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Title: LINEAR CODES AND RECURRENT SEQUENCES.
Creator: HAMLIN, ALLEN CHARLES, Florida Atlantic University
Abstract/Description: In this paper, a brief introduction to coding theory is presented. Linear (block) codes arc briefly discussed along with some of their error (multiple error, burst error) correction and detection properties. Recurrent sequences are discussed in the major portion of the paper, and it is shown that the study of general recurrent sequences is equivalent to the study of sequences associated with irreducible polynomials. The paper concludes with a brief mention of autocorrelation functions and a...
Show moreIn this paper, a brief introduction to coding theory is presented. Linear (block) codes arc briefly discussed along with some of their error (multiple error, burst error) correction and detection properties. Recurrent sequences are discussed in the major portion of the paper, and it is shown that the study of general recurrent sequences is equivalent to the study of sequences associated with irreducible polynomials. The paper concludes with a brief mention of autocorrelation functions and a way of finding the minimal recursion of a recurrent sequence given some terms of the sequence. The paper is an exposition of previously known results. Some modification in notation and proofs has been done to present the material in a unified and more readable manner.
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Date Issued: 1973
PURL: http://purl.flvc.org/fcla/dt/13552
Subject Headings: Coding theory
Format: Document (PDF)

Title: Covert and multilevel visual cryptographic schemes.
Creator: Lopez, Jessica Maria, Florida Atlantic University, Mullin, Ronald C.
Abstract/Description: Visual cryptography concerns the problem of "hiding" a monochrome image among sets of transparencies, known as shares. These are created in such a fashion that certain sets of shares when superimposed, will reveal the image; while other subsets yield no information. A standard model is the (k, n) scheme, where any k shares will reveal the image, but any k - 1 or fewer shares reveal no information. In this thesis, we explain the basic mechanism for creating shares. We survey the literature and...
Show moreVisual cryptography concerns the problem of "hiding" a monochrome image among sets of transparencies, known as shares. These are created in such a fashion that certain sets of shares when superimposed, will reveal the image; while other subsets yield no information. A standard model is the (k, n) scheme, where any k shares will reveal the image, but any k - 1 or fewer shares reveal no information. In this thesis, we explain the basic mechanism for creating shares. We survey the literature and show how to create (k, k) schemes which exist for all k > 2. Then we introduce perfect hash functions, which can be used to construct (k, n) schemes from (k, k) schemes for all 2 < k < n. We introduce generalizations of (k, n) schemes that we call covert cryptographic schemes, and extend this notion to multilevel visual cryptographic schemes. We give conditions for the existence of such schemes, and we conclude with a survey of generalizations.
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Date Issued: 2005
PURL: http://purl.flvc.org/fcla/dt/13206
Subject Headings: Coding theory, Cryptography, Data encryption (Computer science)
Format: Document (PDF)

Title: Implementation and comparison of the Golay and first order Reed-Muller 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 first-order 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 error-correcting 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 first-order 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 error-correcting capability and the practical speed of the Golay code and the first-order Reed-Muller code to meet our goal.
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Date Issued: 2013
PURL: http://purl.flvc.org/fcla/dt/3362579
Subject Headings: Error-correcting codes (Information theory), Coding theory, Computer algorithms, Digital modulation
Format: Document (PDF)

Title: Turbo-coded frequency division multiplexing for underwater acoustic communications between 60 kHz and 90 kHz.
Creator: Pajovic, Milutin., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: The Intermediate Frequency Acoustic Modem (IFAM), developed by Dr. Beaujean, is designed to transmit the command-and-control messages from the top-side to the wet-side unit in ports and very shallow waters. This research presents the design of the turbo coding scheme and its implementation in the IFAM modem with the purpose of meeting a strict requirement for the IFAM error rate performance. To simulate the coded IFAM, a channel simulator is developed. It is basically a multi-tap filter whose...
Show moreThe Intermediate Frequency Acoustic Modem (IFAM), developed by Dr. Beaujean, is designed to transmit the command-and-control messages from the top-side to the wet-side unit in ports and very shallow waters. This research presents the design of the turbo coding scheme and its implementation in the IFAM modem with the purpose of meeting a strict requirement for the IFAM error rate performance. To simulate the coded IFAM, a channel simulator is developed. It is basically a multi-tap filter whose parameters are set depending on the channel geometry and system specifics. The simulation results show that the turbo code is able to correct 89% of the messages received with errors in the hostile channel conditions. The Bose-Chadhuri-Hocquenghem (BCH) coding scheme corrects less that 15% of these messages. The other simulation results obtained for the system operation in different shallow water settings are presented.
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Date Issued: 2009
PURL: http://purl.flvc.org/FAU/215291
Subject Headings: Underwater acoustics, Measurement, Coding theory, Signal processing, Digital techniques
Format: Document (PDF)

