The Shortest Non-Threshold Group Signature Scheme

Digital signature is a hot research topic in recent years. Group digital signature isone important form of digital signature. Due to the existence of threshold secret shar-ing scheme, threshold group digital signatures can be constructed efficiently. How-ever, in real life, most of the group digital signature maybe not be threshold signature.Hence,it is very significant to construct group signature scheme for any non-thresholdaccess structure. Linear secret sharing scheme is a main tool to construct group digitalsignature, so the efficiency of linear secret sharing scheme is the key to in?uence theefficiency of group digital signature. In this thesis,to give access structure, we studyhow to construct the shortest group signature scheme.1. For any given access structure, based on the optimal linear secret sharingscheme from linear code, we construct the shortest non-threshold group signaturescheme, then analysis and prove its security.2. In our protocols, there exist two verification algorithms. One is partial ver-ification in which we can verify which participants are dishonest, the other is totalverification in which we can verify which groups are dishonest.