Over the past decade, Voice over IP (VoIP) has evolved from being a voice communication system into a robust unified communications engine. All VoIP devices rely on a single protocol known as the Session Initiation Protocol (SIP). SIP defines the protocols and communication methods used to establish phone calls and is commonly recognized as an IP-based multimedia communication protocol. Among the various security services recommended for SIP, authentication stands as the most essential. While numerous schemes have been introduced in the literature to enhance SIP security, many of them exhibit high computational costs, which renders them less scalable. Additionally, these schemes often lack compatibility with standard SIP protocols. In this study, we propose a novel authentication and key agreement scheme aimed at securing SIP communications. This proposed scheme is based on the Kerberos protocol and is called Kerberos-SIP (K-SIP). Our scheme significantly reduces computational costs, introduces a single sign-on capability, enables two-way authentication, facilitates secure key agreements among parties, maintains compatibility with SIP, and mitigates various SIP attacks. We thoroughly analyze the security properties inherent in the proposed scheme and, in tandem, investigate its performance characteristics.