Almost-tight identity based encryption against selective opening attack

The paper presents an identity based encryption (IBE) under selective opening attacks (SOA) whose security is almost-tightly related to a set of computational assumptions in composite-order bilinear groups. Our result is a combination of Bellare, Waters and Yilek's method [TCC, 2011] for constructing (not tightly) SOA secure IBE and Hofheinz, Koch and Striecks' technique [PKC, 2015] on building almost-tightly secure IBE in the multi-ciphertext setting. In the paper, we first tune Bellare et al.'s generic construction for SOA secure IBE to show that a one-bit IBE achieving ciphertext indistinguishability under chosen plaintext attack in the multi-ciphertext setting (with one-sided public openability) tightly implies a multi-bit IBE secure under the selective opening attack. Next, we almost tightly reduce such a one-bit IBE to static assumptions in the compositeorder bilinear groups employing the technique of Hofheinz et al. This yields the first SOA secure IBE with almost-tight reduction.