Abstract:

A (k,n) quantum threshold secret sharing scheme based on generator matrix segmentation is proposed in this paper. Compared with the previous classical schemes, our scheme has better security and reliability, and it also has the diversity of encoding with the quantum system, which can improve the difficulty of deciphering. A solution for the issue of matrix cycle period and the problem that some numbers without the primitive element can’t construct generation matrix is derived. The core idea of our scheme is to achieve the secret division by applying the primitive element in the finite domain for generation matrix based on the correspondence between the quantum and classical information, where the generation matrix satisfies that any k column vectors are linearly independent. The transmission process involves quantum secure direct communication (QSDC) based on super-dense coding.

Key words: quantum secret sharing, generator matrix, quantum secure direct communication, super-dense coding