In this paper we propose a complete solution of authentication and key exchange for digital home environments such that mobile devices can securely access the home devices. Some digital home authentication and key exchange protocols performed between mobile devices and home gateways are assisted by the AAA servers, which are provided by telecommunication companies, but they have some security flaws. In our proposed protocol, the necessary security requirements for digital home security mechanisms are satisfied, such as mutual authentication, authenticated key exchange, and forward secrecy. In our digital home security scheme, a mobile device can authenticate his home gateway and exchange a session key with each home device without pre-sharing keys with the home gateway and with the home device. The proposed authentication and key exchange protocol can also cooperate with the AAA server. Furthermore, we propose another authentication and key exchange protocol with forward secrecy between mobile devices and home devices. The computation capabilities of the mobile devices also are considered in our proposed protocols, where we only employ symmetric encryption/decryption and low-cost operations in order to reach the aim of light-weight computation cost.