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Informatica

Group Key Establishment in a Quantum-Future Scenario

María Isabel González Vasco, Ángel Luis Pérez del Pozo, Rainer Steinwandt

Published Jan 1, 2020• 9 citations
Publisher

Abstract

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 ($\mathsf{GAKE}$) 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.

DOI
10.15388/20-infor427

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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.
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.
A group authenticated key exchange (GAKE) protocol allows a set of parties belonging to a certain designated group to agree upon a common secret key through an insecure communication network. In the last few years, many new cryptographic tools have been specifically designed to thwart attacks from adversaries which may have access to (different kinds of) quantum computation resources. However, few constructions for group key exchange have been put forward. Here, we propose a four-round GAKE which can be proven secure under widely accepted assumptions in the Quantum Random Oracle Model. Specifically, we integrate several primitives from the so-called Kyber suite of post-quantum tools in a (slightly modified) compiler from Abdalla et al. (TCC 2007). More precisely, taking as a starting point an IND-CPA encryption scheme from the Kyber portfolio, we derive, using results from Hövelmanns et al. (PKC 2020), a two-party key exchange protocol and an IND-CCA encryption scheme and prove them fit as building blocks for our compiled construction. The resulting GAKE protocol is secure under the Module-LWE assumption, and furthermore achieves authentication without the use of (expensive) post-quantum signatures.
Group authenticated key exchange protocols (GAKE) are cryptographic tools enabling a group of several users communicating through an insecure channel to securely establish a common shared high-entropy key. In the last years, the need to design cryptographic tools which provide security in the presence of attackers with access to quantum resources has become unquestionable; the field dealing with these types of protocols is usually referred to as Post-Quantum Cryptography. The U.S. National Institute for Standards and Technology (NIST) launched in 2017 an open call to find suitable post-quantum public-key algorithms for standardization. In this work, we design a GAKE that can be instantiated with any key encapsulation mechanism (KEM) that satisfies the strong security notion IND-CCA, matching NIST’s requirements for this primitive. We have implemented our GAKE with the four finalist KEMs from the NIST process: Classic McEliece, Kyber, NTRU, and Saber, making use of the open-source library LibOQS where these algorithms are provided. We have conducted a detailed comparative performance analysis of the resulting GAKE protocols, taking into account all the parameter sets proposed in the submissions. We have also made a performance analysis of all the involved building pieces, including the four finalist KEMs. Finally, we also compare our GAKE with a previous proposal implemented with Kyber.
Key establishment is a crucial primitive for building secure channels: in a multi-party setting, it allows two parties using only public authenticated communication to establish a secret session key which can be used to encrypt messages. But if the session key is compromised, the confidentiality of encrypted messages is typically compromised as well. Without quantum mechanics, key establishment can only be done under the assumption that some computational problem is hard. Since digital communication can be easily eavesdropped and recorded, it is important to consider the secrecy of information anticipating future algorithmic and computational discoveries which could break the secrecy of past keys, violating the secrecy of the confidential channel. Quantum key distribution (QKD) can be used generate secret keys that are secure against any future algorithmic or computational improvements. QKD protocols still require authentication of classical communication, however, which is most easily achieved using computationally secure digital signature schemes. It is generally considered folklore that QKD when used with computationally secure authentication is still secure against an unbounded adversary, provided the adversary did not break the authentication during the run of the protocol. We describe a security model for quantum key distribution based on traditional classical authenticated key exchange (AKE) security models. Using our model, we characterize the long-term security of the BB84 QKD protocol with computationally secure authentication against an eventually unbounded adversary. By basing our model on traditional AKE models, we can more readily compare the relative merits of various forms of QKD and existing classical AKE protocols. This comparison illustrates in which types of adversarial environments different quantum and classical key agreement protocols can be secure.
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.