Paralysis Proofs : Secure Dynamic Access Structures for Cryptocurrencies and More

Conventional (M,N )-threshold signature schemes leave users with a painful choice. SettingM = N offers maximum resistance to key compromise. With this choice, though, loss of a single key renders the signing capability unavailable, creating paralysis in systems that use signatures for access control. Lower M improves availability, but at the expense of security. For example, a (3, 3)-multisignature cryptocurrency wallet experiences access-control paralysis upon loss of a single key, but a (2, 3)-multisig allows any two players to collude and steal funds from the third. In this paper, we introduce techniques that address this impasse by making general cryptographic access structures dynamic. Our schemes permit, e.g., a (3, 3)-multisig, to be downgraded to a (2, 3)multisig if a player goes missing. This downgrading is secure in the sense that it occurs only if a player is provably unavailable. Our main tool is what we call a Paralysis Proof, evidence that players, i.e., key holders, are unavailable or incapacitated. Using Paralysis Proofs, we show how to construct a Dynamic Access Structure System, which can securely and flexibly update target access structures without a trusted third party such as a system administrator. We present DASS constructions that combine a trust anchor (a trusted execution environment or smart contract) with a censorshipresistant channel in the form of a blockchain. We offer a formal framework for specifying DASS policies, and define and show how to achieve critical security and usability properties (safety, liveness, and paralysis-freeness) in a DASS. Paralysis Proofs can help address pervasive key-management challenges in many different settings. We present DASS schemes for three important example use cases: recovery of cryptocurrency funds should players become unavailable, returning funds to users when cryptocurrency custodians fail, and remediating critical smartcontract failures such as frozen funds. We report on practical implementations for Bitcoin and Ethereum.