TITLE:
Verifiable Secret Sharing Scheme Based on Certain Projective Transformation
AUTHORS:
Bin Li
KEYWORDS:
Threshold Secret Sharing, Projective Transformation, Nonzero k–Submatrix, Residual Vector of Equations
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.11 No.2,
June
24,
2021
ABSTRACT: The main purpose of verifiable secret sharing scheme is to solve the honesty problem of participants. In this paper, the concept of nonzero k-submatrix and theresidual vector of system of hyperplane intersecting line equations is proposed. Based on certain projective transformations in projective space, a verifiable (t, n)-threshold secret sharing scheme is designed by using the structure of solutions of linear equations and the difficulty of solving discrete logarithm problems. The results show that this scheme can verify the correctness of the subkey provided by each participant before the reconstruction of the master key, and can effectively identify the fraudster. The fraudster can only cheat by guessing and the probability of success is only 1/p. The design of the scheme is exquisite and the calculation complexity is small. Each participant only needs to hold a subkey, which is convenient for management and use. The analysis shows that the scheme in this paper meets the security requirements and rules of secret sharing, and it is a computationally secure and effective scheme with good practical value.