IBE with tight security against selective opening and chosen-ciphertext attacks

The simulation-based, selective opening and chosen-ciphertext ( $$\mathsf {SIM}\text{- }\mathsf {SO}\text{- }\mathsf {CCA}$$ SIM - SO - CCA ) adversary runs in the multi-sender scenario, it may access to the decryption and user-secret key oracles, in addition to corrupt senders adaptively after seeing the ciphertext (hence it can obtain the encrypted messages together with the randomness). An $$\mathsf {SIM}\text{- }\mathsf {SO}\text{- }\mathsf {CCA}$$ SIM - SO - CCA secure $$\mathsf {IBE}$$ IBE scheme aims to provide privacy for uncorrupted senders against such adversaries. In this work we present the first tightly $$\mathsf {SIM}\text{- }\mathsf {SO}\text{- }\mathsf {CCA}$$ SIM - SO - CCA secure identity-based encryption ( $$\mathsf {IBE}$$ IBE ). Our $$\mathsf {SIM}\text{- }\mathsf {SO}\text{- }\mathsf {CCA}$$ SIM - SO - CCA secure $$\mathsf {IBE}$$ IBE employs an identity-based key encapsulation mechanism ( $$\mathsf {IBKEM}$$ IBKEM ) as a building block, concretely, Firstly, we define proper security requirements in the multi-challenge setting for an $$\mathsf {IBKEM}.$$ IBKEM . Then we transform an $$\mathsf {IBKEM}$$ IBKEM with such properties to a $$\mathsf {SIM}\text{- }\mathsf {SO}\text{- }\mathsf {CCA}$$ SIM - SO - CCA secure $$\mathsf {IBE}$$ IBE in a tight way. The security definitions and transformation can be seen as an extension of the framework in the public encryption (PKE) setting (given by Lyu et al. in PKC 2018). Finally, we propose an $$\mathsf {IBKEM}$$ IBKEM in prime order groups satisfying our requirements. The security of our $$\mathsf {IBKEM}$$ IBKEM can be tightly reduced to the standard matrix Diffie–Hellman assumption. Our $$\mathsf {IBKEM}$$ IBKEM leads to a tightly $$\mathsf {SIM}\text{- }\mathsf {SO}\text{- }\mathsf {CCA}$$ SIM - SO - CCA secure $$\mathsf {IBE}$$ IBE and of independent interest.