MS, Kent State University, 2024, College of Arts and Sciences / Department of Computer Science

Cryptography, derived from the Greek word meaning "to hide information," involves techniques for converting readable plaintext into unreadable ciphertext through a process called encryption. Cryptography algorithms are broadly categorized into two types: symmetric key cryptography and asymmetric key cryptography. Symmetric key cryptography is further divided into block ciphers and stream ciphers. Block ciphers, based on their structure, can be classified into two main categories: Substitution-Permutation Networks (SPN) and Feistel Networks (FN). This research focuses on SPN-based block ciphers. In 1949[1], Claude Shannon introduced two fundamental operations required for a robust cryptosystem: substitution and permutation. Substitution, the core component of SPN-based cryptography, is implemented through substitution boxes (S-Boxes), where each element in the plaintext is mapped to another element to achieve nonlinearity and provide the confusion property crucial for security. With the rise of constrained devices, such as the Internet of Things (IoT), there is an increasing demand for lightweight symmetric-key algorithms. However, in many cases, the S-Box contributes the most to the hardware complexity and computational load compared to other linear components. This research addresses this challenge by designing and optimizing a lightweight cryptosystem suitable for resource-limited environments. The thesis makes two key contributions to the field of lightweight cryptography. The first contribution is the development of chaos-based S-Boxes tailored for devices with restricted computational capabilities. By leveraging chaotic maps, the proposed S-Boxes achieve a high degree of nonlinearity and security while maintaining a minimal computational and hardware footprint, making them ideal for IoT and other constrained devices. These chaos-based S-Boxes introduce dynamic, unpredictable substitution patterns that enhance resistance to cryptanalysis techniques such as l (open full item for complete abstract)

Committee: Maha Allouzi Dr (Advisor); Younghun Chae Dr (Committee Member); Lei Xu Dr (Committee Member) Subjects: Computer Engineering; Computer Science

PhD, University of Cincinnati, 2022, Arts and Sciences: Mathematical Sciences

In this digital age, well tested public-key cryptography is vital for the continuing function of society. An example of one of the uses of cryptography is signature schemes which allow us to digitally sign a document. However, quantum computers utilizing Shor's algorithm threaten the security of all the cryptosystem currently in use. What is needed is post-quantum cryptography: classical cryptographic algorithms able to resist quantum attacks. In 2016, NIST put out a call for proposals for post-quantum cryptosystems for standardization. We are currently in the third round of the “competition,” with many different types of schemes being proposed. In 2017, Ward Beullens et al. submitted the Lifted Unbalanced Oil and Vinegar signature scheme to the NIST competition, which is a modification to the Unbalanced Oil and Vinegar Scheme by Patarin. The main modification is called lifting, which is to take a polynomial over a small finite field and view it as a map over some extension field. LUOV made it into the second round of the competition, but two attacks by Ding et al. showed a flaw in the modifications of LUOV. The first attack was the Subfield Differential Attack (SDA) which prompted a change of parameters by the authors of LUOV. The second was the Nested Subset Differential Attack (NSDA), which broke half of the parameters put forward by the authors of LUOV again. Due to the strengths of these attacks and the possibility stronger ones of a similar nature exist, LUOV did not go into the third round. This dissertation shows that such a stronger attack, which will be called NSDA+, is possible. All three of the attacks SDA, NSDA, and NSDA+ are straightforward but powerful in application against the lifting modification. First in chapter 1, we will discuss what is a public key cryptosystem by looking at the original definition of Diffie and Hellman. Then we will talk of the NIST Post-Quantum Standardizat (open full item for complete abstract)

Committee: Jintai Ding Ph.D. (Committee Member); Seungki Kim Ph.D. (Committee Member); Robert Buckingham Ph.D. (Committee Member) Subjects: Mathematics

Doctor of Philosophy (PhD), Wright State University, 2009, Computer Science and Engineering PhD

Security is an important issue related to the storage and communication of data and information. In data and information security, cryptography and steganography are two of the most common security techniques. On one hand, there is cryptography, which is the secret communication between two parties by message scrambling on the sender's side and message unscrambling on the receiver's side so that only the intended receiver gets the secret message. On the other hand, there is steganography, which is the hiding of information in a medium in such a way that no one other than the sender or the intended receiver realizes there is a hidden message. Successful reverse engineering of cryptography and steganography give cryptanalysis and steganalysis respectively. Cryptography and cryptanalysis constitute cryptology (or crypto) while steganography and steganalysis make up steganology (or stegano). This dissertation consists of three parts needed for a scientific study of a cryptanalysis problem. The first part lays out a comparative survey of various cryptology and steganology techniques by analyzing and comparing different methodologies using a set of predefined parameters. This part offers valuable knowledge on the state of the art techniques used on cryptanalysis. The second part proposes a new lossless synthetic stegano-crypto methodology that blends together five cryptography, steganography and compression techniques to form a single methodology for mutual information encryption and hiding in images. The methods that compose the synthetic methodology are SCAN Encryption, SCAN Compression, SCAN Steganography, Least Significant Bit (LSB) Steganography and Regional Steganography with Segmentation. The synthetic methodology plays the role of a complex and difficult technique that we have to work on in an attempt to break it by using a reverse engineering approach. In the third part, a cryptanalysis attack against the proposed synthetic stegano-crypto methodology is presented (open full item for complete abstract)

Committee: Nikolaos Bourbakis PhD (Advisor); Nikolaos Bourbakis PhD (Committee Chair); Soon Chung PhD (Committee Member); Yong Pei PhD (Committee Member); Arnab Shaw PhD (Committee Member); Monish Chatterjee PhD (Committee Member) Subjects: Computer Science

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) Subjects: Mathematics

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