关键词: 认证协议, 模幂运算, 散列函数, SVO逻辑

Abstract: The paper puts forward a new mutual authentication key agreement protocol （NMAKAP），which can be applied in mobile communication.The traditional public key cryptography and digital signature algorithm are substituted by the modular exponentiation based on Abel-group and hash function in NMAKAP to authenticate the identity to reduce the costs of the calculation and implementation.The security of NMAKAP is proved by SVO logic.One of the important methods of formal analysis of security protocol is based on SVO logic.The paper expands the syntax of SVO logic.In addition，authentication goals of SVO logic risked for man-in-middle attack.Thus，the paper proposes a new authentication goal and analyzes the security of the new goal.A mutual authentication key exchange protocol （MAKEP） is also analyzed in the paper.MAKEP reduces the computational complexity of mobile devices largely by?precomputing.However，some scholars thought the MAKEP might conceal the Hijacking attack.By analyzing deeply，the Hijacking in MAKEP dose not exist，and the opinions of the unknown key-share attacking and improving in MAKEP are pointed out.

Key words: authentication protocol, modular exponentiation, hash function, SVO logic