B. Brown on the structure of the automorphism groups of these algebras. Two simple proofs are presented for the beautiful characterization by H. Brandt that in the Cayley algebra A3 = K, conjugation by a unit element a is an automorphism if and only if a is a 6th root of unity. We shall present a geometric proof by M. A. Zorn and a purely algebraic one. The zero divisors of the CayleyDickson algebra A4 are also analyzed in detail.
Show less  Date Issued
 1993
 PURL
 http://purl.flvc.org/fcla/dt/14993
 Subject Headings
 Cayley algebras
 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
 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
 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
 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
 Coset intersection problem and application to 3nets.
 Creator
 Pace, Nicola, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

In a projective plane (PG(2, K) defined over an algebraically closed field K of characteristic p = 0, we give a complete classification of 3nets realizing a finite group. The known infinite family, due to Yuzvinsky, arised from plane cubics and comprises 3nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky, comprises 3nets realizing dihedral groups. We prove that there is no further infinite family and list all...
Show moreIn a projective plane (PG(2, K) defined over an algebraically closed field K of characteristic p = 0, we give a complete classification of 3nets realizing a finite group. The known infinite family, due to Yuzvinsky, arised from plane cubics and comprises 3nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky, comprises 3nets realizing dihedral groups. We prove that there is no further infinite family and list all possible sporadic examples. If p is larger than the order of the group, the same classification holds true apart from three possible exceptions: Alt4, Sym4 and Alt5.
Show less  Date Issued
 2012
 PURL
 http://purl.flvc.org/FAU/3355866
 Subject Headings
 Finite fields (Algebra), Mathematical physics, Field theory (Physics), Curves, Algebraic
 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
 Curve shortening in secondorder lagrangian.
 Creator
 Adams, Ronald Edward, Kalies, William D., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

A secondorder Lagrangian system is a generalization of a classical mechanical system for which the Lagrangian action depends on the second derivative of the state variable. Recent work has shown that the dynamics of such systems c:an be substantially richer than for classical Lagrangian systems. In particular, topological properties of the planar curves obtained by projection onto the lowerorder derivatives play a key role in forcing certain types of dynamics. However, the application of...
Show moreA secondorder Lagrangian system is a generalization of a classical mechanical system for which the Lagrangian action depends on the second derivative of the state variable. Recent work has shown that the dynamics of such systems c:an be substantially richer than for classical Lagrangian systems. In particular, topological properties of the planar curves obtained by projection onto the lowerorder derivatives play a key role in forcing certain types of dynamics. However, the application of these techniques requires an analytic restriction on the Lagrangian that it satisfy a twist property. In this dissertation we approach this problem from the point of view of curve shortening in an effort to remove the twist condition. In classical curve shortening a family of curves evolves with a velocity which is normal to the curve and proportional to its curvature. The evolution of curves with decreasing action is more general, and in the first part of this dissertation we develop some results for curve shortening flows which shorten lengths with respect to a Finsler metric rather than a Riemannian metric. The second part of this dissertation focuses on analytic methods to accommodate the fact that the Finsler metric for secondorder Lagrangian system has singularities. We prove the existence of simple periodic solutions for a general class of systems without requiring the twist condition. Further; our results provide a frame work in which to try to further extend the topological forcing theorems to systems without the twist condition.
Show less  Date Issued
 2014
 PURL
 http://purl.flvc.org/fau/fd/FA00004175, http://purl.flvc.org/fau/fd/FA00004175
 Subject Headings
 Critical point theory (Mathematical analysis), Differentiable dynamical systems, Geometry,Differential, Lagrange equations, Lagrangian functions, Mathematical optimization, Surfaces of constant curvature
 Format
 Document (PDF)
 Title
 Decay for timedependent Schroedinger equations.
 Creator
 Zhou, Zhen, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

We study the decay in time of solutions of Schrodinger equations of the type du/du=idelta u+iV(t)u, establishing that for small potentials and initial data in L1 the solution u satisfies sup[u(x,t)](x element of R)
Show more We study the decay in time of solutions of Schrodinger equations of the type du/du=idelta u+iV(t)u, establishing that for small potentials and initial data in L1 the solution u satisfies sup[u(x,t)](x element of R)Show less  Date Issued
 1996
 PURL
 http://purl.flvc.org/fcla/dt/12463
 Subject Headings
 Mathematics
 Format
 Document (PDF)
 Title
 Derivation of planar diffeomorphisms from Hamiltonians with a kick.
 Creator
 Barney, Zalmond C., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

In this thesis we will discuss connections between Hamiltonian systems with a periodic kick and planar diffeomorphisms. After a brief overview of Hamiltonian theory we will focus, as an example, on derivations of the Hâenon map that can be obtained by considering kicked Hamiltonian systems. We will conclude with examples of Hâenon maps of interest.
 Date Issued
 2011
 PURL
 http://purl.flvc.org/FAU/3329833
 Subject Headings
 Mathematical physics, Differential equations, Partial, Hamiltonian systems, Algebra, Linear, Chaotic behavior in systems
 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)