QSSS-LTE: quantum secret sharing scheme over lattice-based threshold encryption

Abstract This paper proposed a quantum secret sharing scheme over lattice-based threshold encryption: it integrates resplittable threshold public key encryption (RTPKE) and utilizes a lattice-based private key share transmission mechanism to enhance the security of the share distribution process. By leveraging the dynamic key management features of RTPKE, the scheme can flexibly adjust key distribution as required when participants change. During the quantum secret reconstruction process, the decoy particles do not need to be detected by eavesdroppers when transmitted between participants. Instead, this task is performed by a semi-trusted third party (TP), reducing resource consumption and communication overhead. The decoy particles are not chosen from a fixed quantum bases but are instead in completely random quantum bases, making it impossible for an eavesdropper to obtain the correct result through conventional measurements. The probability of the eavesdropper escaping detection after measuring any decoy particle is nearly zero. After each participant performs a unitary operation, they randomly shuffle the sequence of decoy and information particles. When the particles are transmitted back to the TP, the TP uses the sequence information recorded by the participants to restore the original order and extract the information particles, effectively defending against forgery-replay attacks and potential threats from dishonest participants.