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Journal of Experimental and Theoretical Physics Letters

Is there a fundamental limit on the key distribution distance in quantum cryptography?

S. N. Molotkov

Published Jan 1, 2008• 3 citations
Publisher

Abstract

Is there a fundamental limit on the key distribution distance in quantum cryptography? Are there quantum key distribution protocols approaching this limit and how close can they approach this limit? The answer to the first question is both yes and no. A general answer to the first question can be given without considering a particular quantum key distribution protocol and its implementation. The answer to the second question is given by a particular protocol for which the distribution distance is close to the theoretical limit and the achievement of this value is limited by our possibilities of correcting errors using classical codes rather than by the quantum key distribution protocol itself.

DOI
10.1134/s0021364008220128

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Is there a fundamental limit on the key distribution distance in quantum cryptography? Are there quantum key distribution protocols approaching this limit and how close can they approach this limit? The answer to the first question is both yes and no. A general answer to the first question can be given without considering a particular quantum key distribution protocol and its implementation. The answer to the second question is given by a particular protocol for which the distribution distance is close to the theoretical limit and the achievement of this value is limited by our possibilities of correcting errors using classical codes rather than by the quantum key distribution protocol itself.
The main parameter of any quantum cryptography protocol is the critical error Q c to which secret key distribution is possible. The critical error of all known quantum key distribution protocols does not exceed 20%. In this work, a protocol with which secret key distribution is possible to Q c → 50% is described and a simple proof of the security of the protocol is presented using fundamental entropic uncertainty relations. This critical error is a theoretical, but achievable limit, which cannot be improved.
If we combine two secure cryptographic systems, is the resulting system still secure?Answering this question is highly nontrivial and has recently sparked a considerable research effort, in particular, in the area of classical cryptography.A central insight was that the answer to the question is yes, but only within a well-specified composability framework and for carefully chosen security definitions.In this article, we review several aspects of composability in the context of quantum cryptography.The first part is devoted to key distribution.We discuss the security criteria that a quantum key distribution (QKD) protocol must fulfill to allow its safe use within a larger security application (e.g. for secure message transmission); and we demonstrate-by an explicit example-what can go wrong if conventional (non-composable) security definitions are used.Finally, to illustrate the practical use of composability, we show how to generate a continuous key stream by sequentially composing rounds of a QKD protocol.In the second part, we take a more general point of view, which is necessary for the study of cryptographic situations involving, for example, mutually distrustful parties.We explain the universal composability (UC) framework and state the composition theorem that guarantees that secure protocols can securely be composed to larger applications.We focus on the secure composition of quantum protocols into unconditionally secure classical protocols.However, the resulting security definition is so strict that some tasks become impossible without additional security assumptions.Quantum bit commitment is impossible in the UC framework even with mere computational security.Similar problems arise in the quantum bounded storage model and we observe a trade-off between the UC and the use of the weakest possible security assumptions.
Quantum cryptography offers a promising unbreakable cryptographic solution as it ensures perfect secrecy in applications such as quantum key distribution and bit commitment. The focus of this paper is to trace the development of quantum key distribution protocols and discuss the state of the art and open issues in this field. Although the protocols have mathematically proven to be totally secure, it must be emphasized that any real world implementation suffers the limitations of physical devices which can serve as vulnerability for an eavesdropper to exploit. In this paper, we survey the quantum key distribution protocols which exist in literature and explore the attacks to which they are vulnerable. We highlight the main implementation bottlenecks related with each implementation and the solutions proposed thereof.
Quantum cryptography presents a paradigm shift in secure communication, offering the potential for unparalleled security based on the principles of quantum mechanics. This paper explores the design and implementation of a novel cryptographic protocol, termed "Quantum Key Distribution" (QKD), which utilizes quantum-enhanced error correction and measurement to establish a fundamentally more secure key distribution system. The core claim centers on leveraging quantum phenomena to detect and mitigate eavesdropping attempts, fundamentally altering the security landscape beyond the limitations of classical cryptography. We detail the protocol's architecture, focusing on the critical role of quantum-enhanced error correction and measurement in achieving robust key generation. The paper concludes with a discussion of the challenges and future directions for this emerging field.