• Elliptic Curve Cryptography using Computational Intelligence

      Ribaric, Tim; Department of Computer Science
      Public-key cryptography is a fundamental component of modern electronic communication that can be constructed with many different mathematical processes. Presently, cryptosystems based on elliptic curves are becoming popular due to strong cryptographic strength per small key size. At the heart of these schemes is the complexity of the elliptic curve discrete logarithm problem (ECDLP). Pollard’s Rho algorithm is a well known method for solving the ECDLP and thereby breaking ciphers based on elliptic curves for reasonably small key sizes (up to approximately 100 bits in length). It has the same time complexity as other known methods but is advantageous due to smaller memory requirements. This study considers how to speed up the Rho process by modifying a key component: the iterating function, which is the part of the algorithm responsible for determining what point is considered next when looking for the solution to the ECDLP. It is replaced with an alternative that is found through an evolutionary process. This alternative consistently and significantly decreases the number of iterations required by Pollard’s Rho Algorithm to successfully find the sought after solution.
    • Enabling and Measuring Complexity in Evolving Designs using Generative Representations for Artificial Architecture

      Harrington, Adrian; Department of Computer Science (Brock University, 2012-11-07)
      As the complexity of evolutionary design problems grow, so too must the quality of solutions scale to that complexity. In this research, we develop a genetic programming system with individuals encoded as tree-based generative representations to address scalability. This system is capable of multi-objective evaluation using a ranked sum scoring strategy. We examine Hornby's features and measures of modularity, reuse and hierarchy in evolutionary design problems. Experiments are carried out, using the system to generate three-dimensional forms, and analyses of feature characteristics such as modularity, reuse and hierarchy were performed. This work expands on that of Hornby's, by examining a new and more difficult problem domain. The results from these experiments show that individuals encoded with those three features performed best overall. It is also seen, that the measures of complexity conform to the results of Hornby. Moving forward with only this best performing encoding, the system was applied to the generation of three-dimensional external building architecture. One objective considered was passive solar performance, in which the system was challenged with generating forms that optimize exposure to the Sun. The results from these and other experiments satisfied the requirements. The system was shown to scale well to the architectural problems studied.
    • Epidemic Simulation and Mitigation via Evolutionary Computation

      Dubé, Michael; Department of Computer Science
      A global pandemic remains a public health event that presents a unique and unpredictable challenge for those making health related decisions and the populations who experience the virus. Though a pandemic also provides the opportunity for researchers and health administrations around the world to mobilize in the fields of epidemiology, computer science, and mathematics to generate epidemic models, vaccines, and vaccination strategies to mitigate unfavourable outcomes. To this end, a generative representation to create personal contact networks, representing the social connections within a population, known as the Local THADS-N generative representation is introduced and expanded upon. This representation uses an evolutionary algorithm and is modified to include new local edge operations improving the performance of the system across several test problems. These problems include an epidemic's duration, spread through a population, and closeness to past epidemic behaviour. The system is further developed to represent sub-communities known as districts, better articulating epidemics spreading within and between neighbourhoods. In addition, the representation is used to simulate four competing vaccination strategies in preparation for iterative vaccine deployment amongst a population, an inevitability when considering the lag inherent to developing vaccines. Finally, the Susceptible-Infected-Removed (SIR) model of infection used by the system is expanded in preparation for adding an asymptomatic state of infection as seen within the COVID-19 pandemic.
    • A Study of Ordered Gene Problems Featuring DNA Error Correction and DNA Fragment Assembly with a Variety of Heuristics, Genetic Algorithm Variations, and Dynamic Representations

      Hughes, James; Department of Computer Science (Brock University, 2014-08-18)
      Ordered gene problems are a very common classification of optimization problems. Because of their popularity countless algorithms have been developed in an attempt to find high quality solutions to the problems. It is also common to see many different types of problems reduced to ordered gene style problems as there are many popular heuristics and metaheuristics for them due to their popularity. Multiple ordered gene problems are studied, namely, the travelling salesman problem, bin packing problem, and graph colouring problem. In addition, two bioinformatics problems not traditionally seen as ordered gene problems are studied: DNA error correction and DNA fragment assembly. These problems are studied with multiple variations and combinations of heuristics and metaheuristics with two distinct types or representations. The majority of the algorithms are built around the Recentering- Restarting Genetic Algorithm. The algorithm variations were successful on all problems studied, and particularly for the two bioinformatics problems. For DNA Error Correction multiple cases were found with 100% of the codes being corrected. The algorithm variations were also able to beat all other state-of-the-art DNA Fragment Assemblers on 13 out of 16 benchmark problem instances.