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Tutorial on Elliptic Curve Arithmetic and Introduction to Elliptic Curve Cryptography (ECC)
MS, University of Cincinnati, 2017, Engineering and Applied Science: Computer Engineering
This thesis focuses on elliptic curve arithmetic over the prime field GF (p) and elliptic curve cryptography (ECC). ECC over GF(p) has its own arithmetic which is done over elliptic curves of the form y2; ≡ x3;+ax+b (mod p), where p is prime. ECC is gaining importance in security because it uses smaller keys to provide the same security level as the popular RSA. It is the superior cryptographic scheme based on time efficiency and resource utilization. It is more suitable than RSA for DNSSEC and IoT systems and devices. Unlike RSA, which is easily understood, ECC is complicated because of the arithmetic involved. It is not widely understood. We provide a tutorial on elliptic curve arithmetic and also explain the working of the ElGamal cryptosystem. We also describe general hardware-efficient methods to implement ECC such as Montgomery multiplication and projective coordinates. These methods are challenging to understand. Essentially, projective coordinates help reduce the number of inversions required in doing scalar multiplication. If Montgomery multiplication is used, a time-consuming operation like reduction modulo a prime p can be simplified. In this work, we also present a user-friendly Java GUI application to provide education in elliptic curve arithmetic and its applications in cryptosystems. Lastly, we provide a module of questions and solutions to do the same and also enable senior students and graduate students to use ECC in their project work.

#### Committee:

Carla Purdy, Ph.D. (Committee Chair); Wen-Ben Jone, Ph.D. (Committee Member); George Purdy, Ph.D. (Committee Member)

#### Subjects:

Computer Engineering

#### Keywords:

Elliptic Curve Cryptography;ECC Software;Public-Key Cryptography;RSA

Enhancing Security, Privacy, and Efficiency of Vehicular Networks
Doctor of Philosophy, The Ohio State University, 2017, Electrical and Computer Engineering

#### Committee:

Fusun Ozguner, Professor (Advisor); Can Emre Koksal, Professor (Committee Member); Xiaorui Wang, Professor (Committee Member)

#### Subjects:

Computer Engineering; Computer Science; Electrical Engineering; Transportation

#### Keywords:

Vehicular Networks; Public Key Infrastructure; Security; Privacy; Cryptography; Elliptic Curves Cryptography; Pairings; Group Signatures; Trust; Authentication; Grouping; Dedicated Short Range Communication; Beaconing Rate

Improved Cryptographic Processor Designs for Security in RFID and Other Ubiquitous Systems
Doctor of Philosophy, Case Western Reserve University, 2009, EECS - Computer Engineering
In order to provide security in ubiquitous, passively powered systems, especially RFID tags in the supply chain, improved asymmetric key cryptographic processors are presented, tested and compared with others from the literature. The proposed processors show a 12%-20% area and a 31%-45% time improvement. A secure protocol is also presented to minimize cryptographic effort and communication between tag and reader. A set of power management techniques is also presented to match processor performance to available power, resulting in greater range and responsiveness of RFID tags.

#### Committee:

Christos Papachristou, PhD (Committee Chair); Francis L. Merat, PhD (Committee Member); Swarup Bhunia, PhD (Committee Member); Xinmiao Zhang, PhD (Committee Member); Francis G. Wolff, PhD (Committee Member)

#### Subjects:

Computer Science; Electrical Engineering

#### Keywords:

Cryptography; elliptic curve cryptography; power management; RFID; embedded systems

An Exploration of Mathematical Applications in Cryptography
Master of Mathematical Sciences, The Ohio State University, 2015, Mathematics
Modern cryptography relies heavily on concepts from mathematics. In this thesis we will be discussing several cryptographic ciphers and discovering the mathematical applications which can be found by exploring them. This paper is intended to be accessible to undergraduate or graduate students as a supplement to a course in number theory or modern algebra. The structure of the paper also lends itself to be accessible to a person interested in learning about mathematics in cryptography on their own, since we will always give a review of the background material which will be needed before delving into the cryptographic ciphers.

