Abstract: A vector space secret sharingmultisignature scheme without a trusted share distribution center is proposed. In this scheme, there is no trusted share distribution center, and each participant acts as a trusted share distribution center to generate his secret key and distribute the corresponding secret shares to other participants. This scheme combines the mechanism of the vector space secret sharing scheme with that of multisignature. An authorized subset of participants can easily produce their group signature by pooling their secret shares, but an unauthorized subset of participants cannot produce their group signature by doing so. This scheme uses random numbers to protect the secret values generated by the relative secret sharing algorithm and distributed to the participants. Therefore a group signature of an authorized subset of participants cannot be impersonated by any other set of participants, and forgers can be found. Meanwhile any participant can detect wrong secret shares. The validity of the partial signature and the group signature is verified by means of verification equations.

Key words: secret sharing scheme, vector space secret sharing scheme, multisignature