Attacks on one designated verifier proxy signature scheme (Q1760716)

Summary: In a designated verifier proxy signature scheme, there are three participants, namely, the original signer, the proxy signer, and the designated verifier. The original signer delegates his or her signing right to the proxy signer, then the proxy signer can generate valid signature on behalf of the original signer. But only the designated verifier can verify the proxy signature. Several designated verifier proxy signature schemes have been proposed. However, most of them were proven secure in the random oracle model, which has received a lot of criticism since the security proofs in the random oracle model are not sound with respect to the standard model. Recently, by employing Water's hashing technique [\textit{Y. Yu} et al., Comput. Math. Appl. 57, No. 8, 1352--1364 (2009; Zbl 1186.94480)] proposed a new construction of designated verifier proxy signature. They claimed that the new construction is the first designated verifier proxy signature, whose security does not rely on the random oracles. But, in this paper, we will show some attacks on Yu et al.'s scheme. So, their scheme is not secure.