Maybe we could just use something that can't be stolen. Something like a shared secret that is exchanged through secure channels beforehand and then only reside

Maybe we could just use something that can't be stolen. Something like a shared secret that is exchanged through secure channels beforehand and then only resides in the users permanent memory. The second party could even use some kind of novel mathematical function that maps arbitrarily sized secrets to a seemingly random fixed size value that is both sufficiently different for similiar inputs and big enough to avoid collisions. That would allow them to not store the secret in plain text as they could just compare the output of the function with the previously saved one to verify that the secret the user gave is most likely correct.