The inductive approach to verifying cryptographic protocols uses formal methods to rigorously analyze protocol security. This method, based on predicate calculus, handles infinite-state systems and is implemented using Isabelle/HOL. It involves inductively defining protocols as sets of traces, which are lists of communication events. The approach models an attacker who can decrypt messages and forge messages using available keys. Three protocols—Otway-Rees (shared-key), Needham-Schroeder (public-key), and a recursive protocol—are analyzed. The method proves properties such as secrecy and authenticity by induction on traces. It allows for the automated generation of proof scripts, reducing human effort. The approach also includes regularity lemmas, secrecy theorems, and rules for handling attacks. The method has been applied to various protocols, including the Otway-Rees protocol, where an attack was discovered. The inductive method provides a systematic way to verify protocol correctness, ensuring that messages are secure and that agents cannot impersonate each other. The approach is flexible and can be adapted to different protocols, offering insights into protocol structure and security properties.The inductive approach to verifying cryptographic protocols uses formal methods to rigorously analyze protocol security. This method, based on predicate calculus, handles infinite-state systems and is implemented using Isabelle/HOL. It involves inductively defining protocols as sets of traces, which are lists of communication events. The approach models an attacker who can decrypt messages and forge messages using available keys. Three protocols—Otway-Rees (shared-key), Needham-Schroeder (public-key), and a recursive protocol—are analyzed. The method proves properties such as secrecy and authenticity by induction on traces. It allows for the automated generation of proof scripts, reducing human effort. The approach also includes regularity lemmas, secrecy theorems, and rules for handling attacks. The method has been applied to various protocols, including the Otway-Rees protocol, where an attack was discovered. The inductive method provides a systematic way to verify protocol correctness, ensuring that messages are secure and that agents cannot impersonate each other. The approach is flexible and can be adapted to different protocols, offering insights into protocol structure and security properties.