#### Committee:

James Cogdell (Advisor); Rodica Costin (Committee Member)

#### Subjects:

Mathematics; Mathematics Education

#### Keywords:

cryptography; cryptographic ciphers; number theory; elliptic curve cryptography

DESIGN AND PERFORMANCE ANALYSIS OF A SECURE PROCES-SOR SCAN-SP WITH CRYPTO-BIOMETRIC CAPABILITIES
Doctor of Philosophy (PhD), Wright State University, 2009, Computer Science and Engineering PhD
Secure computing is gaining importance in recent times as computing capability is increasingly becoming distributed and information is everywhere. Prevention of piracy and digital rights management has become very important. Information security is mandatory rather than an additional feature. Numerous software techniques have been proposed to provide certain level of copyright and intellectual property protection. Techniques like obfuscation attempt to transform the code into a form that is harder to reverse engineer. Tamper-proofing causes a program to malfunction when it detects that it has been modified. Software watermarking embeds copyright notice in the software code to allow the owners of the software to assert their intellectual property rights. The software techniques discourage software theft, can trace piracy, prove ownership, but cannot prevent copying itself. Thus, software based security firewalls and encryption is not completely safe from determined hackers. This necessitates the need for information security at the hardware level, where secure processors assume importance. In this dissertation, a detailed architecture and instruction set of the SCAN-Secure Processor is proposed. The SCAN-SP is a modified SparcV8 processor architecture with a new instruction set to handle image compression, encryption, information hiding based on SCAN methodology and biometric authentication based on Local Global Graph methodology. A SCAN based methodology for encryption and decryption of 32 bit instructions and data is proposed. The modules to support the new instructions are synthesized in reconfigurable logic and the results of FPGA synthesis are presented. The ultimate goal of the proposed work is a detailed study of the tradeoffs that exists between speed of execution and security of the processor. Designing a faster processor is not the goal of the proposed work, rather exploring the architecture to provide security is of prime importance.

#### Committee:

Nikolaos Bourbakis, PhD (Advisor); Soon M. Chung, PhD (Committee Member); Jack S. N. Jean, PhD (Committee Member); Arnab Kumar Shaw, PhD (Committee Member); Peter Athanas, PhD (Committee Member); Arthur Goshtasby, PhD (Other); Joseph F. Thomas, Jr., PhD (Other)

#### Subjects:

Computer Science; Electrical Engineering; Engineering

#### Keywords:

Secure Processor; Cryptography; Steganography; Biometrics; SCAN methodology; Local-Global graphs

Device Specific Key Generation Technique for Anti-Counterfeiting Methods Using FPGA Based Physically Unclonable Functions and Artificial Intelligence
Master of Science in Electrical Engineering, University of Toledo, 2012, Electrical Engineering

Anti-counterfeiting techniques have entered a new era with the implementation of critical designs and confidential information transfer protocols. The complexity in developing security mechanisms and routing protocols for embedded systems continues to increase; on the other hand, cost and size constraints have been lowered. Trustworthy authentication of a device is of extreme importance for secure protocols. Methodologies for preventing IC piracy have been developed that require a unique signature key for every fabricated chip. Physically Unclonable Functions (PUFs) can be used for such signature generation.

This research implements a key generation process using a novel Ring Oscillator PUF (ROPUFs) design followed by an error correcting code, and a hashing algorithm. The key generation process has been implemented in three phases: ROPUF, Error Correction Process, and a Hashing Algorithm. The ROPUF design takes advantage of the unique characteristic properties of FPGAs. In this work, the ROPUFs are implemented using LUTs, multiplexers and flip flops that are the basic components of the FPGA architecture. The PUF design is followed by an error correction process to rectify any noisy bits in the response due to drastic environmental changes like temperature and voltage fluctuations. Artificial Neural Networks are used for the error correction process. The latter part of the research deals with a hashing function that has been implemented to enhance the security of the key generation process. The hashing function redresses the response bits of the PUF unit to mask the challenge-response pairs.

The proposed PUF circuit is implemented on 5 Xilinx Spartan 2 XC2S100 FPGAs, and an Agilent 16801A Logic Analyzer is used to obtain the PUF responses. The intra-chip and inter-chip responses are analyzed and plotted using Hamming distances. The overall uniqueness of the responses is found to be 49.0625% which is higher when compared to the previous implementations of the conventional ROPUF circuit (43.40%), and the earlier chain-implementation (48.51%). The inter-chip and intra-chip uniqueness factor for the proposed design are 47.929% and 41.91% respectively.

Artificial Neural Networks are tested using the PUF responses of various lengths. The failure rates of the proposed method are below 1 ppm which is lower than the failure rate of BCH codes which is typically 4.8 ppm. The SHA-256 algorithm is optimized using parallel processing techniques to give better throughput results. The delay is reduced to 45 clock cycles.

#### Committee:

Mohammed Niamat, PhD (Committee Chair); Weiqing Sun, PhD (Committee Co-Chair); Mansoor Alam, PhD (Committee Member)

#### Subjects:

Computer Science; Electrical Engineering

#### Keywords:

FPGA; PUF; Cryptography; Security; Error Correcting Code; Neural Network.

