Secure and verifiable vector space secret sharing scheme

This work presents a method to detect cheaters efficiently with a trusted dealer distributing the secret information in the initialization phase and renewing phase by means of the intractability of quadratic residue problem. The vector space secret sharing scheme demands every participant verify the share he receives and those other participants show. When untruthful dealers appear, the scheme can also be extended to find them. Results indicate that this solution is very simple with high security and high information rate. Cheaters can only cheat via guessing with little probability.