Re: asymmetric-key decryption
//Unfortunately, we already have it - it is public-key encryption.//
Could I have some clarification on this please? Because I'm unsure whether you're pointing out something I don't understand, or you just didn't understand what I was proposing.
I was describing a system which
a) I can decrypt easily using my key
b) the government can decrypt using their key, but it requires an industrial-scale infrastructure a day to do so.
c) without either key, can't be decrypted before the heat-death of the universe.
//One of the reasons tri-stability doesn't exist, is due to the basics of mathematical logic that pivot on true/false.//
Are you suggesting here that it's impossible to have a crypto system to have two keys with different complexities of decryption?
Because given that we already have satisfactory sub-systems:
1) crypto systems where the plaintext can be recovered using two independent keys (I think these basically just encrypt a random 'true key' using each key and store them all along with the encoded message)
2) crypto systems where encryption and decryption have different keys (i.e. public key encryption)
3) proof of work functions with selectable difficulty, which (3b) can be iterated to smooth out the success rate
I reckon that combining them together is essentially an engineering exercise. One could bodge it together using existing functions (see below), so it can't be impossible. A more elegant synthesis would be desirable.
If (1) works how I suggest above, it trivially works with public key encryption(2). And we could not store quite all the government's encoding of the true key to get (3). So they'd have to attempt decryption multiple times (which they could do in parallel). Then we repeat this multiple times, so a smaller facility wouldn't occasionally get lucky (3b).
Of course others have pointed out that it's not going to be something the smart crims use, but that's not what they asked for.