Architecture Design and Performance Optimization of Wireless Mesh Networks
PhD, University of Cincinnati, 2010, Engineering : Computer Science and Engineering

Wireless Mesh Network (WMN) is a promising wireless technology in providing high-bandwidth Internet access over a specific coverage area, with relative lower investment cost as compared to traditional access network. In a WMN, a mobile client (MC) can access the Internet through a wireless backbone formed by wireless Mesh Routers (MRs) which are interconnected in a multi-hop fashion while some MRs known as Internet Gateways (IGWs) act as the communication bridges between the wireless backbone and the Internet. The design of the network architecture is a fundamental issue for a WMN and is critical in determining the network performance and providing Quality of Service (QoS) for end users, and thus should be addressed carefully.

A unique characteristic of a WMN is the IGW oriented Internet traffic. Thus, the deployment of IGW is the key problem in the network design, and is investigated in this dissertation. Two IGW oriented network architecture are analyzed, and corresponding QoS requirements and constraints are evaluated. The IGW deployment problem is then formulated as a multiple objectives optimization problem. Besides the linear program approach, some heuristic algorithms are proposed and evaluated. Extensive simulations show the effectiveness of proposed solutions.

To improve the performance of a given WMN, load balancing between different IGW domains is also investigated. A fairness between IGWs domains improves the network performance and provides a better QoS for end users. The fairness index is defined for both homogenous and heterogeneous WMNs. A distributed load balancing scheme is proposed, and three load balancing algorithms based on diffusion methodology are introduced in the proposed scheme.

Authenticated key establishment (AKE) schemes enable two entities (e.g., a client and a server) to share common communication keys in an authentic way. Due to mobility of mesh clients (MCs), a WMN needs have a fast and efficient authentication and key establishment scheme to provide adequate security in client's handoff while meeting the Quality of Service (QoS) requirements. In this dissertation, we discuss the authentication performance requirements imposed by the unique WMN characteristics. Distributed authenticated key establishment schemes are proposed based on hierarchical multi-variable symmetric functions (HMSF) and identity-based cryptography (IBC) respectively, which enable fast key agreement and mutual authentication between network entities in a WMN. In the distributed authenticated key establishment scheme, network entities in a WMN such as MCs and mesh access points (e.g. mesh routers) can authenticate each other and establish pairwise communication keys without any interaction from a centralized authentication center, while substantially reducing the communication overhead and the authentication delay.

#### Committee:

Dharma Agrawal, DSc (Committee Chair); Kenneth Berman, PhD (Committee Member); Chia Han, PhD (Committee Member); Kelly Cohen, PhD (Committee Member); Ernest Hall, PhD (Committee Member)

Computer Science

#### Keywords:

Wireless Mesh Networks;Internet Gateway;Load Balancing;Authenticated Key Establishment;Symmetric Polynomial;Identity-based Cryptography

Square: A New Family of Multivariate Encryption Schemes
PhD, University of Cincinnati, 2009, Arts and Sciences : Mathematical Sciences
We describe and analyze a new family of multivariate encryption schemes, characterized by large characteristic and low-degree core maps. The patriarch system Square is broken, but the next generation of schemes - Square+, Square-, Double Layer Square, and Bivariate Square - all look promising.

#### Committee:

Dr. Jintai Ding (Committee Chair); Dr. Timothy Hodges (Committee Member); Dr. Dieter Schmidt (Committee Member)

Mathematics

#### Keywords:

Multivariate Cryptography; Public Key Encryption Scheme; Odd Characteristic

The application of cryptography to data base security /
Doctor of Philosophy, The Ohio State University, 1976, Graduate School

#### Committee:

Not Provided (Other)

Computer Science

#### Keywords:

Computers;Cryptography

Semi-Regular Sequences over F2
PhD, University of Cincinnati, 2015, Arts and Sciences: Mathematical Sciences
The concept of semi-regular sequences was introduced in order to assess the complexity of Gröumlbner basis algorithms such as F4 for the solution of polynomial equations. Despite the experimental evidence that semi-regular sequences are common, it was unknown whether there existed semi-regular sequences for all n, except in extremely trivial situations. In the present work I prove some results on the existence and non-existence of semi-regular sequences. It was observed by J. Schlather and T. Hodges that if an element of degree d in Β(n)-variables is semi-regular, then we must have n≤3d. In this thesis, I establish precisely when the elementary symmetric polynomial of degree d is semi-regular. In particular, when d=2t and n=3d, the elementary symmetric polynomial of degree d is semi-regular establishing that the bound given by J. Schlather and T. Hodges is sharp for infinitely many n. For the general case of existence of semi-regular sequences Bardet, Faug&egravere and Salvy conjecture that the proportion π(n, m, d1, . . . , dm) of semi-regular sequences over F2 in the set Ε(n, m, d1, . . . , dm) of algebraic systems of m equations of degrees d1, . . . , dm in n-variables tends to 1 as n tends to infinity. In this work, I show that for a fixed choice of (m, d1, . . . , dm), we have that limn→∞ π(n, m, d1, . . . , dm ) — 0 showing that the conjecture is false in this case.

