Generation of Pseudorandom Numbers with help of Elliptic Curves over Finite Fields of Characteristic 2.

This thesis presents an in-depth analysis of pseudorandom number generators (PRNGs) based on elliptic curves defined over finite fields of characteristic 2. Leveraging the algebraic structure and arithmetic of binary fields $\mathbf{F_{2^m}}$, we evaluate the statistical and structural properties of the generated sequences with a focus on their suitability for cryptographic applications. The study includes the implementation of elliptic curve-based PRNGs, examination of their autocorrelation behavior, and statistical randomness assessments using metrics such as mean absolute autocorrelation and correlation matrices, as well as an evaluation of their predictability using neural networks. Our findings highlight both the potential and limitations of such generators, emphasizing the importance of careful curve and field parameter selection to avoid predictability and ensure high entropy in the output sequences. The results contribute to the broader understanding of the reliability of elliptic curve-based randomness sources in binary field environments.