That's a pretty large number of assumptions:

tamper-proof delay line => tamper-proof crypto box ("transformation function with state") => tamper-proof delay line

Why not just put a tamper-proof clock in the tamper-proof crypto box and not bother with the delay lines?

The tamper proof aspect is really secondary to the math question. The idea that if I set up a stream of bits through a transform, that the original state of the transform affects the final outcome after N iterations. If the transform exists, it will ease/eliminate the reliance on the "economics" of cryptography to build a tamper-proof physical device. Here is another implementation of the idea: initialize buffer to '12#fjKL3_*(ASDdj1ll3_13 asdfasd-1-3!#!23' do forever /* actually until the plaintext spews out */ sleep 1 unit for each element in the buffer buffer[ element ] = magictransform( buffer[ element ] ) The initial buffer must be secret! Calculating the intial buffer in such a way that after N iterations the plaintext message appears is what must happen.