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Recently, Chung et al. (2009) proposed a novel and valuable threshold authenticated encryption scheme. Unfortunately, it has a potential weakness: if the secret message involves criminal evidence or illegal content, the designated receiver cannot authenticate the secret message in the later dispute. The authors of this paper aim at enhancing Chung et al.'s scheme by adding the convertibility capability so that the designated receiver can demonstrate that the signature with respect to the message has been signed. And then, the enforcement agency can trace the source of secret messages. In addition to inheriting the advantages of Chung et al.'s scheme, the improved scheme achieves the goal that the designated recipient can convert an authenticated signature into an ordinary signature.
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