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arXiv:quant-ph/0402131

A Generic Security Proof for Quantum Key Distribution

Matthias Christandl, Renato Renner, ARTUR K. EKERT

Published Feb 18, 2004• 72 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.quant-ph/0402131

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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.
Quantum key distribution (QKD), another name for quantum cryptography, is the most advanced subfield of quantum information and communication technology (QICT). The first QKD protocol was proposed in 1984, and since then, more protocols have been proposed. It uses quantum mechanics to enable secure exchange of cryptographic keys. In order to have high confidence in the security of the QKD protocols, such protocols must be proven to be secure against any arbitrary attacks. In this chapter, we discuss and demonstrate security proofs for QKD protocols. Security analysis of QKD protocols can be categorised into two techniques, namely infinite-key and finite-key analyses. Finite-key analysis offers more realistic results than the infinite-key one, while infinite-key analysis provides more simplicity. We briefly provide the background of QKD and also define the basic notion of security in QKD protocols. The cryptographic key is shared between Alice and Bob. Since the key is random and unknown to an eavesdropper, Eve, she is unable to learn anything about the message simply by intercepting the ciphertext. This phenomenon is beyond the ability of classical information processing. We then study some tools that are used in the derivation of security proofs for the infinite- and finite-length key limits.
It seems that quantum key distribution (QKD) may be completely insecure when the message sender Alice always encodes her key bits in a fixed basis. In this paper, we present a QKD protocol with classical Alice, i.e. Alice always encodes her key bit in the {|0〉,|1〉} basis (we call it classical {0,1} basis) and the eavesdropper Eve knows this fact. We prove that our protocol is completely robust against any eavesdropping attack and present the amount of tolerable noise against Eve's individual attack. Next, we present a QKD protocol to demonstrate that secure key bits can be distributed even if neither Alice nor Bob has quantum capacities, and extend this idea to a QKD network protocol with numerous parties who have only classical capacities. Finally, we discuss that quantum is necessary in QKD for security reasons, but both Alice and Bob may be classical.
Quantum key distribution (QKD) is intended to produce cryptographic secret keys between two remote parties, usually called Alice and Bob. Even though QKD has been proven to be unconditionally secure against the eavesdropper, commonly called Eve, practical implementations of QKD may contain vulnerabilities that may lead to the generated secret keys being compromised. In order to detect the presence of the eavesdropper in the channel, in our proposal Alice introduces an interleaved sequence of decoy states which produce a characteristic distribution at Bob's station. Thus, in analyzing such distribution in presence and absence of the eavesdropper Eve, her activity in the channel is detected. This protocol doesn’t require changes at the quantum physical level, but it can be incorporated at the high software level.
In usual security proofs of quantum protocols the adversary (Eve) is expected to have full control over any quantum communication between any communicating parties (Alice and Bob). Eve is also expected to have full access to an authenticated classical channel between Alice and Bob. Unconditional security against any attack by Eve can be proved even in the realistic setting of device and channel imperfection. In this paper we show that the security of quantum key distribution protocols is ruined if one allows Eve to possess a very limited access to the random sources used by Alice. Such knowledge should always be expected in realistic experimental conditions via different side channels.
In contrast to classical public-key cryptosystems, where the security of encoded messages relies on on computational assumptions, Quantum Key Distribution (QKD) enables two distant parties to establish a shared secret key that, when combined with a one-time pad, provides information-theoretically secure encryption, provided that the QKD protocol is supported by a rigorous security proof. In the last decades, security proofs robust against a wide range of eavesdropping strategies have established the theoretical soundness of several QKD protocols. However, most proofs are based on idealized models of the physical systems involved in such protocols and often include assumptions that are not satisfied in practical implementations. This mismatch creates a gap between theoretical security guarantees and actual experimental realizations, making QKD protocols vulnerable to attacks. To ensure the security of real-world QKD systems, it is therefore essential to account for imperfections in security analyses. In this article, we present an overview of recent analytical and numerical developments in QKD security proofs, which provide a versatile approach for incorporating imperfections and re-establishing the security of quantum communication protocols under realistic conditions.
Cryptographic protocols can be classified by the type of security against eavesdropping which they provide. There exist mathematically secure schemes whose security relies on mathematical proofs (like the Vernam cipher discussed below) or conjectures (like public key RSA encryption) about the complexity of deciphering the message without possessing the correct key. The majority of current secure public Internet connections rely on such schemes. Alternatively, a cryptographic setup may provide a physically secure method for communicating. In these setups the security is provided by the physical laws governing the communication protocol. Here we first discuss a provably secure classical communication protocol and then quantum methods for distributing the necessary keys. The BB84 protocol relies on the impossibility of perfectly distinguishing non-orthogonal quantum states from one copy of the quantum system. The scheme was invented in 1984 and is the first of its kind. In contrast, the Ekert91 protocol makes use of Bell correlations between entangled pairs of photons. These correlations are destroyed when Eve attempts to make a measurement on one of the particles but also when imperfections, such as decoherence processes, affect the scheme. As long as no such “elements of reality” are introduced, and Bell correlations violating local realism can be generated by Alice and Bob, no eavesdropper can be present. One-time pads and the Vernam cipher The Vernam cipher is a cryptographic protocol which allows the encryption and decryption protocol to be publicly known. The security of the protocol relies entirely on the key which is private and not publicly known. Alice and Bob share identical n -bit secret key strings (one-time pad).