https://www.sri.com/publication/cyber-formal-methods-pubs/on-the-impossibility-of-basing-identity-based-encryptionon-trapdoor-permutations/
We show that there is no black-box construction of IBE from Trapdoor Permutations (TDP) or even from Chosen Ciphertext Secure Public Key Encryption (CCA-PKE).
identity based encryptionimpossibilitybasingtrapdoor