This paper proffers a secure and anonymous authenticated key exchange (AKE) scheme for SGs, called SAAS-SG, for establishing a secure communication channel between smart meter (SM) and service provider (SPR). SAAS-SG utilizes the hash algorithm, Esch256, and authenticated encryption algorithm AEGIS, to perform the AKE process. Besides, SAAS-SG ensures the integrity and confidentiality of AKE messages while preserving the anonymity of SMs and SPR. Besides, for encrypted transmission in the future, SAAS-SG empowers SMs and SPR to set up an analogous secret session key (SK) after performing the mutual authentication. SK encrypts the sensitive information exchanged between SMs and service providers (SPR) over the public Internet. Moreover, we illustrate that SAAS-SG is capable of resisting different security vulnerabilities by conducting informal and Scyther-based security analyses. In addition, the random oracle model is operated to validate the security of the established secret SK. Furthermore, comparing SAAS-SG with other related AKE schemes explicates that SAAS-SG requires low communication, storage, and computational overheads, respectively, while accomplishing the AKE phase and renders enhanced security features. [ABSTRACT FROM AUTHOR]