What you're asking for is nearly impossible, definitely impractical and not an attack vector you should be thinking about (yet).
The entire web these days is built upon SSL, which utilizes asymmetric cryptographic algorithms to create certificates, which can be validated without having the private set of keys, yet stay incredibly well suited against forgery.
Now, most of that is built with RSA and elliptic curve diffie hellman for key exchanges (btw, if you're interested in cryptography, consider the diffie-hellman key exchange your entry drug :P).
If you don't believe me, log into online banking and look at the certificate.
Even with those algorithms we still require your client to have some prior certificate store which it trusts. All certificates are derived from those certificate authorities.
You are now proposing a 'zero-knowledge proof of knowledge' (sounds stupid, but that's what its called in the literature last i checked - feel free to read a bit on Wikipedia: https://en.wikipedia.org/wiki/Zero-knowledge_proof)
The issue is that passwords normally don't have the necessary complexity (either by low size, or non perfect generation by possibly a human) to be usable in most circumstances as far as i know.
There are algorithms which are suited even in those low complexity cases though (Example of so called Sigma protocols: https://cs.au.dk/~ivan/Sigma.pdf).
Now we come to the final nail in this crypto-coffin:
There exists nothing which is open source for your specific use-case
Or at the very least nothing i know about, and even if there was something, i wouldn't trust some rando implementation, neither should you!
I'm interested in cryptography, that doesn't mean i can build a secure cryptographic system, or determine the security of its implementation