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An effective representation of principals' knowledge can greatly improve the efficiency of cryptographic protocol analysis. In this paper, we propose a mechanism to represent the deductive knowledge contained in a set of terms. Using Dolev-Yao model as an example, we design two algorithms to generate the knowledge representation and derive terms, respectively. We prove that using our knowledge representation, a principal can derive a term by using only constructive operations. To demonstrate the advantages of the proposed approach, we integrate it with Athena to build a new protocol verifier. The new approach will drastically reduce the number of states that are generated and analyzed during protocol verification. Experiments on several cryptographic protocols widely used for evaluating protocol verifiers demonstrate the improvements.