Presently, many identity-based proxy signature (IBPS) schemes have been proposed, but most of them require high computational costs and the proposed security model for IBPS is not enough complete. To overcome this weakness, Gu et al. recently proposed a framework and a detailed security model for IBPS. They also proposed an efficient IBPS scheme and proved the unforgeability of their scheme in the standard model. However, in this letter, we demonstrate that Gu et al.'s scheme fails to satisfy the property of unforgeability because it can not resist the following attacks: after getting a private key, an adversary behaving as a malicious signer can forge a private key on any identity without the help of the private key generator (PKG); after getting a delegation, an adversary behaving as a malicious proxy signer can forge a proxy signing key on any delegation without the agreement of the original signer; after getting a signature, an adversary behaving as a malicious user can forge a signature on any identity without the private key or forge a proxy signature on any warrant without the proxy signing key.

Recently, Au et al. proposed a practical hierarchical identity-based encryption (HIBE) scheme and a hierarchical identity-based signature (HIBS) scheme. In this paper, we point out that there exists security weakness both for their HIBE and HIBS scheme. Furthermore, based on q-ABDHE, we present a new HIBE scheme which is proved secure in the standard model and it is also efficient. Compared with all previous HIBE schemes, ciphertext size as well as decryption cost are independent of the hierarchy depth. Ciphertexts in our HIBE scheme are always just four group elements and decryption requires only two bilinear map computations.