Greg Tito said:
It may seem strange that the best code-breakers in the country are stumped by a code that a high school dropout could devise, but solving ciphers is never a simple process.
This is clearly not your average high school dropout. These people, these "best code-breakers in the country", could break your average high school dropout's code in a fraction of a second. If they can't break it, there's a very good chance that he's using some known incredibly-secure method of encryption. He could have used a one-time pad for instance, which would make his code quite literally unbreakable. (I saw someone said they're "supposed to be unbreakable". They're completely unbreakable. It isn't that we can't think of a good way to break them, it's that you can give a proof showing them to be unbreakable. A basic knowledge of math and cryptanalysis combined with some thought makes it pretty obvious as to how.)
Further cryptanalysis issues: brute-forcing a code is useless against a one-time pad or any similar cipher because you'll find close to an infinite number of plausible messages with no way to know which one is the right one. Brute forcing even a relatively bad modern cipher is also essentially impossible at this point. Someone mentioned quantum computing, but quantum computing isn't projected to provide speeds anywhere close to necessary to make the problem tractable, we're talking computational problems that are several orders of magnitude beyond computational speeds we can even
imagine. In cryptanalysis, you don't, as a rule, ever hope that brute forcing will actually work against modern ciphers, you find some way to massively cut-down on the number of possibilities. There's some pattern to anything that isn't a one-time pad (or other ciphers mathematically equivalent to a one-time pad), so it really comes down to finding such a pattern. Usually, these patterns are disguised by mathematical manipulation as part of the cipher, but given how short these messages are, it'd be hard to hide much.
I'd also honestly wonder if there isn't some form of steganography involved. Clever steganography would render code-breaking completely useless and it isn't really particularly hard to come up with simple schemes. Less dramatic examples would be things like: the code actually deciphers to strings of numbers, only one of which is significant and only a handful of people would know how or why it's significant. Not only would the message remain hidden, code-breakers would have no way to know they'd solved the cipher. Remarkably simple and easy for a high-school dropout to devise.
TL;DR: These people are not bad at code-breaking and it's unlikely that they're simply failing to find a difficult code. It's more likely that the code is either mathematically (one-time pad) or logically (intelligent steganography) impossible to break.
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