Common use of Soundness Clause in Contracts

Soundness. Given a set of honestly generated verification keys, it is difficult to output a verifying SRDS signature (σms, π) on a message m such that the multi-signature σms does not verify on m against any sufficiently large subset of keys. In order to prove that sufficiently many parties agree on a message m, it suffices to certify that there exists an s-size subset of parties (where s is sufficiently large) who agree on the same message m. Therefore, moving forward for SRDS based on multi-signatures, we only focus on proving that exactly s parties agree on a particular message. We now formalize SRDS based on multi-signatures. ∈