In this work, we introduce a novel asymmetric encryption scheme founded on a non-commutative algebraic group defined over a specialized group ring, with the proposed system relying on the computational hardness of both the factorization with discrete logarithm problem (FDLP) and the conjugacy search problem (CSP), which holds a pivotal role in preserving the scheme’s security. Security analysis confirms that the scheme meets basic cryptographic standards, providing a good level of protection against known cryptographic attacks.