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arXiv:quant-ph/0502045 · Physical Review A

Quantum secret sharing between multiparty and multiparty without entanglement

Fengli Yan, Ting Gao

Published Jul 7, 2005• 232 citations
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Abstract

We propose a quantum secret sharing protocol between multiparty ($m$ members in group 1) and multiparty ($n$ members in group 2) using a sequence of single photons. These single photons are used directly to encode classical information in a quantum secret sharing process. In this protocol, all members in group 1 directly encode their respective keys on the states of single photons via unitary operations; then, the last one (the $m\mathrm{th}$ member of group 1) sends $1∕n$ of the resulting qubits to each of group 2. Thus the secret message shared by all members of group 1 is shared by all members of group 2 in such a way that no subset of each group is efficient to read the secret message, but the entire set (not only group 1 but also group 2) is. We also show that it is unconditionally secure. This protocol is feasible with present-day techniques.

DOI
10.1103/physreva.72.012304

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We propose a quantum secret sharing protocol between multiparty (mmm members in group 1) and multiparty (nnn members in group 2) using a sequence of single photons. These single photons are used directly to encode classical information in a quantum secret sharing process. In this protocol, all members in group 1 directly encode their respective keys on the states of single photons via unitary operations; then, the last one (the mthm\mathrm{th}mth member of group 1) sends 1∕n1∕n1∕n of the resulting qubits to each of group 2. Thus the secret message shared by all members of group 1 is shared by all members of group 2 in such a way that no subset of each group is efficient to read the secret message, but the entire set (not only group 1 but also group 2) is. We also show that it is unconditionally secure. This protocol is feasible with present-day techniques.
We propose a scheme of quantum secret sharing between Alice's group and Bob's group with single photons and unitary transformations. In the protocol, one member in Alice's group prepares a sequence of single photons in one of four different states, while other members directly encode their information on the sequence of single photons via unitary operations; after that, the last member sends the sequence of single photons to Bob's group. Then Bob's, except for the last one, do work similarly. Finally the last member in Bob's group measures the qubits. If the security of the quantum channel is guaranteed by some tests, then the qubit states sent by the last member of Alice's group can be used as key bits for secret sharing. It is shown that this scheme is safe.
A quantum secret sharing protocol between multiparty and multiparty based on squeezed state is proposed. In the protocol, the members in the Alice group code the secret information on the quantum states prepared by the members in the Bob group. The groups Alice and Bob share a classical secret. The secret could be reconstructed if and only if all the members of the group Alice or the group Bob collaborate, any part of each group can't reconstruct the secret. Compared with the protocols based on single photon, this protocol is more efficient and realized more simply. The analysis shows that the protocol is secure.
A quantum secret sharing protocol between multiparty and multiparty based on squeezed state is proposed.In the protocol,the members in the Alice group code the secret information on the quantum states prepared by the members in the Bob group.The groups Alice and Bob share a classical secret.The secret could be reconstructed if and only if all the members of the group Alice or the group Bob collaborate,any part of each group can't reconstruct the secret.Compared with the protocols based on single photon,this protocol is more efficient and realized more simply.The analysis shows that the protocol is secure.
Recently, Yan and Gao proposed a quantum secret sharing protocol between multiparty (mmm members in group 1) and multiparty (nnn members in group 2) using a sequence of single photons (Phys. Rev. A \textbf{72}, 012304 (2005)). We find that it is secure if the quantum signal transmitted is only a single photon but insecure with a multi-photon signal as some agents can get the information about the others' message if they attack the communication with a Trojan horse. However, security against this attack can be attained with a simple modification.
Most semi-quantum secret sharing protocols are suitable for the application with three participants. Based on the n-level states, a multiparty semi-quantum secret sharing protocol is proposed. Compared with similar protocols, it has the merits as follows. (1) The dealer only needs to prepare the single photon sequence without using any product state or entangle state. (2) To share a secret, the classical parties need not have the ability of measurement. They only need to reorder the photon sequence and send it to the receiver. (3) The dealer knows nothing about any agent’s secret shadow. Therefore, it is infeasible for the dealer to impersonate the classical participant to pool the secret shadow during the secret recovering phase. (4) Theoretically, the qubit efficiency of the proposed protocol is asymptotically 100%. The protocol is secure against famous attacks such as intercept-resend attack, measurement-resend attack and entangle-measure attack.