Research Of Secure Multi-secret Sharing

(t,n)threshold secret sharing is an important part of cryptography research,widely use in key management,digital signatures,group certification and so on.(t,n)threshold secret sharing is to back up secret to n shares,and all the participants have one share,when the number of the shareholder come to the threshold,they cooperation can recover the secret and otherwise they can't get the secret.Based on secret sharing above,(t,n)threshold multi-secret sharing allow t or more than t participants use few shares to share more secrets.But in general secret sharing,when an attacker has no share comes to a group of participants which is more than threshold,he collects other participants shares,can get the secret.In order to solve this problem,we proposed the security multi-secret sharing,and implement in two different schemes.First,this paper analysis existing multi-secret schemes' problems,and propose security multi-secret sharing.Existing schemes' problems mainly in the number of secrets to shared is restrict to threshold and the number of shareholders,public more information,inefficient and when the number of participants is more than threshold,can't against malicious participants.From these,we propose group oriented multi-secret sharing,in the stage of recover secret,participants form a tight coupled group,binding participants' public information.We use polynomial to realize group oriented multi-secret sharing.In this scheme,dealer only distributes once and shareholder only holds one share can share more secrets.Also the scheme don't use any user or share authentication to against malicious participant attack,improve the security level of multi-secret sharing.At last,we based on Chinese remainder theorem to implement another group oriented multi-secret sharing scheme.In this paper,we improve Asmuth-Bloom's secret sharing scheme,participants only hold two shares,when recover secret,they hide their shares,so can achieve security share more secrets.