Polynomial differential-based strong (n, t, n)-verifiable secret sharing

Basic secret sharing schemes assume that the dealer who divides the secret and distributes shares to participants is a mutually trusted party. The basic idea of free dealer secret sharing (SS) is that each participants acts as a dealer to choose the secret (sub secrets) and generate shares for other participants and then the master secret will be combine of these subs secrets. The t-consistency of shares is a set of n shares that if any subset containing t shares defines the same secret. The author´s scheme based on polynomial differential to fix the problems that had been observed Harn and Lin scheme about the security requirements for t-consistency of shares in Pedersen´s (n, t, n) - SS, and consider the timeliness in Harn and Lin by using the same Pedersen´s (n, t, n) - SS scheme. The author will use polynomial of degree (2t - 1) to share the sub secrets, and the polynomial differential is used for verification purpose.