Paper 2021/005 Original: eprint.iacr.org/2021/005 ↗

Aggregatable Distributed Key Generation

Abstract

In this paper, we introduce a distributed key generation (DKG) protocol with aggregatable and publicly-verifiable transcripts. Compared with prior publicly-verifiable approaches, our DKG reduces the size of the final transcript and the time to verify it from $O(n^2)$ to $O(n log(n))$, where $n$ denotes the number of parties. As compared with prior non-publicly-verifiable approaches, our DKG leverages gossip rather than all-to-all communication to reduce verification and communication complexity. We also revisit existing DKG security definitions, which are quite strong, and propose new and natural relaxations. As a result, we can prove the security of our aggregatable DKG as well as that of several existing DKGs, including the popular Pedersen variant. We show that, under these new definitions, these existing DKGs can be used to yield secure threshold variants of popular cryptosystems such as El-Gamal encryption and BLS signatures. We also prove that our DKG can be securely combined with a new efficient verifiable unpredictable function (VUF), whose security we prove in the random oracle model. % Finally, we experimentally evaluate our DKG and show that the per-party overheads scale linearly and are practical. For $64$ parties, it takes $71$ms to share and $359$ms to verify the overall transcript, while for $8192$ parties, it takes $8$s and $42.2$s respectively.