This paper provides the concepts of non-commutative group embedded with cryptography, a true area, fascinate with advanced high end performance and security. The basis of this non-commutative group is recognized on the hidden subgroup computational problem. The main focal point in this paper is to ascertain the cryptographic schemes on the additional sub group (ASG). ASG is screening the suitable non-commutative platforms for the solution of cryptographic problems. The computational methodology is based on the random polynomials chosen by the communicating to the particular person through secured key exchange, encryption-decryption and authentication schemes. This group supports Diffie-Hellman algorithm (with hash function) to encrypt and decrypt.

Non-commutative group, cryptography, Diffie-Hellman algorithm, semi ring, semi group.