What is the adversary advantage for soundness of a sigma protocol?
No, the advantage of an adversary against soundness in a $\Sigma$-protocol is not 0. In fact, a $\Sigma$-protocol satisfies honest-verifier zero-knowledge, meaning that one can always &quot;cheat&quot; by running the zero-knowledge simulator against an honest verifier, provided that we manage to guess the challenge in advance. This means that any $\Sigma$-protocol will have soundness error at least $1/|S|$, where $S$ is the set of all possible challenges. Most $\Sigma$-protocols from the literature actually achieve this bound exactly.