Modelling Cryptographic Keys in Dynamic Epistemic Logic with DEMO

Abstract

It is far from obvious to find logical counterparts to crytographic protocol primitives. In logic, a common assumption is that agents are perfectly rational and have no computational limitations. This creates a dilemma. If one merely abstracts from computational aspects, protocols become trivial and the difference between tractable and intractable computation, surely an essential feature of protocols, disappears. This way, the protocol gets lost. On the other hand, if one 'merely' (scare quotes indeed) models agents with computational limitations (or otherwise bounded rationality), very obvious aspects of reasoning become problematic. That way, the logic gets lost. We present a novel way out of this dilemma. We propose an abstract logical architecture wherein public and private, or symmetric keys, and their roles in crytographic protocols, all have formal counterparts. Instead of having encryption and decryption done by a principal, the agent sending or receiving messages, we introduce additional, virtual, agents to model that, so that one-way-function aspects of computation can be modelled as constraints on the communication between principals and these virtual counterparts. In this modelling it does not affect essential protocol features if agents are computationally unlimited. We have implemented the proposal in a dynamic epistemic model checker called DEMO.

Efficient Verification of Cryptographic Protocols with Dynamic Epistemic Logic

“…The authors of [3] proposed a method that uses abstract data and deductive rules to prove the results of model checkers. Hans van Ditmarsch et al [7] developed a dynamic epistemic model checker. In the follow-up work (e.g., [7,35,36]), many researchers verified and analyzed security protocols with dynamic epistemic logic.…”

“…Hans van Ditmarsch et al [7] developed a dynamic epistemic model checker. In the follow-up work (e.g., [7,35,36]), many researchers verified and analyzed security protocols with dynamic epistemic logic. The authors of [37] proposed a variant of epistemic logic methods to verify authentication protocols.…”

“…They use the method of model checking to analyze. For example, in the paper [7], the researchers propose two virtual agents to complete encryption and decryption, and construct a model checker to check the protocol. In other papers, KD45 system's belief logic is used.…”

Software Tool Support for Modular Reasoning in Modal Logics of Actions

“…The correctness of the solution has been established, for all k ∈ N using induction, by informal mathematical proof [16] and by mathematical proofs about a formalisation in a Hilbert calculus [34]. It has also been automatically verified, for small values of k, using techniques from model checking [29] (see also [40] for related work) and automated theorem proving [15,39].…”

An Epistemic Foundation for Authentication Logics (Extended Abstract)

“…(It is more common in cryptography, however, to use the random oracle model [12], in which the random function represents a hash function rather than an encryption function, and to use this as the basis for the construction of ciphers.) Van Ditmarsch et al [47] use a similar idea, but their approach is purely epistemic and they do not have probability in their models. The connections that we draw to BAN logic are not developed in this work.…”