Diogenes: Lightweight scalable RSA modulus generation with a dishonest majority

In this work, we design and implement the first protocol for distributed generation of an RSA modulus that can support thousands of parties and offers security against active corruption of an arbitrary number of parties. In a nutshell, we first design a highly optimized protocol for this scale that is secure against passive corruptions, and then amplify its security to withstand active corruptions using lightweight succinct zero-knowledge proofs. Our protocol achieves security with "identifiable abort, "where a corrupted party is identified whenever the protocol aborts, and supports public verifiability.Our protocol against passive corruptions extends the recent work of Chen et al. (CRYPTO 2020) that, in turn, is based on the blueprint introduced in the original work of Boneh-Franklin protocol (CRYPTO 1997, J. ACM, 2001). Specifically, we reduce the task of sampling a modulus to secure distributed multiplication, which we implement via an efficient threshold additively homomorphic encryption scheme based on the Ring-LWE assumption. This results in a protocol where the (amortized) per-party communication cost grows logarithmically in the number of parties. In order to minimize the work done by the parties, we employ a "publicly verifiable"coordinator that is connected to all parties and only performs computations on public data.We implemented both the passive and the active variants of our protocol and ran experiments using 2 to 4, 000 parties. This is the first implementation of any MPC protocol that can scale to more than 1, 000 parties. For generating a 2048-bit modulus among 1, 000 parties, our passive protocol executed in under 6 minutes and the active variant ran in under 25 minutes.