Two polynomials based (t, n) threshold secret sharing scheme with cheating detection

Abstract

A two-polynomial based threshold secret sharing (SS) scheme is proposed by Liu et al., where two functions for detection of share cheating are used. It is found that the scheme is weak as the equations formed by at most (t – 1) dishonest participants in term of unknowns are not equivalent to the cheating detection function, and if one polynomial is kept fixed and other with two cheating detection equations are taken, a set of equations with unknowns exist, and are found to be easily solvable. In this paper, we also propose a two-polynomial based (t, n) threshold SS scheme; however, the polynomials are taken in such a way that they have an arbitrary common coefficient and as a result, both the polynomials are to be modified simultaneously for cheating of shares and incorporates higher cheating detection capability. Some analytical proofs and comparison with other schemes in support of our claims are provided.