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International Symposium on Information Theory and its Applications

Quantum Key Distribution using Extended Mean King’s Problem

Ayumu Nakayama, M. Yoshida, Jun Cheng

Published Oct 1, 2018• 1 citation
Publisher

Abstract

In this paper, we introduce the extended mean king's problem and its solutions. Also, we show a quantum key distribution (QKD) using the extended mean king's problem. By using the quantum key distribution, a sender can share a secret key with each of receivers. Besides, we consider the tolerance to an eavesdropper who makes intercept-resend attacks. As a result, in the case of two receivers, we indicate that the quantum key distribution is robust against the intercept-resend attacks by showing that the error occurs between the secret keys of a sender and receivers.

DOI
10.23919/isita.2018.8664332

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In this paper, we introduce the extended mean king's problem and its solutions. Also, we show a quantum key distribution (QKD) using the extended mean king's problem. By using the quantum key distribution, a sender can share a secret key with each of receivers. Besides, we consider the tolerance to an eavesdropper who makes intercept-resend attacks. As a result, in the case of two receivers, we indicate that the quantum key distribution is robust against the intercept-resend attacks by showing that the error occurs between the secret keys of a sender and receivers.
In 2001, Jefferey Bub proposed a quantum key distribution protocol using the Mean King problem. In the protocol, King chooses one of the observables σ x or σ z , while Alice is required to measure an observable that solves the Mean King problem for three observables σ x , σ y and σ z . The observable employed by Alice is thus rather complicated. In this paper, we give other simple solutions of the Mean King problem for two observables and examine the quantum key distribution protocols using them. Our result shows that not all the solutions of the Mean King problem are available to construct a secure protocol. In addition, we consider a protocol that is tolerant with three attack scenarios and derive a trade-off inequality between Eve's information gain and error probability observed by the legitimate users.
It is anticipated that quantum key distribution enable us to share a secret key while guaranteeing unconditionally security. In this paper, we discuss the quantum key distribution using the Mean King Problem which was proposed by J. Bub in 2001. While this two-way quantum protocol is essentially different from the other one-way protocols like the BB84, it has been shown that Eve cannot gain any information without being detected even in this protocol. Assuming two attack scenarios in this protocol, we derive two trade-off inequalities showing that the larger Eve's information gain is, the higher the detectability becomes. These quantitative inequalities enables the legitimate users to estimate Eve's information gain.
We introduce a quantum key distribution protocol using mean multi-kings' problem. Using this protocol, a sender can share a bit sequence as a secret key with receivers. We consider a relation between information gain by an eavesdropper and disturbance contained in legitimate users' information. In BB84 protocol, such relation is known as the so-called information disturbance theorem. We focus on a setting that the sender and two receivers try to share bit sequences and the eavesdropper tries to extract information by interacting legitimate users' systems and an ancilla system. We derive trade-off inequalities between distinguishability of quantum states corresponding to the bit sequence for the eavesdropper and error probability of the bit sequence shared with the legitimate users. Our inequalities show that eavesdropper's extracting information regarding the secret keys inevitably induces disturbing the states and increasing the error probability.
Employing the fundamental laws of quantum physics, Quantum Key Distribution (QKD) promises the unconditionally secure distribution of cryptographic keys. However, in practical realisations, a QKD protocol is only secure, when the quantum bit error rate introduced by an eavesdropper unavoidably exceeds the system error rate. This condition guarantees that an eavesdropper cannot disguise his presence by simply replacing the original transmission line with a less faulty one. Unfortunately, this condition also limits the possible distance between the communicating parties, Alice and Bob, to a few hundred kilometers. To overcome this problem, we design a QKD protocol which allows Alice and Bob to distinguish system errors from eavesdropping errors. If they are able to identify the origin of their errors, they can detect eavesdropping even when the system error rate exceeds the eavesdropping error rate. To achieve this, the proposed protocol employs an alternative encoding of information in two-dimensional photon states. Errors manifest themselves as quantum bit and as index transmission errors with a distinct correlation between them in case of intercept-resend eavesdropping. As a result, Alice and Bob can tolerate lower eavesdropping and higher system error rates without compromising their privacy.
Abstract A new eavesdropping strategy is proposed for the Quantum Key Distribution (QKD) protocol. This scheme represents a new kind of intercept/resend strategy based on Bell’s theorem. Quantum key distribution (QKD) provides the foremost reliable form of secure key exchange, using only the input-output statistics of the devices to realize information-theoretic security. In this paper, we present an improved QKD protocol that can simultaneously distribute the quantum secret key. We are already using the QKD protocol with simulated results matched completely with the theoretical concepts.
We present and analyze a quantum key distribution protocol based on sending entangled NNN-qubit states instead of single-qubit ones as in the trail-blazing scheme by Bennett and Brassard 1984 (BB84). Since the qubits are sent and acknowledged individually, an eavesdropper is limited to accessing them one by one. In an intercept-resend attack, this fundamental restriction allows one to make the eavesdropper's information on the transmitted key vanish if even one of the qubits is not intercepted. The implied upper bound 1∕(2N)1∕(2N)1∕(2N) for this information is further shown not to be the lowest, as the information can be reduced to less than 30% of that in the BB84 scheme in the case N=2N=2N=2. In general, the protocol is at least as secure as BB84.