Decidability of Parameterised Dolev-Yao Secrecy

2026-08-03

AI Summary

This work addresses the decidability of parametric secrecy in cryptographic protocols under unbounded sessions within the Dolev-Yao model. By introducing global role freshness constraints and a well-typed intruder substitution mechanism, the authors reduce the infinite-state system to a finite representation and establish, for the first time under structural restrictions, that the secrecy problem is decidable. The core contributions include a truncation theorem that reveals an intrinsic connection to the coverability problem in well-structured transition systems (WSTS). Leveraging techniques from symbolic protocol analysis and bound-order relations, the paper demonstrates that any secrecy violation at arbitrary scale must manifest in some bounded instance, thereby enabling fully automated verification.

Abstract

We study the verification of parameterised secrecy for cryptographic protocols in the Dolev-Yao model, where the number of protocol sessions is unbounded and treated as a parameter. This differs fundamentally from classical Dolev-Yao secrecy, which asks whether a protocol leaks a secret irrespective of the number of executions; our question is whether secrecy holds uniformly across all system sizes, where such a size is a parameter. This parameterised perspective captures how attacks scale with the number of participants and provides a formal basis for the empirical effectiveness of small-instance analysis. Secrecy (parameterised or not) is undecidable in general, even under bounded freshness or bounded message size. We identify two structural restrictions that make parameterised secrecy decidable: (i) global bounded freshness per role, and (ii) a Dolev-Yao intruder restricted to well-typed substitutions. Under these assumptions, protocol executions admit a finite representation up to a collapsing map on agents and terms. Our main result is that parameterised secrecy is decidable in this setting. We obtain a cut-off theorem: secrecy violations in systems with arbitrarily many sessions are always witnessed in systems of bounded size. The cut-off is self-contained; more strongly, the induced transition system forms a well-structured transition system (WSTS) under a bound-based ordering, so secrecy also reduces to a coverability problem in WSTS. This provides a structural explanation for the existence of finite witnesses in symbolic protocol analysis and connects Dolev-Yao verification with parameterised verification techniques.

Problem

• parameterised secrecy
• Dolev-Yao model
• decidability
• unbounded sessions
• cryptographic protocols

Innovation

• parameterised secrecy
• Dolev-Yao model
• cut-off theorem
• well-structured transition system
• decidability