The paper discusses the security of public key protocols in network communication, focusing on their vulnerability to active saboteurs who may impersonate users or alter messages. It introduces two models for analyzing protocol security: Cascade Protocols and Name-Stamp Protocols. Cascade Protocols involve the application of encryption-decryption operators, while Name-Stamp Protocols allow users to append, delete, and check names encrypted with the plaintext. The paper provides formal definitions and conditions for protocol security, including the balancing property and the requirement that encryption and decryption operators must be applied correctly. It also presents algorithms to determine the security of these protocols, with complexity analysis. Additionally, it explores the security of protocols against impatient saboteurs, who only initiate conversations without waiting for responses. The paper concludes with detailed proofs and examples to illustrate the concepts and algorithms discussed.The paper discusses the security of public key protocols in network communication, focusing on their vulnerability to active saboteurs who may impersonate users or alter messages. It introduces two models for analyzing protocol security: Cascade Protocols and Name-Stamp Protocols. Cascade Protocols involve the application of encryption-decryption operators, while Name-Stamp Protocols allow users to append, delete, and check names encrypted with the plaintext. The paper provides formal definitions and conditions for protocol security, including the balancing property and the requirement that encryption and decryption operators must be applied correctly. It also presents algorithms to determine the security of these protocols, with complexity analysis. Additionally, it explores the security of protocols against impatient saboteurs, who only initiate conversations without waiting for responses. The paper concludes with detailed proofs and examples to illustrate the concepts and algorithms discussed.