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> The only evidence we have that the cryptography that we commonly use is actually safe is that it's based on "hard" math problems that have been studied for decades or longer by mathematicians without anyone being able to crack them.

Adding to this...

Most crypto I'm aware of implicitly or explicitly assumes P != NP. That's the right practical assumption, but it's still an major open math problem.

If P = NP then essentially all crypto can be broken with classical (i.e. non-quantum) computers.

I'm not saying that's a practical threat. But it is a "known unknown" that you should assign a probability to in your risk calculus if you're a state thinking about handing over the entirety of your encrypted backups to a potential adversary.

Most of us just want to establish a TLS session or SSH into some machines.

While I understand what you're saying, you can extend this logic to such things as faster-than-light travel, over-unity devices, time travel etc. They're just "hard" math problems.

The current state of encryption is based on math problems many levels harder than the ones that existed a few decades ago. Most vulnerabilities have been due to implementation bugs, and not actual math bugs. Probably the highest profile "actual math" bug is the DUAL_EC_DRBG weakness which was (almost certainly) deliberately inserted by the NSA, and triggered a wave of distrust in not just NIST, but any committee designed encryption standards. This is why people prefer to trust DJB than NIST.

There are enough qualified eyes on most modern open encryption standards that I'd trust them to be as strong as any other assumptions we base huge infrastructure on. Tensile strengths of materials, force of gravity, resistance and heat output of conductive materials, etc, etc.

The material risk to South Korea was almost certainly orders of magnitude greater by not having encrypted backups, than by having encrypted backups, no matter where they were stored (as long as they weren't in the same physical location, obviously).

>While I understand what you're saying, you can extend this logic to such things as faster-than-light travel, over-unity devices, time travel etc. They're just "hard" math problems.

No you can't. Those aren't hard math problems. They're Universe breaking assertions.

This is not the problem of flight. They're not engineering problems. They're not, "perhaps in the future, we'll figure out..".

Unless our understanding of physics is completely wrong, then None of those things are ever going to happen.

According to our understanding of physics, which is based on our understanding of maths, the time taken to brute force a modern encryption standard, even with quantum computers, is longer than the expected life of the universe. The likely-hood of "finding a shortcut" to do this is in the same ball-park as "finding a shortcut" to tap into ZPE or "vacuum energy" or create worm-holes. The maths is understood, and no future theoretical advances can change that. It would involve completely new maths to break these. We passed the "if only computers were a few orders of magnitude faster it's feasible" a decade or more ago.

Sorry, I don't think this is true. There is basically no useful proven lower bound on the complexity of breaking popular cryptosystems. The math is absolutely not understood. In fact, it is one of the most poorly understood areas of mathematics. Consider that breaking any classical cryptosystem is in the complexity class NP, since if an oracle gives you the decryption key, you can break it quickly. Well we can't even prove that NP != P, i.e., that there even exists a problem where having such an oracle gives you a real advantage. Actually, we can't even prove that PSPACE != P, which should be way easier than proving NP != P if it's true.

One-time pad is provable secure. But it is not useful for backups, of course.

Even OTP is not secure if others have access to it.

Every castle wall can be broken with money.

How much money is required to decrypt a file encrypted with a 256-bit AES key?

How much person(s) who know the key will take to change country and don't work anymore?

Or how much it is cost to kidnap significant one of key bearer(s)?

I think, it is very reasonable sums for governments of almost any country.

I think you assume that encryption keys are held by people like a house key in their pocket. That's not the case for organizations who are security obsessed. They put their keys in HSMs. They practice defense in depth. They build least-privilege access controls.

OTP can be useful especially for backups. Use a fast random number generator (real, not pseudo), write output to fill tape A. XOR the contents of tape A to your backup datastream and write result to Tape B. Store tape A and B in different locations.

But you have one copy of the key stream. It is not safe. You need at least two places to store at least two copies of the key stream. You cannot store it in non-friendly cloud (and this thread started from backing up government sensitive data into cloud owned by other country, possibly adversary one.

If you have two physically separate places which you could trust key stream, you could use them to backup non-encrypted (or "traditionally" encrypted) data itself, without any OTP.

You may want some redundancy because needing both tapes increases the risk to your backup. You could just backup more often. You could use 4 locations, so you have redundand keystreams and redundant backup streams. But in general, storing the key stream follows the same necessities as storing the backup or some traditional encryption keys for a backup. But in general, your backup already is a redundancy, and you will usually do multiple backups in time intervals, so it really isn't that bad.

Btw, you really really need a fresh keystream for each and every backup. You will have as many keystream tapes as you have backup tapes. Re-using the OTP keystream enables a lot of attacks on OTP, e.g. by a simple chosen plaintext an attacker can get the keystream from the backup stream and then decrypt other backup streams with it. XORing similar backup streams also gives the attacker an idea which bits might have changed.

And there is a difference to storing things unencrypted in two locations: If an attacker, like some evil maid, steals a tape in one location, you just immediately destroy its corresponding tape in the other location. That way, the stolen tape will forever be useless to the attacker. Only an attacker that can steal a pair of corresponding tapes in both locations before the theft is noticed could get at the plaintext.

Thank you for writing this post. This should be the top comment. This is a state actors game, the rules are different.

> could still be valuable to an adversary after decades

What kind of information might be valuable after so long?