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arXiv:quant-ph/0703107 · Physical Review Letters

Quantum Key Distribution with Classical Bob

Michel Boyer, Dan Kenigsberg, Tal Mor

Published Oct 5, 2007• 386 citations
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Abstract

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.

DOI
10.1103/physrevlett.99.140501

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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.
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 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.
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.
Secure key distribution among classical parties is impossible both between two parties and in a network. In this paper, we present a quantum key distribution (QKD) protocol to distribute secure key bits among one quantum party and numerous classical parties who have no quantum capacity. We prove that our protocol is completely robust, i.e., any eavesdropping attack should be detected with nonzero probability. Our calculations show that our protocol may be secure against Eve's symmetrically individual attack.
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.