Secure Multi-Party Computation (SMPC) enables the various parties to collectively compute functions on sensitive inputs without the sensitive information being revealed, yet the problem of scalability, efficiency and security remains a significant issue. To increase the computational security and efficiency of the postulated framework in this paper a framework on algebraic SMPC is defined that is based on discrete algebraic structures and finite group representations. This approach is founded on the group-theoretic encoding, homomorphic mappings and structured secret sharing between algebraic space to provide confidentiality and integrity against semi-honest and malicious adversarial structures. The suggested plan entails use of representation theory to not only compress data, but also easily combine the data to minimize on communication overhead and increase processing speed.