A protocol of quantum secret sharing between multiparty and multiparty with four states was presented. It was shown that this protocol can nullify the Trojan horse attack with a multi-photon signal, the fake-signal attack with Einstein-PodolskyRosen pairs, the attack with single photons, and the attack with invisible photons. In addition, the upper bounds of the average success probabilities were given for dishonest agent eavesdropping encryption using the fake-signal attack with any two-particle entangled states.
quantum secret sharing, security, Einstein-Podolsky-Rosen pairsRecently we proposed a quantum secret sharing (QSS) protocol between multiparty (m members in group 1) and multiparty (n members in group 2) using a sequence of single photons [1] . In our protocol, all members in group 1 directly encode their respective keys on the states of single photons via unitary operations, and then the last one (the mth member of group 1) sends 1/n of the resulting qubits to each of group 2. After each member of group 2 measures the photons, the two groups share the secret messages. Unfortunately, Li et al. [2] pointed out that if the mth party of group 1 is dishonest, she can obtain secret by substituting a sequence of single photons or a sequence of Einstein-Podolsky-Rosen (EPR) pairs generated by herself for the original photons without the detection of the other parties. In this paper, we present a protocol of quantum secret sharing between multiparty and multiparty with four states, which is an improvement over the one in ref. [1], and show that this improved protocol can prevent the dishonest member from this kind of cheating. Moreover, the present protocol is also secure against the Trojan horse attack with a multi-photon signal [3] , the fake-signal attack with EPR pairs [4] and the attack with invisible photons [5] . We also give the upper bounds of the average success probabilities for dishonest agent eavesdropping encryption using the fake-signal attack with any two-particle entangled states.