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Using a probabilistic polynomial-time process calculus de- signed for specifying security properties as observational equivalences, we develop a form of bisimulation that justifies an equational proof sys- tem. This proof system is suciently powerful to derive the semantic se- curity of El Gamal encryption from the Decision Die-Hellman (DDH) assumption. The proof system can also derive the converse: if El Gamal is secure, then DDH holds. While these are not new cryptographic re- sults, these example proofs show the power of probabilistic bisimulation and equational reasoning for protocol security.

Probabilistic Bisimulation and Equivalence for Security Analysis of Network Protocols