The security requirements for cryptographic protocols were divided into shallow requirements and deep requirements. The hierarchy security requirements were illustrated. Using temporal logic and algebra, a formal requirement language was presented and used to describe the formal hierarchy requirements for cryptographic protocols. A model of computation was developed by modifying and extending the Abadi and Tuttle model, combining BAN logic and the NRL Protocol Analyzer. Using this model and theorem proving techniques, the formal requirements of the Otway-Rees protocol was verified.