Computer Science

The security of the current public-key cryptographic schemes, based on integer factorization and discrete logarithm problems, is expected to be totally broken with the development of quantum computers utilizing Shor’s algorithm. As a result, The National Institute of Standards and Technology (NIST) initiated the Post-Quantum Cryptography (PQC) standardization process in 2016, inviting researchers to submit candidate algorithms that are both resistant to quantum attacks and efficient for real world applications. Researchers have since studied various aspects of the candidate algorithms, such as their security against quantum attacks and efficient implementation on different platforms.
In this thesis, we investigate the practical aspects of Post-Quantum Cryptography and contribute to several topics. First, we focus on the knapsack problem and its security under classical and quantum attacks. Second, we improve the secure biometric template generation algorithm NTT-Sec, proposing an enhanced version, NTT-Sec-R, and providing an in-depth design and security analysis. Third, we work on optimizing implementations of the post-quantum secure signature scheme LESS and polynomial inversion algorithms for code-based schemes. Finally, we analyze a proposed countermeasure for the exposure model of SIKE, the isogeny-based scheme that is a candidate in NIST’s Round 4.

In the modern data landscape, vast amounts of unlabeled data are continuously generated, necessitating development of robust unsupervised techniques for handling unlabeled data. This is the case for fraud detection and healthcare sectors analyses, where data is often significantly imbalanced. This dissertation focuses on novel techniques for handling imbalanced data, with specific emphasis on a novel unsupervised class labeling technique for unlabeled fraud detection datasets and unlabeled cognitive datasets. Traditional supervised machine learning relies on labeled data, which is often expensive and difficult to create, particularly in domains requiring expert input. Additionally, such datasets suffer from challenges associated with class imbalance, where one class has significantly fewer examples than another, complicating model training and significantly reducing performance. The primary objectives of this dissertation include developing a novel unsupervised cleaning method, and an innovative unsupervised class labeling method. We validate and evaluate our methods across various datasets, which include two Medicare fraud detection datasets, a credit card fraud detection dataset, and three datasets used for detecting cognitive decline.
Our unique approach involves using an unsupervised autoencoder to learn from dataset features and synthesize labels. Primarily targeting imbalanced datasets, but still effective for balanced datasets, our method calculates an error metric for each instance. This metric is used to distinguish between fraudulent and legitimate cases, allowing us to assign a binary class label. To further improve label generation, we integrate an unsupervised feature selection method that ranks and identifies the most important features without using class labels.

Capturing pedestrian mobility patterns with high fidelity provides a foundation for data-driven decision-making in support of city planning, emergency response, and more. Due to scalability requirements and the sensitive nature of studying pedestrian movements in public spaces, the methods involved must be passive, low-cost, and privacy-centric. Pedestrian localization based on Received Signal Strength Indicator (RSSI) measurements from Wi-Fi probe requests is a promising approach. Probe requests are spontaneously emitted by Wi-Fi-enabled devices, are readily captured by of-the-shelf components, and offer the potential for anonymous RSSI measurement. Given the ubiquity of Wi-Fi-enabled devices carried by pedestrians (e.g., smartphones), RSSI-based passive localization in outdoor environments holds promise for mobility monitoring at scale. To this end, we developed the Mobility Intelligence System (MobIntel), comprising inexpensive sensor hardware to collect RSSI data, a cloud backend for data collection and storage, and web-based visualization tools. The system is deployed along Clematis Street in the heart of downtown West Palm Beach, FL, and over the past three years, over 50 sensors have been installed.
Our research first confirms that RSSI-based passive localization is feasible in a controlled outdoor environment (i.e., no obstructions and little signal interference), achieving ≤ 4 m localization error in more than 90% of the cases. When significant time-varying signal fluctuations are introduced as a result of long-term deployment, performance can be maintained with an overhaul of the problem formulation and an updated localization model. However, when the outdoor environment is fully uncontrolled (e.g., along Clematis Street), the performance decreases to ≤ 4 m error in fewer than 70% of the cases. However, the drop in performance may be addressed through improved sensor maintenance, additional data collection, and appropriate domain knowledge.

The cochlea provides frequency selectivity for acoustic input signal processing in mammals. The excellent performance of human hearing for speech processing leads to examination of the cochlea as a paradigm for signal processing. The components of the hearing process are examined and suitable models are selected for each component's function. The signal processing function is simulated by a computer program and the ensemble is examined for behavior and improvement. The models reveal that the motion of the basilar membrane provides a very selective low pass transmission characteristic. Narrowband frequency resolution is obtained from the motion by computation of spatial differences in the magnitude of the motion as energy propagates along the membrane. Basilar membrane motion is simulated using the integrable model of M. R. Schroeder, but the paradigm is useful for any model that exhibits similar high selectivity. Support is shown for an hypothesis that good frequency discrimination is possible without highly resonant structure. The nonlinear magnitude calculation is performed on signals developed without highly resonant structure, and differences in those magnitudes are signals shown to have good narrowband selectivity. Simultaneously, good transient behavior is preserved due to the avoidance of highly resonant structure. The cochlear paradigm is shown to provide a power spectrum with serendipitous good frequency selectivity and good transient response simultaneously.

This dissertation has two chapters. In the first chapter we talk about the discrete logarithm problem, more specifically we concentrate on the Diffie-Hellman key exchange protocol. We survey the current state of security for the Diffie-Hellman key exchange protocol. We also motivate the reader to think about the Diffie-Hellman key exchange in terms of group automorphisms. In the second chapter we study two key exchange protocols similar to the Diffie-Hellman key exchange protocol using an abelian subgroup of the automorphism group of a non-abelian group. We also generalize group no. 92 of the Hall-Senior table, for arbitrary prime p and study the automorphism group of these generalized group. We show that for those groups, the group of central automorphisms is an abelian group. We use these central automorphisms for the key exchange we are studying. We also develop a signature scheme.

Genetic algorithms (GA) and clustering techniques are used to study and classify materials. An analysis of the convergence speed of GA is carried out using advanced probability theory and random walk concepts. The determination of the ground-state of multicomponent alloys and Ising models with long-range interactions is accomplished using a genetic algorithm. A new GA operator, the domain-flip, is introduced and its efficiency is compared to that of traditional GA operators, crossover and mutation. The domain-flip operator destroys phase-boundaries by flipping all bits of a given domain at the same time. This operator turns out to be crucial in extracting the system from low local minima. Therefore its presence is rather essential to speed up the GA convergence. A study of GA convergence in its last stages, where all chromosomes present in the population are assumed to consist of two well-ordered domains, is performed using random walk theory and probability theory. Exact expressions for the average time needed for at least one chromosome to find the ground-state are derived. Also, the probability for two chromosomes to undergo a successful crossover, meaning the result is the ground-state, are given. Finally, clustering techniques, which belong to the field of Data Mining, are applied to the classification of materials. An improved version of the widely-used clustering algorithm, K-means, is developed. A comparison of the two clustering techniques on a two-dimensional data set shows that the guide-point approach is more powerful than the K-means algorithm. The guide-point algorithm is used successfully to partition a materials data set. This clustering results in extracting useful information from the data set for which no a priori knowledge was assumed.