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I think it's possible they can't, depending on the algorithm used and whether they have low-level access to hardware and/or firmware. It's possible that some of the recommended algorithms were chosen for subtle NSA backdoors, and I'm sure they have a lot of resources to throw at high-value communications, but I'd be surprised if every algorithm in current use, with large enough keys, can be cracked by them. A low-level backdoor in the hardware device itself would be a different matter, and this seems like a more practical approach for the NSA than cracking the encryption directly, particularly where the participants are taking extra care. So I'd say it's possible but not certain that they can hear/read these conversations.
That does presuppose they don't have a direct tap on either or both lines somewhere.
To get around end-to-end encryption the tap would have to be in the phone handset itself or a vulnerability in the code. I wouldn't rule either out.
I can't say much, but I do know they have every computing capacity you can imagine, as well as at least one of every piece of HW, even the stuff that's built in a basement.
Still, as far as is commonly known, mathematically cracking encryption where the algorithm is good and keys are large and unique remains impractical for conventional computers. If they're secretly way ahead on quantum computing (which seems unlikely), or if they have discovered mathematical vulnerabilities in common algorithms that have not been published, then that's a different matter. But as far as we know, it must still be difficult for them to attack encryption directly. You suggest you know more than you can say, but if I were them I'd be looking at putting backdoors into phone/computer hardware to get hold of communications before they are E2E encrypted, and/or placing subtle vulnerabilities in open-source code.
Conventional computers...
What do you think they have? Alien computers? Not even super-computers make a dent in decryption.
If it's anything like their past, they have at least 2 working Quantum computers.
But this is not like the past. Quantum computers is not an step in evolution, it is a jump, as if from no computers to computers. Of course it's possible, but there is no basis or indication for it and so no reason to assume it. Why believe the less likely thing instead of the more likely?
Not a conventional computer. Would you agree?
Which one? A super computer? Its just faster than a conventional computer by a factor that doesn't matter. A quantum computer? The public field would be way closer to that if "the government" had one that would be useful.
Obviously you are not aware a Quantum does not operate like a conventional computer. That's fine. No reason to go further.
Oh, but I am. That's why I said what I said. Even if they have one, it will be severely lacking; indicated by where public research is at.
You can't even concede that Quantum computing is not convententual computing, why would your idea of research be valid?
But I am! Quantum computing is not conventional computing. See!
The OP added conventional computing to their verbiage because they knew what they said was not true of Quantim computing. Thus my response.
Same as you adding the word public to research. Neither of us has any idea on the extent of research by Google, IBM and especially the NSA. Having worked in R&D before, I can tell you that not 50% is known to the public. The NSÀ, who run their own development and research-nothing at all. So, I consider your research argument faulty on its face..