Anonymous (Hierarchical) Identity-Based Encryption from Broader Assumptions

Dottling and Garg (CRYPTO 2017) introduced a non-black-box approach to identity-based encryption (IBE). This paves the way for the first and still the only anonymous IBE (AIBE) scheme from the computational Diffie-Hellman (CDH) assumption of Brakerski et al. (EUROCRYPT 2018). This paper revisits the blinding technique of Brakerski et al. and introduces a suite of blind primitives, extending chameleon encryption, hash encryption, and one-time signature with encryption. Using them, we propose an AIBE scheme from CDH with improved efficiency compared to Brakerski et al., especially in the decryption time. We also propose the first anonymous hierarchical IBE (AHIBE) scheme from CDH and the first AIBE and AHIBE schemes from the phi-hiding assumption, with similar efficiency as their non-anonymous counterparts.