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Informatica

Scalable Authenticated Group Key Establishment in Quantum and Post-Quantum Networks

María Isabel González Vasco, Rainer Steinwandt

Published Jan 1, 2025• 2 citations
Publisher

Abstract

Establishing secure keys over untrusted networks is one of the most fundamental cryptographic tasks. While two-party key establishment protocols are available for many scenarios, even offering resistance to potential adversaries equipped with quantum computing resources, the multi-party scenario is not as well understood. In particular, there is a need to find designs that can make the most of the technologies available to each party involved in a cooperative n-party key establishment. We propose an authenticated key establishment protocol involving $n\geqslant 2$ parties, assuming that some—possibly all—network nodes have the potential to implement quantum key distribution (in pairs), while others only have access to standard technology. The protocol allows for the cooperative construction of a shared secret key from partial keys established by quantum and post-quantum solutions, which in turn can be implemented by different building blocks. We give a formal security analysis of our proposal using a hybrid security model simultaneously capturing quantum and classical actions and capabilities.

DOI
10.15388/25-infor595

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Establishing secure keys over untrusted networks is one of the most fundamental cryptographic tasks. While two-party key establishment protocols are available for many scenarios, even offering resistance to potential adversaries equipped with quantum computing resources, the multi-party scenario is not as well understood. In particular, there is a need to find designs that can make the most of the technologies available to each party involved in a cooperative n-party key establishment. We propose an authenticated key establishment protocol involving n⩾2n\geqslant 2n⩾2 parties, assuming that some—possibly all—network nodes have the potential to implement quantum key distribution (in pairs), while others only have access to standard technology. The protocol allows for the cooperative construction of a shared secret key from partial keys established by quantum and post-quantum solutions, which in turn can be implemented by different building blocks. We give a formal security analysis of our proposal using a hybrid security model simultaneously capturing quantum and classical actions and capabilities.
In cryptography, key establishment protocols are often the starting point paving the way towards secure execution of different tasks. Namely, the parties seeking to achieve some cryptographic task, often start by establishing a common high-entropy secret that will eventually be used to secure their communication. In this paper, we put forward a security model for group key establishment (GAKE\mathsf{GAKE}GAKE) with an adversary that may execute efficient quantum algorithms, yet only once the execution of the protocol has concluded. This captures a situation in which keys are to be established in the present, while security guarantees must still be provided in the future when quantum resources may be accessible to a potential adversary. Further, we propose a protocol design that can be proven secure in this model. Our proposal uses password authentication and builds upon efficient and reasonably well understood primitives: a message authentication code and a post-quantum key encapsulation mechanism. The hybrid structure dodges potential efficiency downsides, like large signatures, of some “true” post-quantum authentication techniques, making our protocol a potentially interesting fit for current applications with long-term security needs.
We show the security of multi-user key establishment on a single line of quantum communication. More precisely, we consider a quantum communication architecture where the qubit generation and measurement happen at the two ends of the line, whilst intermediate parties are limited to single-qubit unitary transforms. This network topology has been previously introduced to implement quantum-assisted secret-sharing protocols for classical data, as well as the key establishment, and secure computing. This architecture has numerous advantages. The intermediate nodes are only using simplified hardware, which makes them easier to implement. Moreover, key establishment between arbitrary pairs of parties in the network does not require key routing through intermediate nodes. This is in contrast with quantum key distribution (QKD) networks for which non-adjacent nodes need intermediate ones to route keys, thereby revealing these keys to intermediate parties and consuming previously established ones to secure the routing process. Our main result is to show the security of key establishment on quantum line networks. We show the security using the framework of abstract cryptography. This immediately makes the security composable, showing that the keys can be used for encryption or other tasks.
Quantum computing has redefined the assumed complexity of different computational tasks, which implies the need for new cryptographic tools that can be considered secure even in the presence of entities that may be able to execute quantum algorithms. In particular, this poses significant challenges for the adaptation of cryptographic implementations, which are particularly relevant in the IoT scenario, where resources are especially limited. In this work, we report on a simple cryptographic protocol for group key establishment, where n > 2 devices interact to establish a key to secure their communication. Our design can actually be seen as a so-called key transport, where a small set of devices cooperatively choose a key that is subsequently distributed to all users over an insecure (and somewhat unstable) network using only cryptographic tools that are claimed to be post-quantum, i.e., resistant to quantum attacks. We give a theoretical description and also describe our experimental results implementing our protocol within networks up to 16 nodes based on ARM Cortex-M4. We believe that this design is a first proof-of-concept of a post-quantum group key exchange protocol in the IoT scenario.
We show the security of multi-user key establishment on a single line of quantum communication. More precisely, we consider a quantum communication architecture where the qubit generation and measurement happen at the two ends of the line, whilst intermediate parties are limited to single-qubit unitary transforms. This network topology has been previously introduced to implement quantum-assisted secret-sharing protocols for classical data, as well as the key establishment, and secure computing. This architecture has numerous advantages. The intermediate nodes are only using simplified hardware, which makes them easier to implement. Moreover, key establishment between arbitrary pairs of parties in the network does not require key routing through intermediate nodes. This is in contrast with quantum key distribution (QKD) networks for which non-adjacent nodes need intermediate ones to route keys, thereby revealing these keys to intermediate parties and consuming previously established ones to secure the routing process. Our main result is to show the security of key establishment on quantum line networks. We show the security using the framework of abstract cryptography. This immediately makes the security composable, showing that the keys can be used for encryption or other tasks.
This paper presents a novel protocol for secure multi-party computation (MPC) leveraging the security of quantum key distribution (QKD). The core claim is to design a protocol that guarantees secure computation among multiple participants. The proposed mechanism utilizes the inherent security of QKD to construct a framework for secure multi-party computation. This approach addresses the limitations of traditional MPC protocols that often rely on computationally intensive assumptions, offering a potentially more robust solution in the face of evolving cryptographic threats. The protocol details the steps involved in generating a shared secret key through QKD, followed by the secure computation process based on the key. We outline the mathematical foundations and formalize the protocol's components, demonstrating its feasibility and potential advantages. The protocol is designed to be adaptable and scalable, offering a viable route toward secure distributed computing in quantum-enhanced environments.