Identity-Based Encryption with (Almost) Tight Security in the Multi-instance, Multi-ciphertext Setting

We construct an identity-based encryption (IBE) scheme that is tightly secure in a very strong sense. Specifically, we consider a setting with many instances of the scheme and many encryptions per instance. In this setting, we reduce the security of our scheme to a variant of a simple assumption used for a similar purpose by Chen and Wee (CRYPTO 2013, Springer, 2013). The security loss of our reduction is \(\textbf{O} (k)\) $\mathbf{O}(k)$ (where \(k \) $k$ is the security parameter). Our scheme is the first IBE scheme to achieve this strong flavor of tightness under a simple assumption. Technically, our scheme is a variation of the IBE scheme by Chen and Wee. However, in order to “lift” their results to the multi-instance, multi-ciphertext case, we need to develop new ideas. In particular, while we build on (and extend) their high-level proof strategy, we deviate significantly in the low-level proof steps.