Improvement of One Anonymous Identity-Based Encryption

In 2009, Seo et al. proposed an anonymous hierarchical identity-based encryption (IBE). The ciphertext consists of (C1, C2, C3, C4), where C1 is the blinded message, C4 is the blinded identity, both C2 and C3 are used as decrypting helpers. To prove its security, the authors defined five games and introduced a strong simulator who is able to select different Setups for those games. In this paper, we optimize the IBE scheme by removing one decrypting helper and the strong simulator. We show its security under the l-computational Diffie-Hellman assumption with a normal simulator who only requires a unique Setup.