Verifiable Quantum Secret Sharing Scheme Based on LDPC Codes

In this paper, we propose a novel verifiable quantum secret sharing scheme tailored for a specific class of low-density parity-check (LDPC) codes. In the proposed protocol, Alice, the dealer, initially utilizes the generator matrix of the chosen LDPC code to calculate all secret shares and distributes individual shares to all participants in a quantum secure direct communication channel. In the distribution phase, each participant computes a hash value based on their respective share and a randomly generated sequence, which is then published. In the recover phase, each participant performs a unitary operation on these received particles and sends them to the next participant using the decoy-photon technique. Furthermore, the last participant performs Bell measurements on the final quantum states to obtain the original secret. At last, we demonstrate our protocol to be secure against intercept-and-resend attack, entangle-and-measure attack and dishonest participant attack. In addition, we present a comparison of our protocol with other existing schemes.