New Language Simplifies Design of Secure Digital Communications Protocols

Researchers are increasingly focused on formal methods for verifying the security of complex cryptographic protocols. Sebastian Mödersheim and Simon Lund of DTU Compute, in collaboration with Alessandro Bruni, Marco Carbone, and Rosario Giustolisi from the IT-University of Copenhagen, introduce CryptoChoreo, a novel choreography language designed to specify these protocols with greater clarity and rigour. This work extends existing -and- notation by incorporating non-deterministic choice, conditional branching, and mutable long-term memory, offering a holistic view of protocol interactions rather than isolated roles. By translating CryptoChoreo into a process calculus and connecting this to the ProVerif tool, the authors demonstrate a practical approach to protocol verification, addressing inherent undecidability challenges and paving the way for more robust cryptographic system design.

This work addresses limitations in existing languages that struggle to represent complex protocol behaviours such as conditional branching, non-deterministic choices, and the use of mutable long-term memory.

CryptoChoreo builds upon the established Alice-and-Bob notation, extending its capabilities to model more realistic and intricate systems. The research introduces a formal semantics for CryptoChoreo achieved through translation to a process calculus, effectively defining how agents parse messages and construct responses within a protocol, even when faced with unpredictable actions from other participants.

This advancement allows for a more intuitive, high-level view of cryptographic protocols, focusing on the overall interaction rather than the isolated steps of individual roles. The semantics accounts for algebraic properties crucial to protocols like Diffie-Hellman key exchange, enabling the system to infer the feasibility of message construction based on established mathematical rules.

Researchers have implemented a computable translation for a representative algebraic theory, demonstrating practical feasibility, despite the general undecidability of verifying such protocols. By connecting CryptoChoreo to the ProVerif verification tool, the team has validated their approach through a series of case studies, showcasing its ability to analyse complex cryptographic designs.

The core innovation lies in extending Alice-and-Bob notation with features previously unavailable in formal languages. Non-deterministic choice allows modelling scenarios where a participant can select from multiple options, while branching enables protocols to adapt based on conditions or database states. Mutable long-term memory introduces the ability to maintain and modify information across multiple protocol executions, essential for modelling server-based systems.

This combination of features provides a powerful tool for specifying protocols with dynamic behaviour and complex interactions, potentially reducing specification errors and improving the reliability of cryptographic systems. The work represents a significant step towards more accessible and robust formal verification of security protocols.

Knowledge frame construction facilitates agent behaviour translation

Initial knowledge frames, crucial for capturing agent understanding during protocol execution, are defined as finite mappings, for instance, [X1 7→t1, . , Xn 7→tn], where Xi represent labels and ti are terms. A concrete frame lacks variables, ensuring immediate usability within the semantics of local behaviours. The research establishes a method for applying these frames as substitutions, denoted F(r), replacing labels Xi with corresponding terms ti; undefined results occur if a recipe contains labels outside the frame’s domain.

Each role begins with an initial knowledge frame, FA, potentially containing variables of type role. This frame is then used to translate CryptoChoreo-level knowledge into the initial knowledge frame for the local behaviour, resulting in a local behaviour incorporating operations like locking, conditional checks, and message handling. An example instruction is lock.XK:= keys[X2], which assigns the value of keys[X2] to the variable XK.

Conditional statements, like if XK .= blank then νXN.unlock.send((key, X2, XN)), demonstrate branching logic based on the value of XK. Message reception is handled via receive(Xkc), followed by verification and potential parsing of the received content. Syntactic sugar streamlines checks and message parsing, employing functions like vsign for signature verification and open for message decomposition.

Operational semantics for local behaviours are defined through two transition relations, → and ⇒, operating on triples (L, F, μ), where L represents local behaviours, F the intruder’s knowledge, and μ the memory map. The initial state is (∅, μ0), with all memory cells initially blank. The ⇒ relation handles atomic sections of local behaviour until a ‘unlock’ instruction is reached, tracking emitted events in a trace.

The → relation allows spawning new role instances with instantiations σ of variables in FA, mapping them to agent names. Honest instantiations apply σ(FA) as a substitution, while dishonest instantiations assign the role to the intruder, denoted by ‘i’. This semantics supports parallel and sequential execution of multiple sessions, modelling compromised agents by granting the intruder initial knowledge.

Formal semantics and process calculus translation of the CryptoChoreo choreography language

A core innovation of this work is the development of CryptoChoreo, a choreography language designed for the precise specification of cryptographic protocols. This language extends standard -and- notation by incorporating non-deterministic choice, conditional branching, and mutable long-term memory, enabling a more comprehensive and intuitive high-level view of protocol behaviour.

The research establishes a formal semantics for CryptoChoreo through translation into a process calculus, meticulously defining how agents parse incoming messages and construct outgoing ones, accounting for algebraic theories and the unpredictable actions of other agents. This translation process inherently addresses potentially undecidable algebraic problems, but a practical implementation is demonstrated for a representative theory, validating the approach’s feasibility.

To facilitate this translation, the study defines functions like vpair, fst, and snd, unary functions used to decompose and verify terms within the protocol, ensuring uniformity across all destructors and verifiers. A verifier for Diffie-Hellman exponentiation is included to satisfy a requirement that every destructor has a corresponding verifier, halting execution if unexpectedly employed.

Private key handling employs an inverse mapping to public keys, streamlining the modelling of public-key infrastructures and allowing agents to easily lookup keys. The methodology relies on a defined theory E, comprising rewrite rules R and congruence B, which allows for the decision of the word problem, determining whether two terms are equivalent, by comparing their normal forms modulo B.

A crucial component is the compose function, which identifies constructive recipes that satisfy a given frame and term, leveraging the concept of an ‘analysed frame’ where all possible terms obtainable through destructors are included. This analysis procedure iteratively applies decryption steps, adding messages to the frame and re-checking existing messages until a stable, correct frame is achieved. The research details how to compute a complete set of checks from the analysed frame, extending the compose procedure to solve recipe composition problems across multiple frames.

The Bigger Picture

The persistent challenge of ensuring secure communication isn’t about inventing new cryptographic algorithms, but about guaranteeing those algorithms are implemented correctly in complex, interacting systems. This work addresses that crucial, often overlooked, aspect with CryptoChoreo, a language designed to formally specify how cryptographic protocols should behave.

For years, protocol design has relied on informal descriptions and ad-hoc testing, leaving room for subtle but devastating flaws. The power of CryptoChoreo lies in its ability to move beyond individual code segments and model the entire ‘dance’ of a protocol, the complete exchange of messages between parties. This isn’t merely an academic exercise in formal methods.

By translating these choreographies into a process calculus and connecting it to existing verification tools like ProVerif, the researchers have demonstrated a pathway towards automated security analysis. The ability to rigorously check protocols against potential attacks, even those stemming from unpredictable agent behaviour, is a significant step forward.

While the current implementation is limited to a specific algebraic theory, the framework is extensible, hinting at broader applicability. However, the undecidability inherent in general cryptographic verification remains a practical constraint. Scaling this approach to handle extremely complex, real-world protocols will require ongoing refinement of the underlying algorithms and potentially, the development of approximation techniques.

Future work might explore integrating CryptoChoreo with model-based testing, combining the rigour of formal verification with the coverage of dynamic analysis. Ultimately, the goal isn’t just to prove protocols correct, but to build tools that make secure protocol design accessible to a wider range of developers, reducing the risk of vulnerabilities creeping into the systems we rely on daily.