Abstract: This paper proposed a scheme in which A-EKE is formed on the basis of conic curve over residue class ring Zn，using ElGamal signature algorithm, and presented the numerical simulation of the scheme. This scheme has combining advantages; A-EKE Protocol using a combination of asymmetric(publi-key) and symmetric(secret-key) cryptography provides security and identification for communication on computer network. A-EKE allows hosts not to store cleartext passwords, and thus can prevent the attacker from mimicking the user to the host. Implementing the scheme using ElGamal signature algorithm also strengthens the scheme. The scheme can secure against active attack, overlay attack,rnan-irrth}rniddle attack,off-Line dictionary attack and password profile cor工iprornise. Cox工iprehensively usin9 the difficulties in factorizing large integer and computing discrete logarithm with Conic Curve over ，the security of this scheme is increased. For the facility of plaintext embedding and the computing of rank and point on conic Cn(a, b)，the scheme has the advantages of speedy operation and easy realization, especially by using the NAF. These advantageous properties of the schemes have pragmatic significance for the design and realization of secure and efficient identity authentication and key negotiation system.

Key words: Residue class ring Zn , Conic curve, EKE, A-EKE, NAF