Title: Massively parallel computation and porting of EPIC research hydro code on Cray-T3D.
Creator: Dutta, Arindum., Florida Atlantic University, Tsai, Chi-Tay
Abstract/Description: The objective of the work is to verify the feasibility of converting a large FEA code into a massively parallel FEA code in terms of computational speed and cost. Sequential subroutines in the Research EPIC hydro code, a Lagrangian finite element analysis code for high velocity elastic-plastic impact problems, are individually converted into parallel code using Cray Adaptive Fortran (CRAFT). The performance of massively parallel subroutines running on 32 PEs on Cray-T3D is faster than their...
Show moreThe objective of the work is to verify the feasibility of converting a large FEA code into a massively parallel FEA code in terms of computational speed and cost. Sequential subroutines in the Research EPIC hydro code, a Lagrangian finite element analysis code for high velocity elastic-plastic impact problems, are individually converted into parallel code using Cray Adaptive Fortran (CRAFT). The performance of massively parallel subroutines running on 32 PEs on Cray-T3D is faster than their sequential counterparts on Cray-YMP. At next stage of the research, Parallel Virtual Machine (PVM) directives is used to develop a PVM version of the EPIC hydro code by connecting the converted parallel subroutines running on multiple PEs of T3D to the sequential part of the code running on single PE. With an incremental increase in the massively parallel subroutines into the PVM EPIC hydro code, the performance with respect to speedup of the code increased accordingly. The results indicate that significant speedup can be achieved in the EPIC hydro code when most or all of the subroutines are massively parallelized.
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Date Issued: 1996
PURL: http://purl.flvc.org/fcla/dt/15249
Subject Headings: Parallel processing (Electronic computers), Computer programs, coding theory, Supercomputers
Format: Document (PDF)

