Building Non-interactive Asynchronous Threshold Signatures For the Blockchain Ecosystem

Abstract

In the blockchain ecosystem, threshold signature schemes hold a special value. They allow any qualified subset of participants (t-out-of-n) to combine its shares and generate a signature that can be verified using a single threshold public key. This provides not only added decentralization but additional security benefits as well. While there are several existing threshold signature schemes, most are either n-out-of-n and/or require consistent availability of the exact same set of participants through several rounds. This, in turn, results in a bottleneck due to during the various stages of the protocol. This thesis, aims to construct a threshold signature scheme that removes this dependence. We achieve this by introducing non-interactive and truly threshold signatures. This implies that once the message to be signed is revealed, the individual signers can simply sign and broadcast their signature. These individual signatures can then be combined easily to construct the signature for the group without any further involvement. Additionally, the signature scheme also uses misbehavior detection to impose accountability for invalid signing. This is done by adding an optional component to the individual signatures that can be removed while calculating the group signature but later invoked for detection. Finally we prove that our scheme is safe against known distributed attacks and has Existentially Unforgeabilility under Chosen Message Attack (EUF-CMA) security in the Random Oracle Model for up to t − 1 malicious participants.