On the Symbolic Analysis of Low-Level Cryptographic Primitives: Modular Exponentiation and the Diffie-Hellman Protocol

Automatic methods developed so far for analysis of security protocols only model a limited set of cryptographic primitives (often, only encryption and concatenation) and abstract from low-level features of cryptographic algorithms. This paper is an attempt towards closing this gap. We propose a symbolic technique and a decision method for analysis of protocols based on modular exponentiation, such as Diffie-Hellman key exchange. We introduce a protocol description language along with its semantics. Then, we propose a notion of symbolic execution and, based on it, a verification method. We prove that the method is sound and complete with respect to the language semantics.