Tate Pairings on Elliptic curve Cryptography are important because they can be used to build efficient Identity-Based Cryptosystems as well as their implementation essentially determines the efficiency of cryptosystems In this work we propose an identity-based encryption based on Tate Pairing on an elliptic curve The scheme was chosen ciphertext security in the random oracle model assuming a variant of computational problem Diffie-Hellman This paper provides precise definitions to encryption schemes based on identity it studies the construction of the underlying ground field their extension to enhance the finite field arithmetic and presents a technique to accelerate the time feeding in Tate pairing algorith
