Transparent Batchable Time-lock Puzzles and Applications to Byzantine Consensus

Abstract

Time-lock puzzles (TLP) are a fascinating type of cryptographic problem that is easy to generate, but takes a certain time to solve, even when arbitrary parallel speedup is allowed. TLPs have wide-ranging applications including fairness, round efficient computation, and more. To reduce the effort needed to solve large numbers of TLPs, prior work has proposed batching techniques to reduce the cost of solving. However, these proposals either require: (1) a trusted setup or (2) the puzzle size be linear in the maximum batch size, which implies setting an a priori bound on the maximum size of the batch. Any of these limitations restrict the utility of TLPs in decentralized and dynamic settings like permissionless blockchains. In this work, we demonstrate the feasibility and usefulness of a TLP that overcomes all the above limitations using indistinguishability obfuscation to show that there are no fundamental barriers to achieving such a TLP construction. As a main application of our TLP, we show how to improve the resilience of consensus protocols toward network-level adversaries in the following settings: (1) We show a generic compiler that boosts the resilience of a Byzantine broadcast protocol $$\varPi $$ as follows: if $$\varPi $$ is secure against $$t<n$$ weakly adaptive corruptions, then the compiled protocol is secure against $$t<n$$ strongly adaptive corruptions. Here, ‘strong’ refers to adaptively corrupting a party and deleting messages that it sent while still honest. Our compiler is round and communication preserving, and gives the first expected constant-round Byzantine broadcast protocol against a strongly adaptive adversary for the dishonest majority setting. (2) We adapt the Nakamoto consensus protocol to a weak model of synchrony where the adversary can adaptively create minority partitions in the network. Unlike prior works, we do not assume that all honest messages are delivered within a known upper bound on the message delay. This is the first work to show that it is possible to achieve consensus in the permissionless setting even after relaxing the standard synchrony assumption.