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arXiv:0807.2158 · Physical Review Letters

Universally Composable Privacy Amplification from Causality Constraints

Lluís Masanes

Published Apr 10, 2009• 146 citations
arXivHTMLPDF

Abstract

We consider schemes for secret key distribution which use as a resource correlations that violate Bell inequalities. We provide the first security proof for such schemes, according to the strongest notion of security, the so-called universally composable security. Our security proof does not rely on the validity of quantum mechanics, it solely relies on the impossibility of arbitrarily fast signaling between separate physical systems. This allows for secret communication in situations where the participants distrust their quantum devices.

DOI
10.1103/physrevlett.102.140501

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We consider schemes for secret key distribution which use as a resource correlations that violate Bell inequalities. We provide the first security proof for such schemes, according to the strongest notion of security, the so-called universally composable security. Our security proof does not rely on the validity of quantum mechanics, it solely relies on the impossibility of arbitrarily fast signaling between separate physical systems. This allows for secret communication in situations where the participants distrust their quantum devices.
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.
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Quantum key distribution allows two parties, traditionally known as Alice and Bob, to establish a secure random cryptographic key if, firstly, they have access to a quantum communication channel, and secondly, they can exchange classical public messages which can be monitored but not altered by an eavesdropper, Eve. Quantum key distribution provides perfect security because, unlike its classical counterpart, it relies on the laws of physics rather than on ensuring that successful eavesdropping would require excessive computational effort. However, security proofs of quantum key distribution are not trivial and are usually restricted in their applicability to specific protocols. In contrast, we present a general and conceptually simple proof which can be applied to a number of different protocols. It relies on the fact that a cryptographic procedure called privacy amplification is equally secure when an adversary's memory for data storage is quantum rather than classical.
In the past few years there was a growing interest in proving the security of cryptographic protocols, such as key distribution protocols, from the sole assumption that the systems of Alice and Bob cannot signal to each other. This can be achieved by making sure that Alice and Bob perform their measurements in a space-like separated way (and therefore signalling is impossible according to the non-signalling postulate of relativity theory) or even by shielding their apparatus. Unfortunately, it was proven in [E. Haenggi, R. Renner, and S. Wolf. The impossibility of non-signaling privacy amplification] that, no matter what hash function we use, privacy amplification is impossible if we only impose non-signalling conditions between Alice and Bob and not within their systems. In this letter we reduce the gap between the assumptions of Haenggi et al. and the physical relevant assumptions, from an experimental point of view, which say that the systems can only signal forward in time within the systems of Alice and Bob. We consider a set of assumptions which is very close to the conditions above and prove that the impossibility result of Haenggi et al. still holds.
This paper explores the foundational principles and practical implications of achieving information-theoretic security through quantum entanglement. Information-theoretic security, independent of computational complexity assumptions, offers unparalleled privacy and integrity. Classical cryptography relies on unproven mathematical hardness, making it vulnerable to future quantum computers. Quantum mechanics, specifically entanglement, provides a novel paradigm for cryptographic protocols with unconditional security, guaranteed by the laws of physics. We detail how entanglement enables certain eavesdropping detection and generates truly random shared secret keys. The discussion encompasses key protocols, the role of Bell inequalities, and theoretical security proofs underpinning these quantum systems. We also address current challenges and future prospects for deploying entanglement-based secure communication networks, highlighting its transformative potential for a future-proof global communication infrastructure. This work synthesizes how quantum entanglement shifts cryptographic assurance from computational assumptions to fundamental physical laws, setting the stage for truly uncompromisable communication. We further acknowledge the ethical considerations and societal implications of such robust encryption.
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.