In this work, a novel mechanism is considered for Asymmetric mode encrypting data. A generator matrix is used to generate a field with a large prime number. The generator matrix, prime number and ternary vector are used as global variables. Those global variables are used to calculate public key and sub keys. Using the Global Variables and Private key, a Digital signature algorithm is proposed which supports the feature like Authenticity of users. The mechanism can also be used in Homomorphic Encryption where computations to be carried out on cipher text and generate an encrypted result which, when decrypted, matches the result of operations performed on the plaintext.