Hierarchical identity-based signature （HIBS） has wide applications in the large network. However,the existing works cannot solve the trade-off between the security and efficiency. The main challenge at present is to construct a high efficient and strong secure HIBS with a low computation cost. In this paper,a new construction of HIBS scheme is proposed. The new scheme achieves the adaptive security which is a strong security in the identity-based cryptography. But our scheme has short public parameters and the private keys size shrinks as the hierarchy depth increases. The signature size is a constant and the cost of verification only requires four bilinear pairings,which are independent of hierarchy depth. Furthermore,under the q-strong computational diffie-Hellman problem （q-SDH） assumption,the scheme is provably secure against existential forgery for adaptive chosen message and identity attack in the standard model.
In this paper, we examine the security of reduced AES-192 and AES-256 against related-key rectangle attacks by exploiting the weakness in the AES key schedule. We find the following two new attacks： 9-round reduced AES-192 with 4 related keys, and 10-round reduced AES-256 with 4 related keys. Our results show that related-key rectangle attack with 4 related keys on 9-round reduced AES-192 requires a data complexity of about 2^101 chosen plaintexts and a time complexity of about 2^174.8 encryptions, and moreover, related-key rectangle attack with 4 related keys on 10-round reduced AES-256 requires a data complexity of about 2^97.5 chosen plaintexts and a time complexity of about 2^254 encryptions. These attacks are the first known attacks on 9-round reduced AES-192 and 10-round reduced AES-256 with only 4 related keys. Furthermore, we give an improvement of the 10-round reduced AES-192 attack presented at FSE2007, which reduces both the data complexity and the time complexity.