Title: A new approach to the inverse kinematic analysis of redundant robots.
Creator: Dutta, Partha Sarathi., Florida Atlantic University
Abstract/Description: A new approach has been developed for inverse kinematic analysis of redundant robots. In case of redundant robots inverse kinematics is complicated by the non-square nature of the Jacobian. In this method the Jacobian and inverse kinematic equation are reduced based on the rank of the Jacobian and the constraints specified. This process automatically locks some joints of the robot at various trajectory points. The reduced inverse kinematic equation is solved by an iterative procedure to find...
Show moreA new approach has been developed for inverse kinematic analysis of redundant robots. In case of redundant robots inverse kinematics is complicated by the non-square nature of the Jacobian. In this method the Jacobian and inverse kinematic equation are reduced based on the rank of the Jacobian and the constraints specified. This process automatically locks some joints of the robot at various trajectory points. The reduced inverse kinematic equation is solved by an iterative procedure to find joint variable values for known task description. The results of computer simulation of the inverse kinematics applied on a redundant planar robot and a redundant moving base robot proved the method to be efficient, and the results can be found within a few iterations with excellent accuracy.
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Date Issued: 1988
PURL: http://purl.flvc.org/fcla/dt/14433
Subject Headings: Parallel processing (Electronic computers), Computer programs, coding theory, Supercomputers
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.
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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: Elliptic curves: identity-based signing and quantum arithmetic.
Creator: Budhathoki, Parshuram, Steinwandt, Rainer, Eisenbarth, Thomas, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: Pairing-friendly curves and elliptic curves with a trapdoor for the discrete logarithm problem are versatile tools in the design of cryptographic protocols. We show that curves having both properties enable a deterministic identity-based signing with “short” signatures in the random oracle model. At PKC 2003, Choon and Cheon proposed an identity-based signature scheme along with a provable security reduction. We propose a modification of their scheme with several performance benefits. In...
Show morePairing-friendly curves and elliptic curves with a trapdoor for the discrete logarithm problem are versatile tools in the design of cryptographic protocols. We show that curves having both properties enable a deterministic identity-based signing with “short” signatures in the random oracle model. At PKC 2003, Choon and Cheon proposed an identity-based signature scheme along with a provable security reduction. We propose a modification of their scheme with several performance benefits. In addition to faster signing, for batch signing the signature size can be reduced, and if multiple signatures for the same identity need to be verified, the verification can be accelerated. Neither the signing nor the verification algorithm rely on the availability of a (pseudo)random generator, and we give a provable security reduction in the random oracle model to the (`-)Strong Diffie-Hellman problem. Implementing the group arithmetic is a cost-critical task when designing quantum circuits for Shor’s algorithm to solve the discrete logarithm problem. We introduce a tool for the automatic generation of addition circuits for ordinary binary elliptic curves, a prominent platform group for digital signatures. Our Python software generates circuit descriptions that, without increasing the number of qubits or T-depth, involve less than 39% of the number of T-gates in the best previous construction. The software also optimizes the (CNOT) depth for F2-linear operations by means of suitable graph colorings.
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Date Issued: 2014
PURL: http://purl.flvc.org/fau/fd/FA00004182, http://purl.flvc.org/fau/fd/FA00004182
Subject Headings: Coding theory, Computer network protocols, Computer networks -- Security measures, Data encryption (Computer science), Mathematical physics, Number theory -- Data processing
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.
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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: Signature schemes in single and multi-user settings.
Creator: Villanyi, Viktoria., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: In the first chapters we will give a short introduction to signature schemes in single and multi-user settings. We give the definition of a signature scheme and explain a group of possible attacks on them. In Chapter 6 we give a construction which derives a subliminal-free RSA public key. In the construction we use a computationally binding and unconditionally hiding commitment scheme. To establish a subliminal-free RSA modulus n, we have to construct the secret primes p and q. To prove p and...
Show moreIn the first chapters we will give a short introduction to signature schemes in single and multi-user settings. We give the definition of a signature scheme and explain a group of possible attacks on them. In Chapter 6 we give a construction which derives a subliminal-free RSA public key. In the construction we use a computationally binding and unconditionally hiding commitment scheme. To establish a subliminal-free RSA modulus n, we have to construct the secret primes p and q. To prove p and q are primes we use Lehmann's primality test on the commitments. The chapter is based on the paper, "RSA signature schemes with subliminal-free public key" (Tatra Mountains Mathematical Publications 41 (2008)). In chapter 7 a one-time signature scheme using run-length encoding is presented, which in the random oracle model offers security against chosen-message attacks. For parameters of interest, the proposed scheme enables about 33% faster verification with a comparable signature size than a construction of Merkle and Winternitz. The public key size remains unchanged (1 hash value). The main cost for the faster verification is an increase in the time required for signing messages and for key generation. The chapter is based on the paper "A one-time signature using run-length encoding" (Information Processing Letters Vol. 108, Issue 4, (2008)).
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Date Issued: 2009
PURL: http://purl.flvc.org/FAU/215289
Subject Headings: Information technology, Security measures, Cryptography, Coding theory, Data encryption (Computer science), DIgital watermarking
Format: Document (PDF)

Title: Static error modeling of sensors applicable to ocean systems.
Creator: Ah-Chong, Jeremy Fred., Florida Atlantic University, An, Edgar
Abstract/Description: This thesis presents a method for modeling navigation sensors used on ocean systems and particularly on Autonomous Underwater Vehicles (AUV). An extended Kalman filter was previously designed for the implementation of the Inertial Navigation System (INS) making use of Inertial Measurement Unit (IMU), a magnetic compass, a GPS/DGPS system and a Doppler Velocity Log (DVL). Emphasis is put on characterizing the static sensor error model. A "best-fit ARMA model" based on the Aikake Information...
Show moreThis thesis presents a method for modeling navigation sensors used on ocean systems and particularly on Autonomous Underwater Vehicles (AUV). An extended Kalman filter was previously designed for the implementation of the Inertial Navigation System (INS) making use of Inertial Measurement Unit (IMU), a magnetic compass, a GPS/DGPS system and a Doppler Velocity Log (DVL). Emphasis is put on characterizing the static sensor error model. A "best-fit ARMA model" based on the Aikake Information Criterion (AIC), Whiteness test and graphical analyses were used for the model identification. Model orders and parameters were successfully estimated for compass heading, GPS position and IMU static measurements. Static DVL measurements could not be collected and require another approach. The variability of the models between different measurement data sets suggests online error model estimation.
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Date Issued: 2003
PURL: http://purl.flvc.org/fcla/dt/12977
Subject Headings: Underwater navigation, Kalman filtering, Error-correcting codes (Information theory), Detectors
Format: Document (PDF)

