A Provably-Unforgeable Threshold Schnorr Signature With an Offline Recovery Party

The increase in the interest in cryptocurrencies, and the consequent need for technological maturity of blockchain-based platforms, has been the fuel for some recent advances in cryptographic research. In this context, digital signature protocols have a central role since they guarantee ownership and control of digital assets. The absence of trusted central authorities in public blockchains, which is the very foundation of this technology, poses some interesting challenges on the management of digital identities. In particular, the computational infeasibility of restoring a lost key is a threat to anyone possessing this kind of digital assets. A possible solution to this problem is to use threshold multi-signatures, partially relying on a recovery-party whose only role, even though of paramount importance, is to intervene in case of key loss. We present a Schnorr multi-party digital signature scheme that supports an offline participant during the key-generation phase, without relying on a trusted third party. Under standard assumptions we prove our scheme secure against adaptive malicious adversaries and capable of achieving the resiliency of the recovery in the presence of a malicious party.