#### Committee:

Timothy Hodges, Ph.D. (Committee Chair); Donald French, Ph.D. (Committee Member); Tara Smith, Ph.D. (Committee Member)

Mathematics

#### Keywords:

Abstract Algebra;Semi-Regular Sequences;Symmetric Polynomials;Cryptography;Regular Sequences;Systems of polynomial equations

A Test of Bell’s Inequality for the Undergraduate Laboratory
BA, Oberlin College, 2004, Physics and Astronomy
The thesis documents the work done over the year to initiate an undergraduate Advanced Laboratory experiment which tests Bell’s inequality. It provides reference theory for the experiment, including explanations of Bell inequalities, basics of nonlinear optics, type-I downconversion and entanglement, and polarization states of the entangled photons. A main result is the equipment and design proposal for the experiment, which will cost a total \$19600, led in price by the \$9000 of a four photodetector array and followed by the \$5000 of a 405nm pump laser. Entangled photons are produced by pumping BBO in a two-crystal geometry. Although most of the light is transmitted, some undergoes type-I parametric downconversion. Degenerate pairs are in a tunable entangled state and can be used to show non-classical behavior. Specifically, a violation of the CHSH Bell inequality can be observed. Usable coincidence rates of several thousand per second are expected. Experimental and data analysis methods are described as the basis of future laboratory documentation. Explanations of equipment alignment and adjustment and data collection are included, as well as derivations of relevant analyses of the experimental data. Lastly the coincidence circuit built for the experiment is reviewed. The circuit costs less than \$40 to construct and demonstrates a coincidence window of between 18ns and 36ns.

#### Subjects:

Experiments; Optics; Physics; Science Education

#### Keywords:

bell; entangle; entangled; entanglement; optics; experiment; inequality; downconversion; nonlinear; photodiode; polarization; coincidence; violation; quantum cryptography;

Asynchronous Physical Unclonable Function using FPGA-based Self-Timed Ring Oscillator
Master of Science in Electrical Engineering, University of Toledo, 2013, College of Engineering
Field Programmable Gate Array (FPGA) security has emerged as a challenging security paradigm in system design. Systems implemented on FPGAs require secure operations and communication. There is a growing concern over the security attributes of FPGAs regarding protecting and securing information processed within them, protecting designs during distribution and protecting intellectual property rights. One of the important aspects of improving the trustworthiness level of FPGAs is enhancing the physical security of FPGAs. A Physical Unclonable Function (PUF) provides a means to enhance physical security of Integrated Circuits (ICs) against piracy and unauthorized access. PUFs exploit the inherent and embedded randomness that occurs during the fabrication process of silicon devices. This thesis presents a novel FPGA-based PUF design technique using asynchronous logic. Significant process variations exist in IC fabrication, which makes each IC unique in its delay characteristics. The statistical delay variation in transistors and wires across FPGA chips is exploited through identically laid-out asynchronous ring oscillators. The asynchronous ring oscillators generate oscillations of varying frequencies when the oscillators are identically mapped on a semiconductor device. These varying frequencies produced by identically mapped self-timed ring oscillators are used to generate unique PUF response bits, which are used in device authentication and cryptographic applications such as generating secret keys and True Random Number Generator (TRNG). Experimental analysis shows that asynchronous oscillators of PUFs generate oscillations of varying frequencies, and the uniqueness for the PUF responses is 49.92%, which is very close to the desired 50% factor.

#### Committee:

Mohammed Niamat (Committee Chair); Robert C Green, II (Committee Member); Weiqing Sun (Committee Member)

#### Subjects:

Computer Engineering; Electrical Engineering

#### Keywords:

FPGA; STRO-PUF; Physical Unclonable Function; PUF; Self-Timed Ring Oscillator; Hardware Cryptography; Asynchronous Logic; Asynchronous Ring Oscillator

