Both worries are about human error, not an actual mathematical objection. And of course any encryption scheme, including any present-day one without a secret government key, is also potentially vulnerable to these sorts of problems. But it seems to me that if you have a large number of experts reviewing both the pure mathematics and the details of the software implementation, the risk of this sort of problem is going to drop to a lot less than that of an intentional leak, it would be more akin to some widely-accepted and peer-reviewed mathematical result turning out to be wrong.
Keep in mind I was responding to an objection by nimelennar that claimed that the idea was impossible in a mathematical sense, so that these sorts of proposals were akin to flat-earthism, not just unsafe when you take into account dangers related to human error. Specifically, nimelennar said
Doesn’t this sound like nimelennar was saying that even in a purely theoretical mathematical sense such a scheme wasn’t possible? And when I objected, and you responded to my objection by citing “the wide range of encryption experts who have repeatedly said that what is being asked for is not technically feasible”, was “technically feasible” supposed to refer to the mathematics of how difficult the key would be to crack, or to other, human-error based concerns? (edit: and I see that in this coment nimelennar has reconsidered his objection after reviewing a paper, noting that the problems raised by cryptographic experts are not about the basic mathematical design)
No, but in the case of many encryption schemes they do–for example, this article in which an expert discusses the time to crack AES using a brute-force approach estimates that with a modern supercomputer it would take 399 seconds to crack a 56-bit key, about 10^18 years to crack a 128-bit key, and about 10^37 years to crack a 192-bit key. Again, if one wants to defend nimelennar’s earlier comment specifically, as opposed to making some more general argument about human error, one should be able to point to a cryptographic expert talking specifically about purely mathematical issues which make it impossible to have a secret key which would be impossible to crack computationally in any reasonable length of time.
