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Security and Communication Networks

A probabilistic quantum key transfer protocol

Abhishek Parakh

Published Mar 13, 2013• 17 citations
Publisher

Abstract

ABSTRACT We propose a protocol to transfer a one‐time pad (in a probabilistic manner) from Alice to Bob, over a public channel. The proposed protocol is unique because Bob merely acts as a receiver of the pad (secret key); that is, Bob does not need to send any message back to Alice unless he detects eavesdropping. Such a secure transfer of one‐time pad, over public channel, is not possible in classical cryptography, and in quantum cryptography, all previous protocols require Bob to send almost as many messages back to Alice as she does to Bob to establish a key. Copyright © 2013 John Wiley & Sons, Ltd.

DOI
10.1002/sec.736

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Cambridge University Press eBooks•Jul 19, 2012•0 citations
ABSTRACT We propose a protocol to transfer a one‐time pad (in a probabilistic manner) from Alice to Bob, over a public channel. The proposed protocol is unique because Bob merely acts as a receiver of the pad (secret key); that is, Bob does not need to send any message back to Alice unless he detects eavesdropping. Such a secure transfer of one‐time pad, over public channel, is not possible in classical cryptography, and in quantum cryptography, all previous protocols require Bob to send almost as many messages back to Alice as she does to Bob to establish a key. Copyright © 2013 John Wiley & Sons, Ltd.
This study shows that secret information can be shared or passed from a sender to a receiver even if not encoded in a secret message. In the protocol designed in this study, no parts of the original secret information ever travel via communication channels between the source and the destination, no encoding/decoding key is ever used. The two communicating partners, Alice and Bob, are endowed with coherent qubits that can be read and set and keep their quantum values over time. Additionally, there exists a central authority that is capable of identifying Alice and Bob to share with each half of entangled qubit pairs. The central authority also performs entanglement swapping. Our protocol relies on the assumption that public information can be protected, an assumption present in all cryptographic protocols. Also any classical communication channel need not be authenticated. As each piece of secret information has a distinct public encoding, the protocol is equivalent to a one-time pad protocol.
Cryptography is processing for securing communication between two people. The opponent wants to know the message that is encrypted using a secret key. Although the opponent can eavesdrop the message sent between the sender and the receiver, the opponent is unable to decrypt to read the message. Therefore, the secret key is very important. The sender and the receiver agree with the secret key in an insecure channel by using key distribution protocol such as the Diffie–Hellman protocol. Since quantum computer is coming soon, Diffie–Hellman protocol is not secure. We will develop a quantum key distribution protocol. The benefit of the quantum system is the quantum state that cannot copy by no‐cloning theorem. Thus, the opponent does not copy and keeps the message that is quantum. In this paper, a novel quantum key distribution protocol between two people (Alice and Bob) based on quantum operators is developed. The opponent (Eve) wants to know the secret key. Although Eve knows this quantum key distribution protocol, Eve does not behave similarly to Alice and Bob. For example, Eve eavesdrops Alice's quantum state that was sent to Bob, and Eve sends another quantum state. Therefore, we cannot control Eve's behavior. So we give the upper bound of mutual information between the user and opponent by using Holevo's bound. We verify the usual security definition for quantum key distribution that is equality‐and‐uniformity and privacy in the mutual information sense.
Unclonable Encryption, introduced by Gottesman in 2003 [Quantum Inform. Comput. 3 (2003) 581], is a quantum protocol that guarantees the secrecy of a successfully transferred classical message even when all keys leak at a later time. We propose an Unclonable Encryption protocol with the additional property that the sender’s key material is allowed to leak even in the case of an unsuccessful run. This extra feature makes it possible to achieve secure quantum encryption even when one of the parties is unable to protect its keys against after-protocol theft. Such an asymmetry occurs e.g. in case of server–client scenarios, where the client device is resource constrained and/or located in a hostile environment. Our protocol makes use of a bidirectional quantum channel in a manner similar to the two-way protocol LM05 [Phys. Rev. Lett. 94 (2005) 140501]. Bob sends random qubit states to Alice. Alice flips the states in a way that depends on the message and a shared key, and sends the resulting states back to Bob. Bob recovers Alice’s message by measuring the flips. We prove that our protocol satisfies the definition of unclonable encryption and additionally that the message remains secure even if all of Alice’s keys leak after the protocol. Furthermore, we show that some of the key materials can be safely re-used. Our security proof is formulated in terms of diamond norms, which makes it composable, and allows for noisy quantum channels. We work out the details only for the asymptotics in the limit of long messages. As a side result, we construct a two-way QKD scheme with a high key rate. We show that its key rate is higher than the rate of the two-way QKD scheme LM05 proven by Beaudry et al. [Phys. Rev. A 88 (2013) 062302] for the case of independent channel noise.
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).