A new efficient group signature scheme based on linear codes

An efficient group signature scheme is presented. The security of this scheme is based on the difficulty of the decoding problem of linear codes, and the security of the ElGamal signature scheme. For a given [n, k, d] code and the corresponding group signature scheme, the lengths of the signatures and the group public key are n+5 and n²+5 respectively. With regard to the computational overhead of this scheme, the signing process is basically the same as the ElGamal scheme but with O(n) arithmetic operations; the procedure of opening a signature is very efficient and needs only O(d²) arithmetic operations. This scheme allows new members to join a group without modifying the group public key. By distributing new membership certificates to some members, a member can be deleted from a group.