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Entropy

From Key Encapsulation to Authenticated Group Key Establishment—A Compiler for Post-Quantum Primitives †

Edoardo Persichetti, Rainer Steinwandt, Adriana Suárez Corona

Published Nov 30, 2019• 8 citations
Publisher

Abstract

Assuming the availability of an existentially unforgeable signature scheme and an (IND- CCA secure) key encapsulation mechanism, we present a generic construction for group key establishment. The construction is designed with existing proposals for post-quantum cryptography in mind. Applied with such existing proposals and assuming their security, we obtain a quantum-safe three-round protocol for authenticated group key establishment that requires only one signature per protocol participant.

DOI
10.3390/e21121183

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Assuming the availability of an existentially unforgeable signature scheme and an (IND- CCA secure) key encapsulation mechanism, we present a generic construction for group key establishment. The construction is designed with existing proposals for post-quantum cryptography in mind. Applied with such existing proposals and assuming their security, we obtain a quantum-safe three-round protocol for authenticated group key establishment that requires only one signature per protocol participant.
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 present a security model for authenticated key establishment that allows for quantum interactions between the adversary and quantum oracles that emulate classical parties, resulting in a truly post-quantum security definition. We then give a generic construction for a secure protocol in the quantum random oracle model by combining a signature scheme which is existentially unforgeable under adaptive quantum chosen message attack in the quantum random oracle model (EUF-qCMA-QRO secure) with an unauthenticated key establishment protocol which is secure against a passive adversary. This construction allows us to give an explicit example of a secure protocol whose security is based on a variant of the Diffie-Hellman problem for isogenies of supersingular elliptic curves; in particular, generic security-strengthening transformations allow us to take a signature scheme which is EUF-CMA-RO secure against a quantum adversary and transform it into an EUF-qCMA-QRO signature scheme, which we combine with a standard secure unauthenticated key establishment protocol to achieve the desired result.
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.
Cryptography underpins the security of modern digital infrastructure, from cloud services to health data. However, many widely deployed systems will become vulnerable after the advent of scalable quantum computing. Although quantum-safe cryptographic primitives have been developed, such as lattice-based digital signature algorithms (DSAs) and key encapsulation mechanisms (KEMs), their unique structural and performance characteristics make them unsuitable for existing protocols. In this work, we introduce a quantum-safe single-shot protocol for machine-to-machine authentication and authorization that is specifically designed to leverage the strengths of lattice-based DSAs and KEMs. Operating entirely over insecure channels, this protocol enables the forward-secure establishment of tokens in constrained environments. By demonstrating how new quantum-safe cryptographic primitives can be incorporated into secure systems, this study lays the groundwork for scalable, resilient, and future-proof identity infrastructures in a quantum-enabled world.
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.