The security of a strong proxy signature scheme with proxy signer privacy protection

In 1996, Mambo et al. first introduced the concept of a proxy signature scheme, and discussed the delegation of the signing capability to a proxy signer. In 2001, Lee et al. constructed a strong non-designated proxy signature scheme. In 2002, Shum and Wei presented an enhancement to the Lee et al.'s scheme to hide the identity of the proxy signer. No one can determine the identity of the proxy signer only from the proxy signature. Moreover, a trusted authority can reveal the proxy signer's identity if needed. However, this paper will show that the Shum-Wei scheme cannot keep the property of the strong unforgeability. That is, not only the proxy signer but also the original signer can generate valid proxy signatures.