# What techniques other than zero-knowledge proofs can prove consistency in one-to-many scenarios?

Assuming that there is a sender and multiple receivers, the sender will send the signature $$\sigma$$ of a certain message $$m$$ to all receivers, and the signatures $$\sigma$$ received by these receivers are the same. Besides zero-knowledge proof, what other technology can realize the consistency proof of signatures?

• Also, what if I want to prove the validity of the signature $\sigma$ on top of the consistency?How can I prove both consistency and signature validity (that is, the signer truly and correctly generated)?
– Anja
Commented Jul 10 at 1:21

• You could use a signature scheme that has unique signatures. That is, for a message $$m$$, there exists a unique signature $$\sigma$$ that correctly verifies. Then, simply by checking their signature on $$m$$, all receivers are convinced by design that they got the same signature.
Note that contrary to what you wrote in the original question, I don't see any reason why zero-knowledge would help here. There's no witness to hide (since $$\sigma$$ is sent to everyone), and no clear statement (you don't want to prove an NP relation, you want to prove that you did something: that you sent a message to someone else. This is unrelated to the type of things ZKP are used to prove).
• If on this basis, then prove that the signature $\sigma$ is valid. Is to prove that the signature $\sigma$ is valid while proving consistency. How should this be proved?