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arXiv:2004.10173

Everlasting Secure Key Agreement with performance beyond QKD in a Quantum Computational Hybrid security model

Vyas, Nilesh, Romain Alléaume

Published Apr 21, 2020• 3 citations
arXivHTMLPDF

Abstract

Extending the functionality and overcoming the performance limitation under which QKD can operate requires either quantum repeaters or new security models. Investigating the latter option, we introduce the \textit{Quantum Computational Hybrid} (QCH) security model, where we assume that computationally secure encryption may only be broken after time much longer than the coherence time of available quantum memories. We propose an explicit $d$-dimensional key distribution protocol, that we call MUB-\textit{Quantum Computational Timelock} (MUB-QCT) where one bit is encoded on a qudit state chosen among $d+1$ mutually unbiased bases (MUBs). Short-term-secure encryption is used to share the basis information with legitimate users while keeping it unknown from Eve until after her quantum memory decoheres. This allows reducing Eve's optimal attack to an immediate measurement followed by post-measurement decoding. \par We demonstrate that MUB-QCT enables everlasting secure key distribution with input states containing up to $O(\sqrt{d})$ photons. This leads to a series of important improvements when compared to QKD: on the functional side, the ability to operate securely between one sender and many receivers, whose implementation can moreover be untrusted; significant performance increase, characterized by a $O(\sqrt{d})$ multiplication of key rates and an extension by $25 {\rm} km \times \log(d)$ of the attainable distance over fiber. Implementable with a large number of modes with current or near-term multimode photonics technologies, the MUB-QCT construction has the potential to provide a radical shift to the performance and practicality of quantum key distribution.

