Enhancing secret sharing security: A cheating detection approach based on inverse polynomial coefficients

Secret sharing is the process of distributing a secret among n shareholders, in such a way that only a subset of them can recover the secret, while unauthorized subsets, referred to as dishonest shareholders, cannot access the secret. During the secret reconstruction phase, when shareholders present their shares, a dishonest shareholder or shareholders can always obtain the secret exclusively by presenting fake shares, thus leaving the honest shareholders with nothing but a fake secret. Detecting cheating is crucial for achieving a fair secret reconstruction. In this paper, it has been proposed a cheating-detecting secret sharing scheme that utilizes polynomial coefficients for cheat detection in secret reconstruction. It is leveraged the invertibility property of polynomial coefficients in the z_q field to detect cheat and employ relationships that follow a linear equation.