If you're interested look up the definition for "Lamport Signatures." It's an algorithm for masking the bits of a message by exchanging a table of hashes prior to signing and then revealing the "secrets" behind said hashes in such a way that you can selectively mask the bits of the message hash that you're wishing to sign.

It's actually a really cool algorithm and probably the most elegant thing I've ever seen in the way of digital signatures - and besides just being something that's really cool: Lamport Signatures have the advantage of being quantum safe too (if you care about that kind of thing.)

To actually answer your question indirectly: you would use a consensus system that understands Lamport signature operations in the "scriptPubKey" (Ethereum could probably do this now.) And note that as Nick ODell has already said: using the hashes alone in this scheme won't work since the moment you publish the transactions with said hash secrets anyone is then free to pluck out those values and double spend the original transaction to a new destination (and this is actually the reason why Peter Todd's proof-of-hash collision scheme in Bitcoin is insecure but still allows us to incentivize whether or not there may be a flaw with the recent SHA algorithms.)

Regarding hash protected M of N multi-sig: there is already a similar smart contract algorithm called "atomic cross-chain contracts" that relies on hash values to be released as part of the protocol to swap coins across blockchains but said algorithm also uses ECDSA public keys to prevent the transactions from being double-spent. So in Bitcoin Multi-sig using hash values will work - though you still need to include an ECDSA pub key to protect them from attackers on the network.

(I hope this helps. You didn't say much about the intended use-case for this.)