Device-independent (DI) cryptography represents the highest level of security, enabling cryptographic primitives to be executed safely on uncharacterized devices. Moreover, with successful proof-of-concept demonstrations in randomness expansion, randomness amplification, and quantum key distribution, the field is steadily advancing toward commercial viability. Critical to this continued progression is the development of tighter finite-size security proofs. In this work, we provide a simple method to obtain tighter finite-size security proofs for protocols based on the CHSH game, which is the nonlocality test used in all of the proof-of-concept experiments. We achieve this by analytically solving key-rate optimization problems based on Rényi entropies, providing a simple method to obtain tighter finite-size key rates.
Device-independent (DI) cryptography represents the highest level of security, enabling cryptographic primitives to be executed safely on uncharacterized devices. Moreover, with successful proof-of-concept demonstrations in randomness expansion, randomness amplification, and quantum key distribution, the field is steadily advancing toward commercial viability. Critical to this continued progression is the development of tighter finite-size security proofs. In this work, we provide a simple method to obtain tighter finite-size security proofs for protocols based on the CHSH game, which is the nonlocality test used in all of the proof-of-concept experiments. We achieve this by analytically solving key-rate optimization problems based on Rényi entropies, providing a simple method to obtain tighter finite-size key rates.
Device-independent security is the gold standard for quantum cryptography: not only is security based entirely on the laws of quantum mechanics, but it holds irrespective of any a priori assumptions on the quantum devices used in a protocol, making it particularly applicable in a quantum-wary environment. While the existence of device-independent protocols for tasks such as randomness expansion and quantum key distribution has recently been established, the underlying proofs of security remain very challenging, yield rather poor key rates, and demand very high quality quantum devices, thus making them all but impossible to implement in practice. We introduce a technique for the analysis of device-independent cryptographic protocols. We provide a flexible protocol and give a security proof that provides quantitative bounds that are asymptotically tight, even in the presence of general quantum adversaries. At a high level our approach amounts to establishing a reduction to the scenario in which the untrusted device operates in an identical and independent way in each round of the protocol. This is achieved by leveraging the sequential nature of the protocol and makes use of a newly developed tool, the “entropy accumulation theorem” of Dupuis, Fawzi, and Renner [ Entropy Accumulation, preprint, 2016]. As concrete applications we give simple and modular security proofs for device-independent quantum key distribution and randomness expansion protocols based on the CHSH inequality. For both tasks, we establish essentially optimal asymptotic key rates and noise tolerance. In view of recent experimental progress, which has culminated in loophole-free Bell tests, it is likely that these protocols can be practically implemented in the near future.
Variational techniques have been recently developed to find tighter bounds on the von Neumann entropy in a completely device-independent (DI) setting. This, in turn, has led to significantly improved key rates of DI protocols, in both the asymptotic limit as well as in the finite-size regime. In this paper, we discuss two approaches towards applying these variational methods for Petz-Rényi divergences instead. We then show how this can be used to further improve the finite-size key rate of DI protocols, utilizing a fully-Rényi entropy accumulation theorem developed in a partner work. Petz-Rényi divergences can also be applied to study DI advantage distillation, in which two-way communication is used to improve the noise tolerance of quantum key distribution (QKD) protocols. We implement these techniques to derive increased noise tolerances for DIQKD protocols, which surpass all previous known bounds.
Device-independent (DI) quantum cryptography provides secure cryptography with minimal trust in, or characterisation of, the used quantum devices. An essential component of DI protocols is the use of randomness extractors for privacy amplification, but these typically require an initial seed of randomness that introduces a potential vulnerability. To solve this problem, the security of seedless extractors was proven in Quantum 9, 1654 (2025). The core idea was to use the Bell violation of the raw data, rather than its min-entropy, as the extractor promise. However, the large fluctuations in the Bell inequality used required many rounds to precisely estimate the Bell violation, consuming substantial randomness and making the protocol very inefficient. In this work, we present a new proof technique based on a truncation method that allows the user to estimate the protocol parameters with an asymptotically vanishing fraction of rounds and, as a consequence, achieves the optimal rate of one key bit per singlet. Notably, we prove this result using seedless extractors that can be implemented efficiently.
The security of finite-length keys is essential for the implementation of device-independent quantum key distribution (DIQKD). Presently, there are several finite-size DIQKD security proofs, but they are mostly focused on standard DIQKD protocols and do not directly apply to the recent improved DIQKD protocols based on noisy preprocessing, random key measurements, and modified CHSH inequalities. Here, we provide a general finite-size security proof that can simultaneously encompass these approaches, using tighter finite-size bounds than previous analyses. In doing so, we develop a method to compute tight lower bounds on the asymptotic keyrate for any such DIQKD protocol with binary inputs and outputs. With this, we show that positive asymptotic keyrates are achievable up to depolarizing noise values of 9.33% , exceeding all previously known noise thresholds. We also develop a modification to random-key-measurement protocols, using a pre-shared seed followed by a "seed recovery" step, which yields substantially higher net key generation rates by essentially removing the sifting factor. Some of our results may also improve the keyrates of device-independent randomness expansion.
Device-independent (DI) protocols have experienced significant progress in recent years, with a series of demonstrations of DI randomness generation or expansion, as well as DI quantum key distribution. However, existing security proofs for those demonstrations rely on a typical assumption in DI cryptography, that the devices do not leak any unwanted information to each other or to an adversary. This assumption may be difficult to perfectly enforce in practice. While there exist other DI security proofs that account for a constrained amount of such leakage, the techniques used are somewhat unsuited for analyzing the recent DI protocol demonstrations. In this work, we address this issue by studying a constrained leakage model suited for this purpose, which should also be relevant for future similar experiments. Our proof structure is compatible with recent proof techniques for flexibly analyzing a wide range of DI protocol implementations. With our approach, we compute some estimates of the effects of leakage on the keyrates of those protocols, hence providing a clearer understanding of the amount of leakage that can be allowed while still obtaining positive keyrates.
The entropy accumulation theorem—and its subsequent generalized version—is a powerful tool in the security analysis of many device-dependent and device-independent cryptography protocols. However, it has the drawback that the finite-size bounds it yields are not necessarily optimal; furthermore, it relies on the construction of an affine min-tradeoff function, which can often be challenging to construct optimally in practice. In this work, we address both of these challenges simultaneously by deriving a new entropy accumulation bound. Our bound yields significantly better finite-size performance and can be computed as an intuitively interpretable convex optimization, without any specification of affine min-tradeoff functions. Furthermore, it can be applied directly at the level of Rényi entropies if desired, yielding fully-Rényi security proofs. Our proof techniques are based on elaborating on a connection between entropy accumulation and the frameworks of quantum probability estimation or f -weighted Rényi entropies; in the process, we obtain some new results with respect to those frameworks as well. In particular, those findings imply that our bounds apply to prepare-and-measure protocols without the virtual tomography procedures or repetition-rate restrictions previously required for entropy accumulation.