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arXiv:2504.19702 · International Conference on Quantum Communications, Networking, and Computing (QCNC)

Security of a Secret Sharing Protocol on the Qline

Alex B. Grilo, Lucas Hanouz, Anne Marin

Published Apr 6, 2026• 0 citations
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Abstract

Secret sharing is a fundamental primitive in cryptography, and it can be achieved even with perfect security. However, the distribution of shares requires computational assumptions, which can compromise the overall security of the protocol. While traditional Quantum Key Distribution (QKD) can maintain security, its widespread deployment in general networks would incur prohibitive costs. In this work, we present a quantum protocol for distributing additive secret sharing of 0, which we prove to be composably secure within the Abstract Cryptography framework. Moreover, our protocol targets the Qline, a recently proposed quantum network architecture designed to simplify and reduce the cost of quantum communication. Once the shares are distributed, they can be used to securely perform a wide range of cryptographic tasks, including standard additive secret sharing, anonymous veto, and symmetric key establishment.

DOI
10.1109/qcnc69040.2026.00056

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Secret sharing is a fundamental primitive in cryptography, and it can be achieved even with perfect security. However, the distribution of shares requires computational assumptions, which can compromise the overall security of the protocol. While traditional Quantum Key Distribution (QKD) can maintain security, its widespread deployment in general networks would incur prohibitive costs. In this work, we present a quantum protocol for distributing additive secret sharing of 0, which we prove to be composably secure within the Abstract Cryptography framework. Moreover, our protocol targets the Qline, a recently proposed quantum network architecture designed to simplify and reduce the cost of quantum communication. Once the shares are distributed, they can be used to securely perform a wide range of cryptographic tasks, including standard additive secret sharing, anonymous veto, and symmetric key establishment.
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.
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.
The counter-intuitive features of quantum mechanics make it possible to solve problems and perform tasks that are beyond the abilities of non-quantum (classical) computers and communication devices. The field of quantum information processing studies how we can achieve such improvements by representing information as quantum states.One of the early achievements of quantum information processing is the development of quantum key distribution (QKD). QKD protocols allow two participants (Alice and Bob) to achieve the classically-impossible task of generating a secret shared key even if their adversary is computationally unlimited.Unfortunately, the security promises of QKD are true only in theory; practical implementations of QKD deviate from the theoretical protocols, and many of these deviations give rise to practical attacks. In this research thesis, we study the security properties of various QKD protocols in many practical settings:First, we study practical security of semiquantum key distribution (SQKD) protocols, where either Alice or Bob is non-quantum (classical). Following practical security problems in previous SQKD protocols, we suggest a new SQKD protocol (the "Mirror protocol") which can be securely implemented, and we prove it robust and secure against a wide range of attacks (the "uniform collective attacks").Then, we study "composable security" of the first QKD protocol created by Bennett and Brassard (BB84). BB84 has its unconditional security proved against adversaries performing the most general attacks in a theoretical (idealized) setting; however, some security approaches do not prove "composable security", which requires the secret key to remain secret even when Alice and Bob actually use it for cryptographic purposes. We generalize an algebraic security approach for BB84, making it prove composable security of BB84 (and many variants of BB84) against the most general attacks.Finally, we analyze an important practical attack (named "Bright Illumination"), showing how it can be modeled as a theoretical "Reversed-Space" attack.Overall, all results aim to enhance our understanding on how to bridge the gap between theory and practice in various sub-fields of QKD, and they may help solve a major open problem in the field of QKD: constructing a realistic QKD implementation that can be proved truly and unconditionally secure against any possible attack.
Quantum cryptography is information-theoretically secure owing to its solid basis in quantum mechanics. However, generally, initial implementations with practical imperfections might open loopholes, allowing an eavesdropper to compromise the security of a quantum cryptographic system. This has been shown to happen for quantum key distribution (QKD). Here we apply experience from implementation security of QKD to several other quantum cryptographic primitives. We survey quantum digital signatures, quantum secret sharing, source-independent quantum random number generation, quantum secure direct communication, and blind quantum computing. We propose how the eavesdropper could in principle exploit the loopholes to violate assumptions in these protocols, breaking their security properties. Applicable countermeasures are also discussed. It is important to consider potential implementation security issues early in protocol design, to shorten the path to future applications.
Quantum cryptography is information-theoretically secure owing to its solid basis in quantum mechanics. However, generally, initial implementations with practical imperfections might open loopholes, allowing an eavesdropper to compromise the security of a quantum cryptographic system. This has been shown to happen for quantum key distribution (QKD). Here we apply experience from implementation security of QKD to several other quantum cryptographic primitives. We survey quantum digital signatures, quantum secret sharing, source-independent quantum random number generation, quantum secure direct communication, and blind quantum computing. We propose how the eavesdropper could in principle exploit the loopholes to violate assumptions in these protocols, breaking their security properties. Applicable countermeasures are also discussed. It is important to consider potential implementation security issues early in protocol design, to shorten the path to future applications.
Secret sharing is a multiparty cryptographic primitive that can be applied to a network of partially distrustful parties for encrypting data that is both sensitive (it must remain secure) and important (it must not be lost or destroyed).When sharing classical secrets (as opposed to quantum states), one can distinguish between protocols that leverage bipartite quantum key distribution (QKD) and those that exploit multipartite entanglement.The latter class are known to be vulnerable to so-called participant attacks and, while progress has been made recently, there is currently no analysis that quantifies their performance in the composable, finite-size regime, which has become the gold standard for QKD security.Given this-and the fact that distributing multipartite entanglement is typically challenging-one might well ask is there any virtue in pursuing multipartite entanglement-based schemes?Here, we answer this question in the affirmative for a class of secret-sharing protocols based on continuous-variable graph states.We establish security in a composable framework and identify a network topology, specifically a bottleneck network of lossy channels, and parameter regimes within the reach of present-day experiments for which a multipartite scheme outperforms the corresponding QKD-based method in the asymptotic and finite-size setting.Finally, we establish experimental parameters where the multipartite schemes outperform any possible QKD-based protocol.This is one of the first concrete compelling examples of multipartite entangled resources achieving a genuine advantage over point-to-point protocols for quantum communication and represents a rigorous, operational benchmark to assess the usefulness of such resources.