Fair secret sharing scheme using asymmetric bivariate polynomial

Abstract

In Shamir's (t,n) secret sharing scheme,any m (m≥t) participants can reconstruct the secret,and any less than t participants can't get any information about the secret.However,if there are more than t participants in the secret reconstruction phase,Shamir's secret reconstruction phase can not prevent external attackers from knowing the secret,while internal attackers can release a fake share to deceive honest participants during the secret reconstruction process.A rational threshold secret sharing scheme using asymmetric bivariate polynomial with unknown rounds is proposed.Then it shows its fairness and security against non-cooperative attack with synchronization,non-cooperative attack with a synchronization,cooperative attack with synchronization and cooperative attack with a synchronization.

Keywords

• threshold secret sharing;asymmetric bivariate polynomial;fairness;attack model