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Symmetric encryption and the mathematical properties of Pythagorean Triples are both well-established fields of study. However, the potential for applying Pythagorean Triples to cryptographic systems remains a significantly under-explored area of research. Building upon previous methods that utilized Pythagorean Triples for symmetric encryption, this paper introduces a novel secure communication protocol that incorporates this approach. Specifically, we adapt previous Pythagorean Triple encryption schemes into a robust Feistel network implementation and analyze its resistance to simple statistical tests and linear cryptanalysis. The protocol is proposed as a potential alternative to the widely adopted TLS standard, and we detail its design architecture, key design choices, and provide an analysis of its performance and foundational security attributes.