Semi-quantum key distribution (SQKD) protocols allow for the establishment of a secret key between two users Alice and Bob, when one of the two users (typically Bob) is limited or “classical” in nature. Recently it was shown that protocols exists when both parties are limited/classical in nature if they utilize the services of a quantum server. These protocols are called mediated SQKD protocols. This server, however, is untrusted and, in fact, adversarial. In this paper, we reconsider a mediated SQKD protocol and derive a new proof of unconditional security for it. In particular, we derive a new lower bound on its key rate in the asymptotic scenario. Furthermore, we show this new lower bound is an improvement over prior work, thus showing that the protocol in question can tolerate higher rates of error than previously thought.Semi-quantum key distribution (SQKD) protocols allow for the establishment of a secret key between two users Alice and Bob, when one of the two users (typically Bob) is limited or “classical” in nature. Recently it was shown that protocols exists when both parties are limited/classical in nature if they utilize the services of a quantum server. These protocols are called mediated SQKD protocols. This server, however, is untrusted and, in fact, adversarial. In this paper, we reconsider a mediated SQKD protocol and derive a new proof of unconditional security for it. In particular, we derive a new lower bound on its key rate in the asymptotic scenario. Furthermore, we show this new lower bound is an improvement over prior work, thus showing that the protocol in question can tolerate higher rates of error than previously thought.

Quantum Information and ComputationJul 1, 20167 citations

Scalable Mediated Semi-quantum Key Distribution

Chong‐Qiang Ye, Jian Li, Xiu‐Bo Chen +1 more

Mediated semi-quantum key distribution (M-SQKD) permits two limited "semi-quantum" or "classical" users to establish a secret key with the help of a third party (TP), in which TP has fully quantum power and may be untrusted. Several protocols have been studied recently for two-party scenarios, but no one has considered M-SQKD for multi-party scenarios. In this paper, we design a circular M-SQKD protocol based on Bell states, which offers an approach to realizing multiple "classical" users' key distribution. Then, we prove the protocol is unconditional security in the asymptotic scenario. The protocol's key rate and noise tolerance can be derived by utilizing the parameters observed in the channel. The results show that our protocol may hold similar security to a fully quantum one. We also compare the proposed protocol with similar protocols in terms of noise tolerance, qubit efficiency, communication cost, and scalability. Finally, the security proof method of this paper may contribute to studying the security of other circular semi-quantum cryptography protocols.Mediated semi-quantum key distribution (M-SQKD) permits two limited "semi-quantum" or "classical" users to establish a secret key with the help of a third party (TP), in which TP has fully quantum power and may be untrusted. Several protocols have been studied recently for two-party scenarios, but no one has considered M-SQKD for multi-party scenarios. In this paper, we design a circular M-SQKD protocol based on Bell states, which offers an approach to realizing multiple "classical" users' key distribution. Then, we prove the protocol is unconditional security in the asymptotic scenario. The protocol's key rate and noise tolerance can be derived by utilizing the parameters observed in the channel. The results show that our protocol may hold similar security to a fully quantum one. We also compare the proposed protocol with similar protocols in terms of noise tolerance, qubit efficiency, communication cost, and scalability. Finally, the security proof method of this paper may contribute to studying the security of other circular semi-quantum cryptography protocols.

arXiv:2205.06528May 13, 20220 citations

Multi-Mediated Semi-Quantum Key Distribution

Walter O. Krawec

A semi-quantum key distribution (SQKD) protocol allows two users A and B to establish a shared secret key that is secure against an all-powerful adversary E even when one of the users (e.g., B) is semi-quantum or classical in nature while the other is fully-quantum. A mediated SQKD protocol allows two semi-quantum users to establish a key with the help of an adversarial quantum server. We introduce the concept of a multi-mediated SQKD protocol where two (or more) adversarial quantum servers are used. We construct a new protocol in this model and show how it can withstand high levels of quantum noise, though at a cost to efficiency. We perform an information theoretic security analysis and, along the way, prove a general security result applicable to arbitrary MM-SQKD protocols. Finally, a comparison is made to previous (S)QKD protocols.A semi-quantum key distribution (SQKD) protocol allows two users A and B to establish a shared secret key that is secure against an all-powerful adversary E even when one of the users (e.g., B) is semi-quantum or classical in nature while the other is fully-quantum. A mediated SQKD protocol allows two semi-quantum users to establish a key with the help of an adversarial quantum server. We introduce the concept of a multi-mediated SQKD protocol where two (or more) adversarial quantum servers are used. We construct a new protocol in this model and show how it can withstand high levels of quantum noise, though at a cost to efficiency. We perform an information theoretic security analysis and, along the way, prove a general security result applicable to arbitrary MM-SQKD protocols. Finally, a comparison is made to previous (S)QKD protocols.