Title: Distinguishability of Public Keys and Experimental Validation: The McEliece Public-Keyed Cryptosystem.
Creator: Pham, Hai, Steinwandt, Rainer, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: As quantum computers continue to develop, they pose a threat to cryptography since many popular cryptosystems will be rendered vulnerable. This is because the security of most currently used asymmetric systems requires the computational hardness of the integer factorization problem, the discrete logarithm or the elliptic curve discrete logarithm problem. However, there are still some cryptosystems that resist quantum computing. We will look at code-based cryptography in general and the...
Show moreAs quantum computers continue to develop, they pose a threat to cryptography since many popular cryptosystems will be rendered vulnerable. This is because the security of most currently used asymmetric systems requires the computational hardness of the integer factorization problem, the discrete logarithm or the elliptic curve discrete logarithm problem. However, there are still some cryptosystems that resist quantum computing. We will look at code-based cryptography in general and the McEliece cryptosystem specifically. Our goal is to understand the structure behind the McEliece scheme, including the encryption and decryption processes, and what some advantages and disadvantages are that the system has to offer. In addition, using the results from Courtois, Finiasz, and Sendrier's paper in 2001, we will discuss a digital signature scheme based on the McEliece cryptosystem. We analyze one classical algebraic attack against the security analysis of the system based on the distinguishing problem whether the public key of the McEliece scheme is generated from a generating matrix of a binary Goppa code or a random binary matrix. The idea of the attack involves solving an algebraic system of equations and we examine the dimension of the solution space of the linearized system of equations. With the assistance from a paper in 2010 by Faugere, Gauthier-Umana, Otmani, Perret, Tillich, we will see the parameters needed for the intractability of the distinguishing problem.
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Date Issued: 2015
PURL: http://purl.flvc.org/fau/fd/FA00004535, http://purl.flvc.org/fau/fd/FA00004535
Subject Headings: Coding theory, Combinatorial analysis, Data encryption (Computer science), Data transmission systems -- Security measures, Information theory, McEliece, Robert J. -- Influence, Public key cryptography
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.
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Date Issued: 2017
PURL: http://purl.flvc.org/fau/fd/FA00004840, http://purl.flvc.org/fau/fd/FA00004840
Subject Headings: Computer networks--Security measures., Computer security., Computers--Access control--Code words., Cyberinfrastructure., Computer network architectures., Cryptography., Number theory--Data processing.
Format: Document (PDF)

Coding theory (9)	+ -
Data encryption (Computer science) (6)	+ -
Cryptography (4)	+ -
Computer programs (2)	+ -
Error-correcting codes (Information theory) (2)	+ -

Parallel processing (Electronic computers) (2)	+ -
Supercomputers (2)	+ -
coding theory (2)	+ -
Ciphers (1)	+ -
Combinatorial analysis (1)	+ -
Combinatorial designs and configurations (1)	+ -
Computer algorithms (1)	+ -
Computer network architectures. (1)	+ -
Computer network protocols (1)	+ -
Computer networks -- Security measures (1)	+ -
Computer networks--Security measures. (1)	+ -
Computer security (1)	+ -
Computer security. (1)	+ -
Computers--Access control--Code words. (1)	+ -
Cryptography. (1)	+ -
Cyberinfrastructure. (1)	+ -
DIgital watermarking (1)	+ -
Data transmission systems -- Security measures (1)	+ -
Design and construction (1)	+ -
Detectors (1)	+ -
Digital modulation (1)	+ -
Digital techniques (1)	+ -
Group theory (1)	+ -
Information technology (1)	+ -
Information theory (1)	+ -

Florida Atlantic University (9)	+ -
Charles E. Schmidt College of Science (7)	+ -
Department of Mathematical Sciences (7)	+ -
Steinwandt, Rainer (2)	+ -
Ah-Chong, Jeremy Fred. (1)	+ -

An, Edgar (1)	+ -
Budhathoki, Parshuram (1)	+ -
College of Engineering and Computer Science (1)	+ -
Department of Ocean and Mechanical Engineering (1)	+ -
Dutta, Arindum. (1)	+ -
Dutta, Partha Sarathi. (1)	+ -
Eisenbarth, Thomas (1)	+ -
HAMLIN, ALLEN CHARLES (1)	+ -
Karabina, Koray (1)	+ -
Lopez, Jessica Maria (1)	+ -
Magliveras, Spyros S. (1)	+ -
Matheis, Kenneth. (1)	+ -
Mithila, Shifat P. (1)	+ -
Mullin, Ronald C. (1)	+ -
Pajovic, Milutin. (1)	+ -
Pham, Hai (1)	+ -
Shukina, Olga. (1)	+ -
Sramka, Michal (1)	+ -
Tsai, Chi-Tay (1)	+ -
Villanyi, Viktoria. (1)	+ -

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