Almost-Tight Identity Based Encryption Against Selective Opening Attack

The paper presented an identity based encryption (IBE) under selective opening attack (SOA) whose security is almost-tightly related to a set of computational assumptions. 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 particular, we first tuned 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 publicly openability) tightly implies a multi-bit IBE secure under selective opening attack. Next, we almost-tightly reduced such a one-bit IBE to static assumptions in the composite-order bilinear groups employing the technique of Hofheinz et al. This yielded the first SOA secure IBE with almost-tight reduction.