Providing security support for mobile ad hoc networks (MANETs) is challenging task. Masquerading and eavesdropping are major threats to the security of wireless communications and mobile networks. The scheme proposed in this paper describes the framework to solve the security threats by designing a address based cryptography scheme. An address-based cryptography scheme (ACS) as a combination of ad hoc node address and public key cryptography. ACS is a certificateless public key cryptography solution in that public keys of mobile nodes are directly derivable from their known ad hoc node address plus some common information. Thus, it eliminates the need for certificate-based authenticated public-key distribution essential in conventional public-key management schemes. ACS is an efficient construction method of address-based public/private keys cryptography, which not only ensures high-level authentication to node exchange information, but also enables efficient network-wide secure key update via a single broadcast message. It also provides general information about how to choose the secret key sharing parameters used with public key cryptography to meet desirable levels of security and authentication. The advantages of ACS over existing certificate-based solutions are justified through extensive simulations. The proposed scheme ACS gives a new innovation towards more effective and efficient security design for MANETs.