Abstract
In this paper, a new construct of hierarchical identity-based signature(HIBS) scheme is proposed at first. It has many advantages over those available, such as fully secure without using random oracles, efficient signing algorithm. Additionally, it is provably secure under the computational Diffie-Hellman(CDH) assumption. This assumption is more natural than many of the hardness assumptions recently introduced to HIBS in the standard model. However, the length of its private key and signature increases as the hierarchy depth expands. Then a modified scheme is presented. The signature of modified scheme consists of three group elements and the private keys size shrinks as the identity depth increases. Under the h-CDH assumption, it is provable security in full security model without using random oracles.
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