Cryptanalysis of secret-sharing multi-signature scheme without trusted centre

In this paper, a new secret-sharing multi-signature scheme without trusted center is analyzed, and a forged attack is given. By using this attack, any attacker can easily forge a valid secret-sharing multi-signature, so that the scheme is not secure. In order to solve this problem, an improved scheme is given, in which all the signers participating in the signing jointly determine the needed signature parameters and only in the case of the signers with the threshold number working together can an effective secret-sharing multi-signature be generated. It is proved that the improved scheme is more secure and effective in resisting the above-mentioned forged attack.