This article is a part of a research endeavor focused on creating a quantum-resistant cryptosystem for secure encryption and decryption. Our approach employs a challenging word problem while emphasizing cost-effective implementation. Previous research has involved the development of encryption schemes based on high-order groups, offering potential security enhancements. The choice of the non-abelian group is a critical factor in shaping the encryption algorithms, feasibility of implementation, and system parameters. Our central objective is to design a cryptosystem that effectively thwarts quantum cryptanalysis. To achieve this, we employ a logarithmic signature along with a random cover across an entire finite non-abelian group. Our unique contribution lies in optimizing finite group selection, parameters, and circuit solutions for the logarithmic signature to meet specific security and implementation criteria. Within this paper, we introduce an encryption scheme utilizing automorphisms of the Ree functional field and propose a method for enhancing resistance to cryptanalysis through the binding of session keys.