Weeell, let's take a step back here. First of all, I don't understand what you are trying to prove. That when requesting data from some URL some certain reply comes back?
Even if you were to prove that, the API / backend could always change - so you could at most prove that it did return said data at a certain point in time.
You also don't really need to publish that on the blockchain, instead simply send the proof to the people interested in said proof and call it a day.
Precisely, for the example case I want to prove that the URL contained a specific nonce
at a certain point in time, publishing the proof to the blockchain would be the equivalent to timestamping, so that I can't be using a proof from last week to prove that the nonce was present yesterday, even if it is no longer there today.
You're also correct in that proving ownership or knowledge of something can be easily done using
Zero-Knowledge Proof algorithms and no secure element is needed for that.
I suppose my question is more about what class of computational problems I can expect to have a zero-knowledge proof of knowledge, and how to determine the amount of data necessary to store such a proof.
For example, can you use the same strategy to formulate a zero-knowledge proof for the above example and also to prove that a result of a visual classification problem was calculated using a specific open-source neural net without modification?