Abstract: A new digital signature scheme, i.e., the secret sharing RSA digital signature scheme based on the vector space access structure, is proposed, which includes the threshold RSA signature scheme as a particular case. In this scheme, the vector space secret sharing scheme is established in a finite ring, so that N participants share the secret in the RSA signature shceme. This scheme can assure that the group signature can be easily produced by the cooperation of the participants in an authorized subset in the vector space access structure Γ and it is impossible for them to generate a group signature by the cooperation of the participants in an unauthorized subset. Compared with the existing schemes, this scheme does not require inversion operations, and thus can find wide applications.

Key words: vector space secret sharing scheme, RSA, digital signature, group signature