IEEE Globecom Workshops (GC Wkshps)Dec 1, 201910 citations

Mediated semi-quantum key distribution with improved efficiency

Julia Guskind, Walter O. Krawec

Abstract Mediated semi-quantum key distribution involves the use of two end-users who have very restricted, almost classical, capabilities, who wish to establish a shared secret key using the help of a fully-quantum server who may be adversarial. In this paper, we introduce a new mediated semi-quantum key distribution protocol, extending prior work, which has asymptotically perfect efficiency. Though this comes at the cost of decreased noise tolerance, our protocol is backwards compatible with prior work, so users may easily switch to the old (normally less efficient) protocol if the noise level is high enough to justify it. To prove security, we show an interesting reduction from the mediated semi-quantum scenario to a fully-quantum entanglement based protocol which may be useful when proving the security of other multi-user quantum key distribution protocols.Abstract Mediated semi-quantum key distribution involves the use of two end-users who have very restricted, almost classical, capabilities, who wish to establish a shared secret key using the help of a fully-quantum server who may be adversarial. In this paper, we introduce a new mediated semi-quantum key distribution protocol, extending prior work, which has asymptotically perfect efficiency. Though this comes at the cost of decreased noise tolerance, our protocol is backwards compatible with prior work, so users may easily switch to the old (normally less efficient) protocol if the noise level is high enough to justify it. To prove security, we show an interesting reduction from the mediated semi-quantum scenario to a fully-quantum entanglement based protocol which may be useful when proving the security of other multi-user quantum key distribution protocols.

arXiv:2111.01627Quantum Science and TechnologyMay 27, 202233 citations

Mediated semiquantum key distribution

Walter O. Krawec

In this work, we design a quantum key distribution protocol, allowing two limited semiquantum or ``classical'' users to establish a shared secret key with the help of a fully quantum server. A semiquantum user can prepare and measure qubits only in the computational basis and so must rely on this quantum server to produce qubits in alternative bases and also to perform alternative measurements. However, we assume that the server is untrusted and we prove the unconditional security of our protocol even in the worst case: when this quantum server is an all-powerful adversary. We also compute a lower bound of the key rate of our protocol, in the asymptotic scenario, as a function of the observed error rate in the channel, allowing us to compute the maximally tolerated error of our protocol. Our results show that a semiquantum protocol may hold similar security to a fully quantum one.In this work, we design a quantum key distribution protocol, allowing two limited semiquantum or ``classical'' users to establish a shared secret key with the help of a fully quantum server. A semiquantum user can prepare and measure qubits only in the computational basis and so must rely on this quantum server to produce qubits in alternative bases and also to perform alternative measurements. However, we assume that the server is untrusted and we prove the unconditional security of our protocol even in the worst case: when this quantum server is an all-powerful adversary. We also compute a lower bound of the key rate of our protocol, in the asymptotic scenario, as a function of the observed error rate in the channel, allowing us to compute the maximally tolerated error of our protocol. Our results show that a semiquantum protocol may hold similar security to a fully quantum one.

arXiv:1411.6024Physical Review AMar 25, 2015178 citations

A single-state semi-quantum key distribution protocol and its security proof

Wei Zhang, Daowen Qiu

Semi-quantum key distribution (SQKD) can share secret keys by using less quantum resource than its fully quantum counterparts, and this likely makes SQKD become more practical and realizable. In this paper, we present a new SQKD protocol by introducing the idea of B92 into semi-quantum key distribution and prove its unconditional security. In this protocol, the sender Alice just sends one qubit to the classical Bob and Bob just prepares one state in the preparation process. Indeed the classical user's measurement is not necessary either. This protocol can reduce some quantum communication and make it easier to be implemented. It can be seen as the semi-quantum version of B92 protocol, comparing to the protocol BKM2007 as the semi-quantum version of BB84 in fully quantum cryptography. We verify it has higher key rate and therefore is more efficient. Specifically we prove it is unconditionally secure by computing a lower bound of the key rate in the asymptotic scenario from information theory aspect. Then we can find a threshold value of errors such that for all error rates less than this value, the secure key can be established between the legitimate users definitely. We make an illustration of how to compute the threshold value in case of the reverse channel is a depolarizing one with parameter $p$ . Though the threshold value is a little smaller than those of some existed SQKD protocols, it can be comparable to the B92 protocol in fully quantum cryptography.Semi-quantum key distribution (SQKD) can share secret keys by using less quantum resource than its fully quantum counterparts, and this likely makes SQKD become more practical and realizable. In this paper, we present a new SQKD protocol by introducing the idea of B92 into semi-quantum key distribution and prove its unconditional security. In this protocol, the sender Alice just sends one qubit to the classical Bob and Bob just prepares one state in the preparation process. Indeed the classical user's measurement is not necessary either. This protocol can reduce some quantum communication and make it easier to be implemented. It can be seen as the semi-quantum version of B92 protocol, comparing to the protocol BKM2007 as the semi-quantum version of BB84 in fully quantum cryptography. We verify it has higher key rate and therefore is more efficient. Specifically we prove it is unconditionally secure by computing a lower bound of the key rate in the asymptotic scenario from information theory aspect. Then we can find a threshold value of errors such that for all error rates less than this value, the secure key can be established between the legitimate users definitely. We make an illustration of how to compute the threshold value in case of the reverse channel is a depolarizing one with parameter $p$. Though the threshold value is a little smaller than those of some existed SQKD protocols, it can be comparable to the B92 protocol in fully quantum cryptography.

arXiv:1612.03087Dec 3, 201612 citations

p

. Though the threshold value is a little smaller than those of some existed SQKD protocols, it can be comparable to the B92 protocol in fully quantum cryptography.