In this paper, the authors propose an Elliptic Curve Cryptography that addresses both false data injection attacks and DOS attacks. Elliptic Curve Cryptography is a public key Cryptography. Elliptical Curve Cryptography (ECC) is a public key encryption technique based on elliptic curve theory that can be used to create faster, smaller, and more efficient cryptographic keys. ECC systems are well suited for applications that need long-term security requirements. Every user taking part in public key cryptography will take a pair of keys, a public key and a private key. Only the particular user knows the private key whereas the public keys are distributed to all users taking part in the communication.