Why would you need proof that it has been backdoored? The fact that it can be backdoored should be enough to disregard it for all uses right from the start.
With Dual_EC_DRBG, everyone knew that it could be back doored. It's not some guess, or "maybe it could have". It was obviously designed to be back doored. It should have been called "NSA_BACKDOOR_RNG", because that's literally what it is.
And yes, all organisations that are not under the thumb of the US Government laughed at the transparent attempt to introduce a back door and rejected Dual_EC_DRBG. Only US-based companies use it, which ought to give you a hint.
People who live in an evidence-based rational world don’t skip the evidence step and go straight to possibilities and counterfactuals.
An outcome of this is the requirement to treat all possibilities as certainties, regardless of evidence.
In this way, entire sections of industry will auto-assume the backdoor was both deliberate, and used both both friendlies & hostiles.
If you propose a clearly questionable security practice in some arbitrary bureaucracy, the assumption is it's incompetence because that happens all the time and no one detects it until it's already in production.
If you propose a clearly questionable security practice to a cryptography standards body, the expectation is that you get laughed out of the room. Even the possibility of a backdoor would make everyone skeptical, which would be useless in a standard because no one would trust it.
And yet it made it through the standards process for some reason, but there is only one plausible reason.
That’s fine. But they should be equally paranoid of all substitute products/services that use other recommendations from NIST, right? Are there greater than zero products on the (US) market with no encryption in the system recommended by NIST?
Also, I don’t think I was limiting my thinking to a customer of the weak encryption product. I was also thinking through the lens of legal implications.
But by the time Dual_EC_DRBG was published, we already had alternatives that were better in just about every way, including being much less likely to contain a backdoor.
That's easily a billion dollar motivation right there, and I can't imagine a bunch of low-paid government drones resisting that cash prize. Everyone has a price.
Hence, there's a level of trust that can be gained through observation of failures to abuse backdoors. If they don't exist, they can't be abused. If they exist, then they must be used/abused, otherwise what's the point? Such usage will be eventually discovered. E.g.: The use of the Dual_EC_DRBG back-door to tap into Juniper VPN connections by the Chinese government was discovered and made public.
Of the people I know that work with highly privileged materials, none would take advantage or abuse something like this, even with such a high payout. Even if they did, how would they continue to live comfortably? That said, it just takes one person under the right circumstances to act maliciously, which is why screening and compartmentalization is critically important for these organizations.