Remote medical operations, including telesurgery and telemedicine, enable surgeons to deliver care across geographic barriers using advanced robotics and high-speed networks such as 5G and fiber. These systems require secure transmission of video, audio, and control signals to ensure patient confidentiality and operational reliability. This review examines the protocols and encryption algorithms central to secure teleoperations, including TLS/SSL, IPsec, AES-GCM, ECC-based key exchange, and HMAC integrity verification. We present the algorithmic flow of a secure session, outlining authentication, key agreement, encrypted communication, and continuous monitoring. Key challenges—latency, jitter, network reliability, cybersecurity threats, compliance, and legal issues—are analyzed alongside emerging performance benchmarks. Comparative insights highlight benefits such as accessibility, collaboration, and safety, as well as drawbacks including cost, complexity, and regulatory hurdles. The paper emphasizes that integrating robust cryptographic protocols with low-latency networking is essential for safe, resilient, and scalable remote surgical practices.