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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

High Speed Clock Glitching
Master of Science in Electrical Engineering, Cleveland State University, 2015, Washkewicz College of Engineering
In recent times, hardware security has drawn lot of interest in the research community. With physical proximity to the target devices, various fault injection hardware attack methods have been proposed and tested to alter their functionality and trigger behavior not intended by the design. There are various types of faults that can be injected depending on the parameters being used and the level at which the device is tampered with. The literature describes various fault models to inject faults in clock of the target but there are no publications on overclocking circuits for fault injection. The proposed method bridges this gap by conducting high-speed clock fault injection on latest high-speed micro-controller units where the target device is overclocked for a short duration in the range of 4-1000 ns. This thesis proposes a method of generating a high-speed clock and driving the target device using the same clock. The properties of the target devices for performing experiments in this research are: Externally accessible clock input line and GPIO line. The proposed method is to develop a high-speed clock using custom bit-stream sent to FPGA and subsequently using external analog circuitry to generate a clock-glitch which can inject fault on the target micro-controller. Communication coupled with glitching allows us to check the target’s response, which can result in information disclosure. This is a form of non-invasive and effective hardware attack. The required background, methodology and experimental setup required to implement high-speed clock glitching has been discussed in this thesis. The impact of different overclock frequencies used in clock fault injection is explored. The preliminary results have been discussed and we show that even high-speed micro-controller units should consider countermeasures against clock fault injection. Influencing the execution of Tiva C Launchpad and STM32F4 micro-controller units has been shown in this thesis. The thesis details the method used for the testing and the parameters used in the process are included. The implementation and design of the clock-glitch prototype system on the FPGA-clock jitter cleaner platform is discussed in this research. Glitching the execution of high-frequency targets is the goal of this project.

#### Committee:

Chansu Yu, PhD. (Committee Chair); Pong Chu, PhD. (Committee Member); Sanchita Mal-Sarkar, PhD. (Committee Member); Swarup Bhunia, PhD. (Committee Member)

#### Subjects:

Electrical Engineering; Engineering

#### Keywords:

Fault Injection; Clock glitching; Hardware attacks; RSA; High-speed clock; ARM Cortex-M4

Internalizing Symptoms Moderate Pre- to Post-Treatment Associations between Externalizing Psychopathology and Respiratory Sinus Arrhythmia among Preschoolers with ADHD
Master of Arts, The Ohio State University, 2016, Psychology
Respiratory sinus arrhythmia (RSA), an index of parasympathetic-linked cardiac activity, is a reliable biomarker of emotion regulation capabilities, given appropriate stimulus conditions. Low resting RSA and excessive RSA reactivity (withdrawal) to emotion evocation are associated consistently with clinical levels of internalizing and externalizing psychopathology. Moreover, concurrently elevated levels of both internalizing and externalizing symptoms predict greater RSA reactivity to emotion evocation than either alone. No studies, however, have examined whether internalizing symptoms moderate longitudinal associations between RSA and externalizing psychopathology among preschoolers treated for behavior problems. I assessed resting RSA and RSA reactivity to emotion evocation, both before and after preschool children (n=99) with ADHD participated in the Incredible Years intervention, and compared their responding to that of age-matched, typically developing controls (n=33). Different associations between externalizing symptoms and RSA were observed depending on levels of internalizing symptoms. Children with high externalizing scores and low internalizing scores exhibited reductions in resting RSA from pre- to post-treatment, whereas children with high externalizing scores and high internalizing scores exhibited increases in resting RSA. Finally, high externalizing scores and high internalizing scores predicted greater RSA withdrawal to emotion evocation following the intervention. Implications for contemporary models of emotion regulation are discussed.

#### Committee:

Theodore Beauchaine, Ph.D. (Advisor); Michael Vasey, Ph.D. (Committee Member); Mary Fristad, Ph.D., ABPP (Committee Member)

#### Subjects:

Clinical Psychology

#### Keywords:

RSA, HRV, internalizing, externalizing, intervention

RSA, Public-Key Cryptography, and Authentication Protocols
Master of Science in Mathematics, Youngstown State University, 2012, Department of Mathematics and Statistics
In the modern electronic age, secure communication is vital to the efficient workings in all areas of life. From governmental proceedings and military devices to personal banking and email, securely communicating between parties has become a necessity that has furthered research in the field of cryptography. This thesis is an introduction to a particular type of cryptography, public-key cryptography, and examines the basics of RSA and ElGamal cryptosystems. Worked-out examples for these types of encryption, decryption and authentication protocols are explored, as well.

#### Committee:

Jacek Fabrykowski, PhD (Advisor); Thomas Smotzer, PhD (Committee Member); George Yates, PhD (Committee Member)

#### Subjects:

Applied Mathematics; Mathematics

#### Keywords:

RSA; ElGamal; public-key; encryption; authentication protocol

Master of Arts, Case Western Reserve University, 2013, Psychology