Guessing, or dictionary, attacks arise when an intruder exploits the fact that certain data like passwords may have low entropy, i.e. stem from a small set of values. In the case of off-line guessing, in particular, the intruder may employ guessed values to analyze the messages he has observed. Previous attempts at formalizing off-line guessing consist of extending a Dolev-Yao-style intruder model with inference rules to capture the additional capabilities of the intruder concerning guessable messages. While it is easy to convince oneself that the proposed rules are correct, in the sense that an intruder can actually perform such “guessing steps”, it is difficult to see whether such a system of inference rules is complete in the sense that it captures all the kinds of attacks that we would intuitively call “guessing attacks”. Moreover, the proposed systems are specialized to particular sets of cryptographic primitives and intruder capabilities. As a consequence, these systems are helpful to discover some off-line guessing attacks but are not fully appropriate for formalizing what off-line guessing precisely means and verifying that a given protocol is not vulnerable to such guessing attacks.
In this paper, we give a formalization of off-line guessing by defining a deduction system that is uniform and general in that it is independent of the overall protocol model and of the details of the considered intruder model, i.e. cryptographic primitives, algebraic properties, and intruder capabilities.