Cryptanalysis and Improvement of a HIBE and HIBS without Random Oracles

Recently, Au et al. proposed a practical HIBE scheme and a hierarchical identity-based signature (HIBS) scheme. They claimed that both their schemes were proven to be secure without relying on random oracle. However, in this paper, we show that their HIBE scheme is not chosen plaintext attack (CPA) secure. We also point out that their HIBS scheme does not possess the unforgeability property, and there is one mistake in their security proof. In order to overcome these drawbacks, we propose an improved method.