Scalable Registration-Based Encryption from Lattices

Registration-Based Encryption (RBE) is a public-key encryption mechanism which allows a user to register their identity (e.g. email address) and self-generated public key with a key curator (e.g. an organisation). The key curator aggregates these keys into a compact digest. Using only this digest and the recipient’s identity, anyone can encrypt messages to any registered user. As the key curator is not entrusted with any secrets, RBE presents a solution to the key escrow problem, which impedes the adoption of Identity-Based Encryption. This makes RBE an attractive solution for secure communication with and among members of an organisation while preserving user privacy. Despite recent advances [Döttling-Kolonelos-Lai-Lin-Malavolta-Rahimi, EUROCRYPT’23; Fiore-Kolonelos-de-Perthuis, ASIACRYPT’23], practical constructions of RBE are still limited to a small number of registered users (e.g. 1024), lack post-quantum security, or have ciphertext sizes scaling in the order of GB. The predominant way towards constructing practical RBE is a generic transformation from Laconic Encryption (LE). In this work, we identify an efficiency bottleneck in this transformation and present a new primitive called Batched Laconic Encryption (BLE) which admits a more succinct transformation to RBE. Our resulting RBE scheme is the first post-quantum construction that simultaneously supports a large number of registered users and asymptotically outperforms all comparable RBE schemes. Concretely, for at most 2^30 registered users at 128-bit security, our scheme achieves a ciphertext size of 7 MB, improving on previously reported results by three orders of magnitude. We confirm our results through an open-source prototype implementation demonstrating that all algorithms execute within a few milliseconds. The post-quantum security of our construction is based on the standard Learning with Errors assumption, and our analysis enables several tweaks to significantly reduce ciphertext sizes in practical deployments.