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arXiv:1204.4235 · Physical Review A

Comment on “Security proof for cryptographic protocols based only on the monogamy of Bell's inequality violations”

Won-Young Hwang, Oleg Gittsovich

Published Apr 17, 2012• 5 citations
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Abstract

Recently, Pawlowski [Phys. Rev. A 82, 032313 (2010)] claimed to have proven the security of a quantum key distribution by using only the monogamy of Bell's inequality violations. In the proof, however, he tacitly assumed that the eavesdropper's outcome is binary. The assumption cannot be justified because Eve's (eavesdropper's) power can only be limited by natural principle. We provide a counterexample for a step of the proof.

DOI
10.1103/physreva.85.046301

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In this reply, I address the comment by Hwang and Gittsovich on my paper [Phys. Rev. A 82, 032313 (2010)]. The authors of the Comment pointed out that I used an implicit assumption that the alphabet of the eavesdropper was binary. They claimed that such an assumption was unrealistic. Here, I show that, even without this assumption, the main result of my paper still holds.

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Recently, Pawlowski [Phys. Rev. A 82, 032313 (2010)] claimed to have proven the security of a quantum key distribution by using only the monogamy of Bell's inequality violations. In the proof, however, he tacitly assumed that the eavesdropper's outcome is binary. The assumption cannot be justified because Eve's (eavesdropper's) power can only be limited by natural principle. We provide a counterexample for a step of the proof.
We show that monogamy of Bell's inequality violations, which is strictly weaker condition than the no-signaling principle is enough to prove security of quantum key distribution. We derive our results for a whole class of monogamy constraints and generalize our results to any theory that communicating parties may have access to. Some of these theories do not respect the no-signaling principle yet still allow for secure communication. This proves that no signaling is only a sufficient condition for the possibility of secure communication, but not the necessary one. We also present some new qualitative results concerning the security of existing quantum key distribution protocols.
Standard quantum key distribution protocols are provably secure against eavesdropping attacks, if quantum theory is correct. It is theoretically interesting to know if we need to assume the validity of quantum theory to prove the security of quantum key distribution, or whether its security can be based on other physical principles. The question would also be of practical interest if quantum mechanics were ever to fail in some regime, because a scientifically and technologically advanced eavesdropper could perhaps use postquantum physics to extract information from quantum communications without necessarily causing the quantum state disturbances on which existing security proofs rely. Here we describe a key distribution scheme provably secure against general attacks by a postquantum eavesdropper limited only by the impossibility of superluminal signaling. Its security stems from violation of a Bell inequality.
Recently, Lucamarini et al. proposed the device-independent entanglement-based Bennett 1992 protocol [Phys. Rev. A 86, 032325 (2012)]. By exploiting the results in device-independent quantum key distribution with the Clauser-Horne-Shimony-Holt inequality, they claimed the security of their protocol. We will show, however, the way of encoding and the process for the latent eavesdropper to obtain the illegal information are different in these two protocols. Thus the security of their protocol cannot rely on Bell's theorem only.
We analyze a cryptographic protocol for generating a distributed secret key from correlations that violate a Bell inequality by a sufficient amount, and prove its security against eavesdroppers, constrained only by the assumption that any information accessible to them must be compatible with the non-signaling principle. The claim holds with respect to the state-of-the-art security definition used in cryptography, known as universally-composable security. The non-signaling assumption only refers to the statistics of measurement outcomes depending on the choices of measurements; hence security is independent of the internal workings of the devices - they do not even need to follow the laws of quantum theory. This is relevant for practice as a correct and complete modeling of realistic devices is generally impossible. The techniques developed are general and can be applied to other Bell inequality-based protocols. In particular, we provide a scheme for estimating Bell-inequality violations when the samples are not independent and identically distributed.
The information causality principle (IC)(\mathcal{IC})(IC) was originally proposed as a promising means to understand the extent of quantum nonlocality without invoking the full mathematical formalism of quantum theory. Beyond the foundational significance, the problem of bounding nonlocal correlations by reasonable physical principles has meaningful practical consequences, particularly for device-independent (DI) cryptographic security. In this work, we advance in this direction, demonstrating that the IC\mathcal{IC}IC is enough to ensure DI security on quantum key distribution (QKD) protocols. Security is proven for a range of theoretically quantum-attainable parameters against individual attacks by a potentially postquantum eavesdropper. This result follows as a consequence of a strong form of monogamy of Bell's inequality violations, which we prove to be implied by the recently proposed multipartite formulation for IC\mathcal{IC}IC. Additionally, we demonstrate that the original bipartite formulation of IC\mathcal{IC}IC fails to imply monogamy relations, and hence, ensure security of DIQKD, thus stressing the necessity of the multipartite framework.