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We present a formal logic for quantitative reasoning about securityproperties of network protocols. The system allows us to derive concretesecurity bounds that can be used to choose key lengths and other securityparameters. We provide axioms for reasoning about digital signatures and randomnonces, with security properties based on the concrete security of signatureschemes and pseudorandom number generators (PRG). The formal logic supportsfirst-order reasoning and reasoning about protocol invariants, taking concretesecurity bounds into account. Proofs constructed in our logic also provideconventional asymptotic security guarantees because of the way that concretebounds accumulate in proofs. As an illustrative example, we use the formallogic to prove an authentication property with concrete bounds of asignature-based challenge-response protocol.

A Symbolic Logic with Concrete Bounds for Cryptographic Protocols