A Novel Approach for Verifiable Secret Sharing by using a One Way Hash   Function
  Threshold secret sharing schemes do not prevent any malicious behavior of the dealer or shareholders and so we need verifiable secret sharing, to detect and identify the cheaters, to achieve fair reconstruction of a secret. The problem of verifiable secret sharing is to verify the shares distributed by the dealer. A novel approach for verifiable secret sharing is presented in this paper where both the dealer and shareholders are not assumed to be honest. In this paper, we extend the term verifiable secret sharing to verify the shares, distributed by a dealer as well as shares submitted by shareholders for secret reconstruction, and to verify the reconstructed secret. Our proposed scheme uses a one way hash function and probabilistic homomorphic encryption function to provide verifiability and fair reconstruction of a secret. 
Keyur Parmar, Devesh Jinwala
cs.CR