A secure designated confirmer signature scheme

Many previous designated confirmer signature schemes are vulnerable to adaptive attackers. This paper discusses the scheme based on Schnorr, finds the reason for its insecurity and shows how the confirmer forges signatures of the signer. Then, we present a new designated confirmer signature scheme, whose security against adaptive adversaries is proven to depend on reasonable security assumptions. Furthermore, the new designated confirmer signature can be turned into an ordinary signature, with the corresponding conversion algorithm given.