For the privacy protection, Nguyen first proposed an asymmetric concurrent signature scheme with signers’ anonymity in 2005. Except correctness, unforgeability, and fairness, Nguyen’s scheme satisfies two
new properties: Anonymity and unlinkability. To satisfy the anonymity property, Nguyen’s scheme has identification flaw that signers cannot identify each other during the exchange protocol. So an attacker makes use
of this flaw to trick signers to exhaust signers’ computation resources. However, the concurrent signature schemes with signers’ ambiguity do not have this identification flaw. So the identification property is defined
for the concurrent signature scheme with signers’ anonymity. Then our asymmetric concurrent scheme is proposed to provide both anonymity and identification. Our improved scheme satisfies identification, anonymity,
and unlinkability at the same time. With identification, anonymity, and unlinkability, the signers’privacy is protected well without flaws.