You don't have to believe anything.
There's a large difference between public/private key cryptography and internet passwords being stored as computed hashes for authentication comparison.
People would like to think MD5 is one way encryption to compare passwords, but now that you can spin up a super computer on AWS in 5 minutes within registering, it's not a fantastic thing to be able to break even a well thought out password.
Is your cryptography good enough to beat that? They're decrypting SSH transport in real time on a national basis. (again, they can do that because it's published and used as a standard)
The little company I worked for had maybe a few tens of millions in budget, but the government has trillions. Think about what you can do if you put trillions of dollars on any given task.
and yes, my mechanism, though I can't really say it's mine because I developed it for another company, is the shiznit...