Rendering Secured Connectivity in a Wireless IoT Mesh Network with WPAN's and VANET's
PhD, University of Cincinnati, 2017, Engineering and Applied Science: Computer Science and Engineering
A ubiquitous pervasive network incorporates today’s Internet of Things/Internet of Everything Paradigm: Everything becomes smart with at least one microprocessor and a network interface. All these are under an umbrella of IoT/IoE paradigm where everything is network capable and connected. In most of the cases, these devices have multiple microprocessors and network interfaces at their disposal. In such a scenario, bringing every application to specific network on the same platform is critical, specifically for Sensor Networks, Cloud, WPANs and VANETs. While, enforcing and satisfying the requirements of CIA triad with non-repudiation universally is critical as this can solve multiple existing problems of ISM band exhaustion, leading to excessive collisions and contentions. Cooperative Interoperability also enables universal availability of data across all platforms which can be reliable and fully synchronized. Plug and play universal usability can be delivered. Such a network necessitates robust security and privacy protocols, spanning uniformly across all platforms. Once, reliable data access is made available, it leads to an accurate situation aware decision modeling. Simultaneous multiple channel usage can be exploited to maximize bandwidth otherwise unused. Optimizing Content delivery in hybrid mode which will be the major chunk of network traffic as predicted for near future of IoE. Now, such a proposed hybrid network does sound very complicated and hard to establish and maintain. However, this is the future of networks with huge leaps of technological advancement and ever dropping prices of hardware coupled with immensely improved capabilities, such a hybrid ubiquitous network can be designed and deployed in a realistic scenario. In this work, we go through not only looking into the issues of the large scale hybrid WMN, but also minutely discovering every possible scenario of direct mesh clients or sub-nets (VANET, Cloud or BAN) associated to it. Further, we propose to design and implement a robust all around security and privacy for each and every possible unit of such a large network. Special focus is provided to the application of a BAN in medical usage with intricate details is provided in form of our recent endeavor, along with an ongoing work for a wearable device patent, Smart Shoe (Patent Pending). The concepts explained with this example are equally applicable to any such Wireless Personal Area Networks (WPAN’s).

#### Committee:

Dharma Agrawal, D.Sc. (Committee Chair); Richard Beck, Ph.D. (Committee Member); Yizong Cheng, Ph.D. (Committee Member); Rashmi Jha, Ph.D. (Committee Member); Wen-Ben Jone, Ph.D. (Committee Member); Marepalli Rao, Ph.D. (Committee Member)

Computer Science

#### Keywords:

IoT;Mesh Networks;Security;Ubiquitous Networks;Vehicular Networks;Cryptography

Inverted Edwards Coordinates (Maire Model of an Elliptic Curve)
Master of Sciences, Case Western Reserve University, 2014, Applied Mathematics
Edwards curves are a fairly new way of expressing a family of elliptic curves that contain extremely desirable cryptographic properties over other forms that have been used. The most notable is the notion of a complete and unified addition law. This property makes Edwards curves extremely strong against side-channel attacks. In the analysis and continual development of Edwards curves, it has been seen in the original Edwards form that the use of inverted coordinates creates a more efficient addition/doubling algorithm. Using inverted coordinates, the field oper- ations drop from 10M + 1S (given correctly chosen curve parameters), to 9M + 1S. The sarcrifice is the loss of completeness, but unification remains. This pa- per examines the use of the inverted coordinates system over the binary Edwards form, and shows the underlying advantages of this transformation

#### Committee:

David Singer, PhD (Advisor); Elisabeth Werner, PhD (Committee Member); Johnathan Duncan, PhD (Committee Member)

#### Subjects:

Computer Science; Mathematics

#### Keywords:

elliptic curves; elliptic curve cryptography; edwards curves; ECDHKE; ECDSA; maire form; elliptic addition

Security of Unbalanced Oil-Vinegar Signature Scheme
PhD, University of Cincinnati, 2012, Arts and Sciences: Mathematical Sciences

We explore ideas for oil-vinegar signature schemes in the multivariate polynomial cryptography.

In the first half, we focus on TTS (Tame Transformation Signature) systems. We find a structure attack to defeat a family of TTS systems. Then we have the related complexity analysis to claim that a family of TTS systems can be broken in the time complexity O(261).

In the second half, we discuss the algebraic attack for the randomly built unbalanced oil-vinegar signature systems with different characteristics. Then we explore the security of those general oil-vinegar systems under F4 algorithm attack.

#### Committee:

Jintai Ding, PhD (Committee Chair); Dieter Schmidt, PhD (Committee Member); Ning Zhong, PhD (Committee Member)

#### Subjects:

Applied Mathematics

#### Keywords:

Signature Scheme; Cryptanalysis; Cryptography; TTS; F4; multivariate polynomial

HARDWARE IMPLEMENTATION OF A NOVEL ENCRYPTION ALGORITHM
MS, University of Cincinnati, 2006, Engineering : Computer Engineering
Multivariate cryptosystem is a novel cryptographic system which can offer very high security even for small key sizes. This particular feature makes this scheme very appealing for small and low-power computing devices. In this thesis work, we have implemented encryption algorithm of the symmetric multivariate cryptographic invention in hardware and evaluated its performance. Initially, the cryptographic system was implemented in software which formed the golden reference model of the system. A prototype for the cryptographic system was then built with encryption implemented in hardware and decryption in software. Hardware for the encryption algorithm was realized using an FPGA (Field Programmable Gate Array) as the hardware development platform. User can exercise the cryptographic application through a user-friendly interface. Resource utilization and performance of the encryption system were measured from the FPGA implementation. In the next phase of the thesis, a dedicated ASIC (Application Specific Integrated Circuit) was designed to implement the encryption algorithm. This ASIC was fabricated by MOSIS on AMI 0.5 micron process technology and tested successfully after manufacture. Performance of the Encryptor ASIC has been measured. This thesis work lays the foundation for achieving the long term goal of developing a smart-card like chip card with the cryptographic ASIC embedded in it.

