Pairing Based Elliptic Curve Cryptosystem for Message Authentication

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 generates keys through the properties of the elliptic curve equation instead of the traditional method of generation as the product of very large prime numbers. Because ECC helps to establish equivalent security with lower computing power and battery resource usage, it is becoming widely used for mobile applications. Recently the bilinear pairing such as Weil Pairing or Tate Pairing on elliptic curves and hyper elliptic curves has been found various applications in cryptography. Several identity-based cryptosystems using bilinear pairings of elliptic curves or hyper elliptic curves were presented. Blind signature and ring signature are very useful to provide the user’s anonymity and the signer’s privacy. The proposed method focuses an IDbased ring signature scheme which is based on the pairings with elliptic curve cryptography. The proposed method is used to reduce the number of computation of the pairing for the verification of the id based signature and also decoding of the id based public key cryptosystems with authentication by factor of 2.