DOI
10.48550/arxiv.2004.10173

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Extending the functionality and overcoming the performance limitation under which QKD can operate requires either quantum repeaters or new security models. Investigating the latter option, we introduce the \textit{Quantum Computational Hybrid} (QCH) security model, where we assume that computationally secure encryption may only be broken after time much longer than the coherence time of available quantum memories. We propose an explicit ddd-dimensional key distribution protocol, that we call MUB-\textit{Quantum Computational Timelock} (MUB-QCT) where one bit is encoded on a qudit state chosen among d+1d+1d+1 mutually unbiased bases (MUBs). Short-term-secure encryption is used to share the basis information with legitimate users while keeping it unknown from Eve until after her quantum memory decoheres. This allows reducing Eve's optimal attack to an immediate measurement followed by post-measurement decoding. \par We demonstrate that MUB-QCT enables everlasting secure key distribution with input states containing up to O(d)O(\sqrt{d})O(d​) photons. This leads to a series of important improvements when compared to QKD: on the functional side, the ability to operate securely between one sender and many receivers, whose implementation can moreover be untrusted; significant performance increase, characterized by a O(d)O(\sqrt{d})O(d​) multiplication of key rates and an extension by 25km×log⁡(d)25 {\rm} km \times \log(d)25km×log(d) of the attainable distance over fiber. Implementable with a large number of modes with current or near-term multimode photonics technologies, the MUB-QCT construction has the potential to provide a radical shift to the performance and practicality of quantum key distribution.
Extending the functionality and overcoming the performance limitation of QKD requires either quantum repeaters or new security models. Investigating the latter option, we introduce the Quantum Computational Timelock (QCT) security model, assuming that computationally secure encryption may only be broken after time much longer than the coherence time of available quantum memories. These two assumptions, namely short-term computational security and noisy quantum storage, have so far already been considered in quantum cryptography, yet only disjointly. A practical lower bound on time, for which encryption is computationally secure, can be inferred from assumed long-term security of the AES256 encryption scheme (30 years) and the value of coherence time in experimental demonstrations of storage and then retrieval of optically encoded quantum information, at single-photon level range from a few nanoseconds to microseconds. Given the large gap between the upper bound on coherence time and lower bound on computational security time of an encryption scheme, the validity of the QCT security model can be assumed with a very high confidence today and also leaves a considerable margin for its validity in the future. Using the QCT security model, we propose an explicit d-dimensional key agreement protocol that we call MUB-Quantum Computational Timelock (MUB-QCT), where a bit is encoded on a qudit state using a full set of mutually unbiased bases (MUBs) and a family of pair-wise independent permutations. Security is proved by showing that upper bound on Eve's information scales as O(1=d). We show MUB-QCT offers: high resilience to error (up to 50% for large d) with fixed hardware requirements; MDI security as security is independent of channel monitoring and does not require to trust measurement devices. We also prove the security of the MUB-QCT protocol, with multiple photons per channel use, against non-adaptive attacks, in particular, proactive MUB measurement where eve measures each copy in a different MUB followed by post-measurement decoding. We prove that the MUB-QCT protocol allows secure key distribution with input states containing up to O(d) photons which implies a significant performance boost, characterized by an O(d) multiplication of key rate and a significant increase in the reachable distance. These results illustrate the power of the QCT security model to boost the performance of quantum cryptography while keeping a clear security advantage over classical cryptography.
We introduce an explicit construction for a key distribution protocol in the Quantum Computational Timelock (QCT) security model, where one assumes that computationally secure encryption may only be broken after a time much longer than the coherence time of available quantum memories.Taking advantage of the QCT assumptions, we build a key distribution protocol called HM-QCT from the Hidden Matching problem for which there exists an exponential gap in one-way communication complexity between classical and quantum strategies.We establish that the security of HM-QCT against arbitrary i.i.d. attacks can be reduced to the difficulty of solving the underlying Hidden Matching problem with classical information. Legitimate users, on the other hand, can use quantum communication, which gives them the possibility of sending multiple copies of the same quantum state while retaining an information advantage. This leads to an everlasting secure key distribution scheme over n bosonic modes. Such a level of security is unattainable with purely classical techniques. Remarkably, the scheme remains secure with up to O ( n log ⁡ ( n ) ) input photons for each channel use, extending the functionalities and potentially outperforming QKD rates by several orders of magnitudes.
The HM-QCT protocol, presented by Mazzoncini et al. in 2025, uses a unique feature of quantum information to achieve quantum key distribution (QKD) with secret-key rates beyond standard constructions. The protocol has been designed in the hybrid quantum-computational time-lock (QCT) security model which imposes two independent (but related) restrictions on the attacker: (1) a computationally secure encryption scheme which a successful attacker must break within a narrow timeframe and (2) an assumption that the attacker can only store quantum information with low fidelity. We first review the protocol and its two-assumption model by presenting, in explicit form, the two natural "harvest now, decrypt later" strategies against it, one using quantum memory and one using classical memory. We show how each is excluded by exactly one of the two assumptions, so that harvesting resistance rests on their conjunction and on the presumed existence of a technological gap: the adversary's quantum memory must decohere much faster than the time it takes to break the short-term encryption. Finally, we introduce HM-PRF , a variant that replaces the short-term encryption with a pseudorandom function (PRF) , evaluated locally. By eliminating the transmission of enciphered classical information, the adversary does not need to race an impending expiry event. We compare the security of our construction against the original and argue that our PRF-based assumption yields a more realistic adversary. It simply requires the existence of one-way functions rather than a predicted lasting limitation of quantum computation and memory technology.
Quantum resistance is vital for emerging cryptographic systems as quantum technologies continue to advance towards large-scale, fault-tolerant quantum computers. Resistance may be offered by quantum key distribution (QKD), which provides information-theoretic security using quantum states of photons, but may be limited by transmission loss at long distances. An alternative approach uses classical means and is conjectured to be resistant to quantum attacks, so-called post-quantum cryptography (PQC), but it is yet to be rigorously proven, and its current implementations are computationally expensive. To overcome the security and performance challenges present in each, here we develop hybrid protocols by which QKD and PQC inter-operate within a joint quantum-classical network. In particular, we consider different hybrid designs that may offer enhanced speed and/or security over the individual performance of either approach. Furthermore, we present a method for analyzing the security of hybrid protocols in key distribution networks. Our hybrid approach paves the way for joint quantum-classical communication networks, which leverage the advantages of both QKD and PQC and can be tailored to the requirements of various practical networks.
The security of quantum cryptography relies on the foundations of quantum mechanics, in contrast to traditional public key cryptography which relies on the computational difficulty of certain mathematical functions, and cannot provide any indication of eavesdropping or guarantee of key security. The proposal present in this work develops a quantum key distribution model to safeguard security in large networks, in the directions of classical cryptography and quantum cryptography. Two three-party Quantum key distribution are used in this model, one with implicit user authentication and the other with explicit mutual authentication, are proposed to demonstrate the merits of the new combination. The performance of Quantum Key Distribution (QKD) systems have notably progressed since the early experimental demonstrations. The current evolutions in QKD research indicate that the pace of this progression is very likely to be maintained, if not increased, in the future years. In parallel to these improvements of QKD techniques, commercial products are also being developed, making QKD deployment a feasible alternative for securing real data networks. Deployment of a real QKD network is however far from being straightforward. It requires development of a network architecture connecting multiple users that may possibly be very far away from each other. Considering the fact that the existing QKD links are only point-to-point, and intrinsically limited in distance, deployment of a practical QKD network structure is a nontrivial problem. The proposed work describes the proposed architecture for a QKD network specify the requirements relevant to the network design, protocols, and services. The objective of this specification is to define the major components and their main features The proposal provides security against such attacks as man-in-the-middle, eavesdropping and replay. It also improves the efficiency of the quantum key distribution which contains the fewest number of communication rounds among existing Quantum key distributions. In this model two parties can share and use a long-term secret (repeatedly). To prove the security of the proposed schemes, this proposed model provides a primitive called the Unbiased-Chosen Basis (UCB) assumption with the quantum key in angular positions.
So far, quantum communication has promised unconditionally secure information transfer through protocols such as quantum key distribution. The practical deployment of QKD faces severe limitations due to decoherence, photon loss, and limited transmission distances in optical fibers and free space. The current systems are not scalable and require trusted relays, which are costly and introduce security vulnerabilities. This paper solves the core problem of the range extension in quantum networks by proposing HQRP, a novel hybrid quantum repeater protocol, for high-rate entanglement distribution in which single-spin photon transducers are combined with multiplexed ensemble-based atomic frequency comb memories. The HQRP uniquely combines the principles of twin-field QKD and error-corrected entanglement swapping, achieving secret key rates of tens of bits per second over 1000 km with only nine repeater nodes. Simulations demonstrate a5x\mathbf{5 x}5ximprovement of the key rate with respect to traditional measurement-device-independent QKD without repeaters, including robustness against 20 % photon loss. These results demonstrate the feasibility of using near-term hardware, such as room-temperature telecom-compatible memories, and pave the way toward global quantum networks. The effective efficiency of the protocol in practical environments is still affected by variations in environmental temperatures, which affect AFC memories, and require sub-nanosecond timing precision to coordinate nodes over1000 km\mathbf{1 0 0 0 ~ k m}1000 km. Future versions will employ adaptive timing based on machine learning to address these engineering issues. Index Terms-Quantum repeaters, entanglement distribution, QKD, decoherence mitigation, hybrid quantum networks.