#### Keywords:

cryptography; FPGA; multivariate cryptosystem; encryption hardware

Cryptanalysis of Rational Multivariate Public Key Cryptosystems
PhD, University of Cincinnati, 2010, Arts and Sciences : Mathematical Sciences

In 1989, Tsujii, Fujioka, and Hirayama proposed a family of multivariate public key cryptosystems, where the public key is given as a set of multivariate rational functions of degree 4 [22]. We call these the Rational Multivariate Public Key Cryptosystems (RMPKC). These cryptosystems are constructed via composition of two quadratic rational maps into one quartic rational map, which becomes the public key. In this paper, we present a cryptanalysis of RMPKC.

This cryptanalysis demonstrates success against two separate problems in mathematics which are difficult to solve: factorization of maps and solving multivariate non-linear polynomial equations. We first perform a factorization of the public key quartic rational map into two components which are quadratic. We then attack each quadratic component, providing a way to solve the quadratic equations.

Our cryptanalysis is of the strong type. We take a public key and create a private key. The cryptanalyst can decrypt a message equally as fast as the owner of the original private key.

Our work involving the factorization of maps starts applying work published by Faugere and Perret, who set out to do basically the same thing. Their method, however, was insufficient to attach RMPKC. We enhance the method using projections to lower dimensions.

Our work involving the solution of quadratic equations is inspired by a thorough analysis of the structure of RMPKC and identification of weaknesses within.

#### Committee:

Jintai Ding, PhD (Committee Chair); Timothy Hodges, PhD (Committee Member); Dieter Schmidt, PhD (Committee Member)

Mathematics

#### Keywords:

cryptography;multivariate public key;factorization of maps;quartic;rational;cryptanalysis

Hardware Trojan Detection in Cryptography IP Cores by Library Encoding Method
Master of Science in Engineering (MSEgr), Wright State University, 2015, Electrical Engineering
Security is the primary issue in current internet world through both software and hardware. The ever increase in demand of consumer electronics requires less design cycle. To speedup design cycle, companies are approaching third parties for common applications IPs like USB, cryptography, DSP etc. These third parties can introduce a malicious content, which is called Trojan. Trojan in the netlist can activate only with special input/trigger. Available Trojan detection techniques like delay, area, power fingerprinting techniques and Automatic Test Pattern Generator (ATPG) method are not suitable as they take more time, less accurate. This thesis presents a hardware Trojan detection in cryptography IP cores by library encoding method. The final netlist of cryptography IP cores are encoded and decoded by using a script written in python to protect the design from Trojan insertion. This method of encoding and decoding detects even 0.0008% of Trojan area and disable the Trojan from activation.

#### Committee:

Saiyu Ren, Ph.D. (Advisor); Raymond Siferd, Ph.D. (Committee Member); Jiafeng Xie, Ph.D. (Committee Member)

#### Subjects:

Electrical Engineering

#### Keywords:

Hardware Trojan, Cryptography IP, Library Encoding, Netlist

Security Mechanisms for Mobile Ad Hoc and Wireless Sensor Networks
PhD, University of Cincinnati, 2008, Engineering : Computer Science and Engineering

Wireless Ad Hoc Networks have emerged as an advanced networking paradigm based on collaborative efforts among multiple self-organized wireless communication devices. Without the requirement of a fixed infrastructure support, wireless ad hoc networks can be quickly deployed anywhere at any time when needed. The decentralized nature, minimal configuration and quick deployment of wireless ad hoc networks make them suitable for various applications, from disaster rescue, target tracking to military conflicts. Wireless ad hoc networks can be further categorized into mobile ad hoc networks (MANETs), wireless sensor networks (WSNs), and wireless mesh networks (WMNs) depending on their applications.

Security is a big challenge in wireless ad hoc networks due to the lack of any infrastructure support, dynamic network topology, shared radio medium, and resource-constrained wireless users. Most existing security mechanisms applied for the Internet or traditional wireless networks are neither applicable nor suitable for wireless ad hoc network environments. In MANETs, routing security is an extremely important issue, as the majority of the standard routing protocols assume non-hostile environments. Once deployed in a hostile environment and working in an unattended mode, existing routing protocols are vulnerable to various attacks. To address these concerns, we propose an anonymous secure routing protocol for MANETs in this dissertation, which can be incorporated with existing routing protocols and achieve enhanced routing security with minimum additional overheads.

