No, not you had a central government location that had the private key and data flowed via telecommunications to that central location for things to get signed and then the signature flowed back.

As far as the cracking thing is concerned, you are right, some ciphers have been cracked, but they often get cracked gradually whereby we start finding algorithms that yield higher and higher statistical probabilities of cracking the key. The government should replace the keys and ciphers long before the cipher is actually cracked.

For example DES was “cracked” (well, some financial institutions still even use that because it’s still often difficult enough to decrypt) but part of that is because the government didn’t really give the public much time to test it before adopting. Most of that is also because computers have gotten quicker. But as the key gets larger the quickness needed exponentially increases and computers bandwidth is advancing at a limited rate and most cryptographers take that rate vs bandwidth needed to crack a cipher in a reasonable period of time into consideration. WEP was cracked but only because it wasn’t really designed to be a mainstream standard, it was designed by a bunch of people who just wanted some temporary way of encrypting data. It was later adopted as a mainstream standard and the cipher it uses still hasn’t really been cracked (I believe it uses RC4), just the poor WEP implementation. Heck, Diffie-Hellman key exchange still hasn’t been cracked.

But regardless encryption is a cat and mouse game. Keys expire and are replaced by new keys and ciphers get updated and replaced. The point is that it’s highly unlikely that a key will suddenly get cracked by some random person because cracking this stuff is a gradual process whereby when we do start to get even remotely close to cracking it we replace the cipher long before it gets cracked. Heck, many of the ciphers that are considered “cracked” and that have been replaced by better ciphers are still pretty secure even today.