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Bitcoin, Ethereum and other blockchain-based cryptocurrencies, as deployed today, cannot support more than several transactions per second. Off-chain payment channels, a “layer 2” solution, are a leading approach for cryptocurrency scaling. They enable two mutually distrustful parties to rapidly send payments between each other and can be linked together to form a payment network, such that payments between any two parties can be routed through the network along a path that connects them. We propose a novel payment channel protocol, called Sprites. The main advantage of Sprites compared with earlier protocols is a reduced “collateral cost,” meaning the amount of money × time that must be locked up before disputes are settled. In the Lightning Network and Raiden, a payment across a path of ` channels requires locking up collateral for Θ(`∆) time, where ∆ is the time to commit an on-chain transaction; every additional node on the path forces an increase in lock time. The Sprites construction provides a constant lock time, reducing the overall collateral cost to Θ(` + ∆). Our presentation of the Sprites protocol is also modular, making use of a generic state channel abstraction. Finally, Sprites improves on prior payment channel constructions by supporting partial withdrawals and deposits without any on-chain transactions. 

The growing adoption of digital assets---including but not limited to cryptocurrencies, tokens, and even identities---calls for secure and robust digital assets custody. A common way to distribute the ownership of a digital asset is (M, N)-threshold access structures. However, traditional access structures leave users with a painful choice. Setting M = N seems attractive as it offers maximum resistance to share compromise, but it also causes maximum brittleness: A single lost share renders the asset permanently frozen, inducing paralysis. Lowering M improves availability, but degrades security. In this paper, we introduce techniques that address this impasse by making general cryptographic access structures dynamic. The core idea is what we call Paralysis Proofs, evidence that players or shares are provably unavailable. Using Paralysis Proofs, we show how to construct a Dynamic Access Structure System (DASS), which can securely and flexibly update target access structures without a trusted third party. We present DASS constructions that combine a trust anchor (a trusted execution environment or smart contract) with a censorship-resistant channel in the form of a blockchain. We offer a formal framework for specifying DASS policies, and show how to achieve critical security and usability properties (safety, liveness, and paralysis-freeness) in a DASS. To illustrate the wide range of applications, we present three use cases of DASSes for improving digital asset custody: a multi-signature scheme that can "downgrade" the threshold should players become unavailable; a hybrid scheme where the centralized custodian can't refuse service; and a smart-contract-based scheme that supports recovery from unexpected bugs.