Cloud communication is an intrinsic aspect of cloud architecture. It is an internet-based communication that enables access to millions of cloud services. These services are provided using TCP/UDP-based communications and protected by traditional security protocols (e.g., SSL/ TLS/DTLS). However, security threats in cloud communications become the most serious issue nowadays. To address some of the shortcomings of traditional security protocols, we propose a secure cloud communication architecture (Graphene) for both TCP- and UDP-based communications. Graphene can provide security for data-in-transit and authenticity of cloud users and cloud service providers. It protects the communication channel against most common attacks such as man-in-the-middle (including eavesdropping, sniffing, identity spoofing, and data tampering), sensitive information disclosure, replay, compromised-key, repudiation, and session hijacking attacks. This work also involves the designing of a novel high-performance cloud-focused security protocol that works for both TCP and UDP communications. Especially for UDP, it uses an asynchronous re-transmission mechanism to ensure datagram delivery. This protocol efficiently utilizes the strength and speed of symmetric block encryption with Galois/Counter mode, cryptographic hash, public key cryptography, and ephemeral key-exchange. It provides faster reconnection facility for supporting frequent connectivity and dealing with connection trade-offs. The security analysis of Graphene shows promising protection against the above discussed attacks. Graphene also outperforms TLSv1.3 (the latest stable version among the SSL successors) and DTLSv1.2 (the latest stable version of datagram TLS) in performance and bandwidth consumption significantly and shows reasonable memory usage at the server side.