In WSNs, key distribution and management is the core issue of any security approaches. Due to extremely resource-constrained sensor nodes and lack of any infrastructure support, traditional public-key based key distribution and management mechanisms are commonly considered as too expensive to be employed in WSNs. In this dissertation, we propose two efficient pairwise key pre-distribution and management mechanisms for both distributed and hierarchical large-scale WSNs, which enable establishing secure links between any two sensor nodes located within their communication range. As we know, sensing and communication are two fundamental characteristics of WSNs, and they cannot be addressed separately. Existing work on sensing coverage mainly focus on how to use the minimum number of sensors to achieve a required coverage, while security constraints are not sufficiently addressed. We propose an effective key distribution approach for randomly deployed WSNs, based on random graph theory and a realistic random key pre-distribution mechanism, in order to achieve both robust sensing coverage and secure connectivity simultaneously in a hostile deployment environment.

#### Committee:

Dharma Agrawal (Committee Chair); Jerome Paul (Committee Member); Wen-Ben Jone (Committee Member); Chia-Yung Han (Committee Member); Ernest Hall (Committee Member)

#### Subjects:

Communication; Computer Science

#### Keywords:

Wireless Ad Hoc Network; Mobile Ad Hoc Network (MANET); Wireless Sensor Network (WSN); Routing; Security; Cryptography; Key Management; Distributed Wireless Network; Hierarchical Wireless Network; Sensing Coverage; Secured Connectivity

A Portable and Improved Implementation of the Diffie-Hellman Protocol for Wireless Sensor Networks
Master of Science in Mathematics, Youngstown State University, 2009, Department of Mathematics and Statistics
Wireless sensor nodes generally face serious limitations in terms of computational power, energy supply, and network bandwidth. One of the biggest challenges faced by researches today is to provide effective and secure techniques for establishing cryptographic keys between wireless sensor networks. Public-key algorithms (such as the Diffie-Hellman key-exchange protocol) generally have high energy requirements because they require computational expensive operations. So far, due to the limited computation power of the wireless sensor devices, the Diffie-Hellman protocol is considered to be beyond the capabilities of today's sensor networks. We analyzed existing methods of implementing Diffie-Hellman and proposed a new improved method of implementing the Diffie-Hellman key-exchange protocol for establishing secure keys between wireless sensor nodes. We also provide an easy-to-use implementation of the Elliptic Curve Diffie-Hellman key-exchange protocol for use in wireless sensor networks.

#### Committee:

Graciela Perera, PhD (Advisor); John Sullins, PhD (Committee Member); Jamal Tartir, PhD (Committee Member)

#### Subjects:

Communication; Computer Science; Information Systems; Mathematics

#### Keywords:

Wireless Sensor Networks; Sun SPOTS; Diffie-Hellman Key-Exchange Protocol; Elliptic Curve Cryptography; Elliptic Curve Diffie-Hellman; Portable Diffie-Hellman

The Knapsack Problem, Cryptography, and the Presidential Election
Master of Science in Mathematics, Youngstown State University, 2012, Department of Mathematics and Statistics

The 0-1 Knapsack Problem is an NP-hard optimization problem that has been studied extensively since the 1950s, due to its real world significance. The basic problem is that a knapsack with a weight capacity c is to be filled with a subset of n items. Each item i, has a weight value wi and a profit value pi. The goal is to maximize total profit value without the having the total weight exceed the capacity.

In this thesis, the 0-1 Knapsack Problem is introduced and some of the research and applications of the problem are given. Pisinger's branch-and-bound algorithm that will converge to an optimal solution is presented. One of the earliest applications of the knapsack problem, the knapsack cryptosystems, is then discussed. The earliest knapsack cryptosystem, the Merkle-Hellman Cryptosystem, is described along with how Adi Shamir broke this cryptosystem. Generating functions are then used to provide a number of solutions to a knapsack problem. Using the generating function of the knapsack problem, the paper concludes with an application on the Electoral College.

#### Committee:

Nathan Ritchey, PhD (Advisor); Jozsi Jalics, PhD (Committee Member); Jacek Fabrykowski, PhD (Committee Member)

Mathematics

#### Keywords:

Knapsack Problem; Cryptography; Generating Functions

The Elliptic Curve Group Over Finite Fields: Applications in Cryptography
Master of Science in Mathematics, Youngstown State University, 2012, Department of Mathematics and Statistics
It is the intent of this thesis to study the mathematics, and applications behind the elliptic curve group over Fp. Beginning with the definition of the '+' operation,under which the points on the elliptic curves form an abelian group. Then moving to a brief introduction to both public, and private key cryptography. This will lead into an explanation of the discrete logarithm problem along with an implementation using the elliptic curve group over Fp. This thesis will conclude with an exploration Lenstra's factoring algorithm using the elliptic curve group.

