no such thing as unbreakable encryption
Colloquial term which we all understand. Nobody short of the NSA can crack properly implemented modern encryption, and even that takes concerted use of resources - not something easily done on a large scale.
Your claim that no encryption is unbreakable is in practice false.
The fact is if it takes more time to break the encryption than the utility of the encrypted data's value, it is, for all practical purposes, unbreakable. . . or if there is just not enough time left before the universe dies a heat death to break the encryption, which with our current technology is the case.
The current state of the art is that 256 bit AES encryption can only be broken by brute force, trying every possible key until you find the right one that will decrypt the data. Most of our financial industry uses 128 bit AES encryption which they think is sufficient for their purposes in handling Trillions of dollars of transactions securely. . . as does many of our governmental agencies. So far, the Financial industry has been correct. I won't judge the security of our government. They are rapidly moving to 256 bit AES.
Apple, for example uses a key that takes the user's passcode of whatever length (it can be anything from four numbers to a complex passcode of up to 256 characters made up of the 223 alphanumeric and symbols accessible through the keyboard) and entangles it with the 128 characters of a Universal Unique ID imbedded in the device to create the key used to make the encryption.
For example, if the user elects to use a 16 character complex passcode using upper and lower case letters mixed with numbers and symbols, that passcode would be then entangled with the 128 character UUID of the device to construct a 144 character key. The number of possible keys is 144223.
Calculating from that, it turns out that if we were to use the fastest supercomputer in the world technologically available to us, which could try and compare 100,000 keys per second to see if each key resulted in anything sensible in the data, and if it did not, then going on to the next potential key (this is at a rate of 3 TRILLION possible keys per year), it would take 5.62 undecillion (5.62 X 10195 years before all possible keys could be tested.
The half-life of a proton is estimated to be only 1030 years and by 1078 or 1080 years, all matter in the Universe would have devolved to a soup of sub-atomic particles. . . long before that supercomputer, if it still existed, was even half-way done trying keys.
If you made that supercomputer even a TRILLION times faster, it would merely knock off only 12 zeros off the number of years it would take to try all the number of keys, making it take only 5.62 X 10183 years. . . before all keys had been tried.
It is pretty obvious that any information held by such an encryption would be moot long before it could be broken.
This is what has these governments' panties in such a wad. . . they cannot possibly break the encryption.
The only way they can get in is to get the owner of the device to give them the passcode. . . and if that owner refuses, to torture it out of him.
In practice there is. How do you know when you’ve successfully broken the encryption? When the cleartext makes sense? But...for a full size key that isn’t reused, there should be a key that produces a given ciphertext from any arbitrary cleartext of the same length. Thus, how do you know that your “readable” cleartext is the right readable cleartext?
True, given enough time and computing resources, you could eventually crack any encryption. But most data justifying encryption is time sensitive, and if it is going to take a couple of hundred years, the data is probably not going to be very helpful once it is finally accessed...