LaKey: Efficient Lattice-Based Distributed PRFs Enable Scalable Distributed Key Management

Distributed key management (DKM) services are multi-party services that allow their users to outsource the generation, storage, and usage of cryptographic private keys, while guaranteeing that none of the involved service providers learn the private keys in the clear. This is typically achieved through distributed key generation (DKG) protocols, where the service providers generate the keys on behalf of the users in an interactive protocol, and each of the servers stores a share of each key as the result. However, with traditional DKM systems, the key material stored by each server grows linearly with the number of users. An alternative approach to DKM is via distributed key derivation (DKD) where the user key shares are derived ondemand from a constant-size (in the number of users) secretshared master key and the corresponding user's identity, which is achieved by employing a suitable distributed pseudorandom function (dPRF). However, existing suitable dPRFs require on the order of 100 interaction rounds between the servers and are therefore insufficient for settings with high network latency and where users demand real-time interaction. To resolve the situation, we initiate the study of latticebased distributed PRFs, with a particular focus on their application to DKD. Concretely, we show that the LWE-based PRF presented by Boneh et al. at CRYPTO'13 can be turned into a distributed PRF suitable for DKD that runs in only 8 online rounds, which is an improvement over the start-of-the-art by an order of magnitude. We further present optimizations of this basic construction. We show a new construction with improved communication efficiency proven secure under the same "standard" assumptions. Then, we present even more efficient constructions, running in as low as 5 online rounds, from non-standard, new lattice-based assumptions. We support our findings by implementing and evaluating our protocol using the MP-SPDZ framework (Keller, CCS '20). Finally, we give a formal definition of our DKD in the UC framework and prove a generic construction (for which our construction qualifies) secure in this model.