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Proxy re-encryption (PRE) can be classified as single-hop PRE and multi-use PRE according to the times which the ciphertext is transformed. Finding a unidirectional, multi-use, and chosen ciphertext attack (CCA) secure PRE is presented as an open problem by Canetti et al. Wang claimed to resolve this problem by proposing the first multi-use CCA-secure unidirectional PRE scheme. But Zhang et al. have shown their proposal is not CCA-secure by giving concrete attacks. In this paper, we propose an improvement for Wang-Multi-Use-PRE to resist Zhang’s attack. But we also found that different with single-hop PRE, multi-use PRE without randomize encrypt key in its re-encryption algorithm could be vulnerable to attack. According to this principle we find a new type attack to multi-use CCA-secure PRE named proxy bypass attack. Then we give concrete attacks on Wang-Multi-Use-PRE scheme. This attack is also effective for other multi-use scheme.