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International Symposium on Information Theory and its Applications

Quantum key distribution using Mean King problem with modified measurement schemes

M. Yoshida, Takayuki Miyadera, Hideki Imai

Published Oct 1, 2012• 3 citations
OpenAlex

Abstract

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.

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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.
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.
We investigate the security against the intercept/resend and translucent attacks on the quantum key distribution protocol based on the pre- and post-selection effect. In 2001, Bub proposed the quantum cryptography scheme, which was an application of the so-called mean king’s problem. We evaluate a probability that legitimate users cannot detect eavesdropper’s malicious acts for Bub’s protocol. We also estimate a probability that the eavesdropper guesses right at the random secret key one of the legitimate users tries to share with the other one. From rigorous mathematical and numerical analyses, we conclude that Bub’s protocol is weaker than the Bennett–Brassard protocol of 1984 (BB84) against both the intercept/resend and translucent attacks. Because Bub’s protocol uses a two-way quantum channel, the analyses of its security are tough to accomplish. We refer to their technical points accurately in the current paper. For example, we impose some constraints upon the eavesdropper’s strategies in order to let their degrees of freedom be small.
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.
Cryptanalysis is an important branch in the study of cryptography, including both the classical cryptography and the quantum one. In this paper we analyze the security of two three-party quantum key distribution protocols (QKDPs) proposed recently, and point out that they are susceptible to a simple and effective attack, i.e., the dense-coding attack. It is shown that the eavesdropper Eve can totally obtain the session key by sending entangled qubits as the fake signal to Alice and performing collective measurements after Alice's encoding. The attack process is just like a dense-coding communication between Eve and Alice, where a special measurement basis is employed. Furthermore, this attack does not introduce any errors to the transmitted information and consequently will not be discovered by Alice and Bob. The attack strategy is described in detail and a proof for its correctness is given. Finally, the root cause of this insecurity and a possible way to improve these protocols are discussed.