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arXiv:0812.4835 · Physical Review A

Semiquantum key distribution

Michel Boyer, Ran Gelles, Dan Kenigsberg, Tal Mor

Published Mar 30, 2009• 298 citations
arXivHTMLPDF

Abstract

Secure key distribution between two remote parties is impossible when both are classical, unless some unproven (and arguably unrealistic) computation-complexity assumptions are made, such as the difficulty of factorizing large numbers. On the other hand, a secure key distribution is possible when both parties are quantum. What is possible when only one party (Alice) is quantum, yet the other (Bob) has only classical capabilities? Recently, a semiquantum key distribution protocol was presented [M. Boyer, D. Kenigsberg, and T. Mor, Phys. Rev. Lett. 99, 140501 (2007)], in which one of the parties (Bob) is classical, and yet, the protocol is proven to be completely robust against an eavesdropping attempt. Here we extend that result much further. We present two protocols with this constraint and prove their complete robustness against attacks: we prove that any attempt of an adversary to obtain information (and even a tiny amount of information) necessarily induces some errors that the legitimate parties could notice. One protocol presented here is identical to the one referred to above; however, its robustness is proven here in a much more general scenario. The other protocol is very different as it is based on randomization.

DOI
10.1103/physreva.79.032341

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Secure key distribution between two remote parties is impossible when both are classical, unless some unproven (and arguably unrealistic) computation-complexity assumptions are made, such as the difficulty of factorizing large numbers. On the other hand, a secure key distribution is possible when both parties are quantum. What is possible when only one party (Alice) is quantum, yet the other (Bob) has only classical capabilities? Recently, a semiquantum key distribution protocol was presented [M. Boyer, D. Kenigsberg, and T. Mor, Phys. Rev. Lett. 99, 140501 (2007)], in which one of the parties (Bob) is classical, and yet, the protocol is proven to be completely robust against an eavesdropping attempt. Here we extend that result much further. We present two protocols with this constraint and prove their complete robustness against attacks: we prove that any attempt of an adversary to obtain information (and even a tiny amount of information) necessarily induces some errors that the legitimate parties could notice. One protocol presented here is identical to the one referred to above; however, its robustness is proven here in a much more general scenario. The other protocol is very different as it is based on randomization.
Secure key distribution among two remote parties is impossible when both are classical, unless some unproven (and arguably unrealistic) computation-complexity assumptions are made, such as the difficulty of factorizing large numbers. On the other hand, a secure key distribution is possible when both parties are quantum. What is possible when only one party (Alice) is quantum, yet the other (Bob) has only classical capabilities? We present two protocols with this constraint, and prove their robustness against attacks: we prove that any attempt of an adversary to obtain information (and even a tiny amount of information) necessarily induces some errors that the legitimate users could notice.
Secure key distribution among two remote parties is impossible when both are classical, unless some unproven computation-complexity assumptions are made, such as the difficulty of factorizing large numbers. On the other hand, a secure key distribution is possible when both parties are quantum. What is possible when only one party (Alice) is quantum, yet the other (Bob) has only classical capabilities? We present a protocol with this constraint and prove its robustness against attacks: we prove that any attempt of an adversary to obtain information necessarily induces some errors that the legitimate users could notice.
For several decades it was believed that information-secure key distribution requires both the sender and receiver to have the ability to generate and/or manipulate quantum states. Earlier, we showed that quantum key distribution in which one party is classical is possible [Boyer, Kenigsberg, and Mor, Phys. Rev. Lett. 99, 140501 (2007)]. A surprising and very nice extension of that result was suggested by Zou, Qiu, Li, Wu, and Li [Phys. Rev. A 79, 052312 (2009)]. Their paper suggests that it is sufficient for the originator of the states (the person holding the quantum technology) to generate just one state. The resulting semiquantum key distribution, which we call here ``quantum key distribution with classical Alice'' is indeed completely robust against eavesdropping. However, their proof (that no eavesdropper can get information without being possibly detected) is faulty. We provide here a fully detailed and direct proof of their very important result.
Boyer, Kenigsberg, and Mor [Phys.Rev.Lett.99, 140501(2007)] proposed a novel idea of semi-quantum key distribution where a key can be securely distributed between Alice who can perform any quantum operation and Bob who is classical. Extending the idea of “semiquantum” to other tasks of quantum information processing is of interest and worth considering. In this article, we consider the issue of semi-quantum secret sharing where a quantum participant Alice can share a secret key with two classical participants Bobs. After analyzing the existing protocol, we propose a new protocol of semi-quantum secret sharing. Our protocol is more realistic, since it utilizes product states instead of entangled states. We prove that any attempt of an adversary to obtain information necessarily induces some errors that the legitimate users could notice. 1
Unconditionally secure key distribution is impossible using classical communication only. However, by providing Alice and Bob with quantum capable hardware the task becomes possible. How quantum does a protocol need to be, though, in order to gain this advantage? In 2007, Boyer et al., proposed "semi-quantum key distribution" where only Alice need be quantum while Bob need only limited classical" capabilities. Several protocols were proposed and proven secure in the perfect qubit scenario" but not necessarily against realistic attacks (with one exception being recently published in (PRA 96 062335)). In this paper, we devise a new SQKD protocol and analyze its security against certain practical attacks.
The quantum key distribution protocol with classical Bob, well known as semiquantum key distribution, has been proposed a few years back (Boyer et al., PRL 2007, PRA 2009). In this protocol Alice has the same capability as in the traditional BB84 protocol, but Bob is limited by the constraint that he can measure or prepare qubits only in {∣0>,∣1>}\{|0>, |1>\}{∣0>,∣1>} basis and reflect any other qubit (or in other words, let it go undisturbed). In this scheme the qubits travel from Alice to Bob and then again from Bob to Alice. We study an eavesdropping strategy on this scheme that listens to the channel in both the directions. With the same level of disturbance induced in the channel, Eve can be extract more information using our two-way strategy than what can be obtained by the direct application of one-way eavesdropping in case of BB84 protocol. Towards resisting this eavesdropping strategy, we modify the semiquantum scheme by incorporating a Hadamard gate at Bob's end.