#### Committee:

Jacek Fabrykowski, Ph.D. (Advisor); Neil Flowers, Ph.D. (Committee Member); Thomas Smotzer, Ph.D. (Committee Member)

#### Keywords:

Elliptic Curve Group; Cryptography

EFFICIENT IMPLEMENTATION OF ELLIPTIC CURVE CRYPTOGRAPHY IN RECONFIGURABLE HARDWARE
Master of Sciences (Engineering), Case Western Reserve University, 2012, EECS - Electrical Engineering
Elliptic curve cryptography (ECC) has emerged as a promising public-key cryptography approach for data protection. It is based on the algebraic structure of elliptic curves over finite fields. Although ECC provides high level of information security, it involves computationally intensive encryption/decryption process, which negatively affects its performance and energy-efficiency. Software implementation of ECC is often not amenable for resource-constrained embedded applications. Alternatively, hardware implementation of ECC has been investigated – in both application specific integrated circuit(ASIC) and field programmable gate array (FPGA) platforms – in order to achieve desired performance and energy efficiency. Hardware reconfigurable computing platforms such as FPGAs are particularly attractive platform for hardware acceleration of ECC for diverse applications, since they involve significantly less design cost and time than ASIC. In this work, we investigate efficient implementation of ECC in reconfigurable hardware platforms. In particular, we focus on implementing different ECC encryption algorithms in FPGA and a promising memory array based reconfigurable computing framework, referred to as MBC. MBC leverages the benefit of nanoscale memory, namely, high bandwidth, large density and small wire delay to drastically reduce the overhead of programmable interconnects. We evaluate the performance and energy efficiency of these platforms and compare those with a purely software implementation. We use the pseudo-random curve in the prime field and Koblitz curve in the binary field to do the ECC scalar multiplication operation. We perform functional validation with data that is recommended by NIST. Simulation results show that in general, MBC provides better energy efficiency than FPGA while FPGA provides better latency.

#### Committee:

Swarup Bhunia (Advisor); Christos Papachristou (Committee Member); Frank Merat (Committee Member)

#### Subjects:

Electrical Engineering

#### Keywords:

Elliptic curve cryptography; ECC; MAHA; MBC; FPGA; low-power; encryption; security

BioCompT - A Tutorial on Bio-Molecular Computing
MS, University of Cincinnati, 2013, Engineering and Applied Science: Computer Engineering
DNA computing is a new and interesting development that connects computer science to molecular biology. The idea of DNA computing arose from Adleman's 1994 experiment in which he showed how to solve the Hamiltonian path problem (HPP) in polynomial time using oligonucleotides of DNA. DNA computing enables massive parallelism at the molecular level and is one of the technologies being explored by researchers as a supplement to traditional silicon-based computing. But many computer scientists and computer engineers have little knowledge of biology and therefore find it difficult to get started in the field of DNA computing. Thus the aim of this work is to provide a tutorial to introduce DNA computing to a wider audience and to show some examples of how DNA computing can be simulated using agent-based techniques and can be applied to solve complex problems. Currently our system consists of four sections: DNA structure and behavior, basic DNA computation, DNA-based cryptography, and using agent based modeling and simulation to explore DNA behavior. We also provide a small assessment test to enable users to test themselves and evaluate their knowledge of the topics covered. The system is modular in design and can easily be modified or extended to include more information on each topic or to include additional examples of DNA computing.

#### Committee:

Carla Purdy, Ph.D. (Committee Chair); George Purdy, Ph.D. (Committee Member); Anca Ralescu, Ph.D. (Committee Member)

#### Subjects:

Computer Engineering

#### Keywords:

DNA Computing;agent-based modeling;DNA based cryptography;Bio-molecular computing;DNA structure and behavior;tutorial on DNA computing;

Fast Signature Schemes Over Odd Characteristic
PhD, University of Cincinnati, 2009, Arts and Sciences : Mathematical Sciences
We explore ideas for speeding up HFE-based signature schemes. In particular, we propose three HFEv-based systems with odd characteristic and secret core maps of low degree. In two of these schemes, the core map is quadratic. Changing the characteristic of the system has a profound effect, which we attempt to explain and also demonstrate through experiments. We discuss known attacks which could possibly topple such systems, especially algebraic attacks. After testing the resilience of these schemes against F4, we suggest parameters that yield acceptable security levels.

#### Committee:

Jintai Ding (Committee Chair); Timothy Hodges (Committee Member); Dieter Schmidt (Committee Member)

Mathematics

#### Keywords:

Cryptography; Signature Schemes; Odd Characteristic