You show the recovered key and plaintext and demonstrate that they match the ciphertext.
The chance that several gigabytes of encrypted data accidentally happen to decrypt with wrong key to a different several gigabytes of perfectly valid data is rather slim, which means that any key which produces valid data is the key you are looking for.
"Deniable Encryption" is the term.
Even in the case of illegally obtained evidence, there are techniques like parallel construction [1] that they can use to make their cases. They also have the so-called "clean hands" exception, which allows allows the government to introduce evidence into trial that was illegally obtained by a third party when the government did not play any role in obtaining that information [2].
The US legal system was designed to seem exceedingly fair on its surface, while allowing for unconscionable abuses by those skilled in maneuvering through its loopholes.
Proving this is very hard though.
You're probably thinking of "inevitable discovery", which says that illegally obtained information can be used anyway if the prosecution can show that they would have obtained it anyway. Parallel construction is something intelligence agencies do in order to hide how they obtained information in the first place (whether legal or otherwise).
Or rather, if one of those leads ends up being complicit in the charges, you have to prove as the prosecution how you came to that conclusion. You can't just say "we started investigations, then magic, then we interviewed this guy and figured it out."
Historically, when the FBI or some other organization helps but doesn't want to be named as part of the process (to protect their secret methods of accessing or collecting information), prosecutors will do something called "parallel construction," in which they build an alternative timeline to how they could have come by the information that led to the new interviews.
It's interesting that in this case, with the FBI publicly acting in support, they're giving up the ghost on that and opening themselves to perhaps being called for testimony. I'm curious how they'd use state secrets protections to get around having to explain their process, and whether a local/appellate/superior court justice(s) would allow it.
If you obtain information that is not reliable, you can act on it (and convince judge to give you warrants) just probably not use it in real trial.
I also think it depends if you want more information for the current suspect or you are on a fishing expedition
Failing to propose a believable narrative for each increase in magnitude in the burden of proof may cause the entire case to fail in the US.
If you collect evidence on someone that would ordinarily require probable cause when that person should be enjoying the presumption of innocence, that evidence is inadmissible, as is all investigation that depends on it to proceed.
Parallel construction is taking theatrical steps ex post facto to defraud the courts into believing that evidence is not only admissible at trial, but also a reasonable basis for further investigation. If the FBI performs mass suspicionless surveillance on presumed innocent victims, finds evidence of a crime, then notifies another agency to contrive reasonable suspicion, then probable cause, to uncover the same evidence via a legally plausible narrative, that is kicking civil rights square in the teeth. Furthermore, it encourages otherwise innocent activities to be considered as reasonable suspicion, and promotes aggressive police tactics to manufacture probable cause out of reasonable suspicion, or bully people into providing consent or confessions. You get "judge dog" approving search warrants whenever the K-9 cop signals him to provide probable cause. And it combines with forfeiture to become even worse.
When "accidental discovery" evidence is admissible, that is a significant weakening of the public's protections against government, as it provides additional avenues for parallel construction, such as dropping a smoke bomb through a window and pulling a fire alarm, such that responding fire department personnel can notice "drug paraphernalia" and tip the police, who get a warrant based on the tip and conduct a search for drugs. This encourages obstruction of services to promote public safety, such as disabling alarms or blocking emergency calls. When "clean hands" evidence is admissible, one "dirty hands" cop--or a paid informant--just needs to pretend to be an anonymous member of the public to tip off the "clean hands" cop. My own non-judge opinion is that poisonous fruit is when one law is broken in pursuit of enforcing another, not just when someone's rights are infringed.
Presumption of innocence isn't directly enshrined in the US constitution. Local prosecutors and governments can and do abrogate it.
The SCotUS opinion in Coffin v US stated the following:
"The principle that there is a presumption of innocence in favor of the
accused is the undoubted law, axiomatic and elementary, and its enforcement
lies at the foundation of the administration of our criminal law.
...the exclusion of an important element of proof can be justified by
correctly instructing as to the proof admitted. The evolution of the
principle of the presumption of innocence, and its resultant, the doctrine
of reasonable doubt, make more apparent the correctness of these views, and
indicate the necessity of enforcing the one in order that the other may
continue to exist."
They can also get away with doing the exact opposite in their practice, only to be overturned at great personal expense to individuals with few resources.
I don't see how the prosecution has met the burden of proof, beyond a reasonable doubt, unless they show their work. Otherwise this is way too easy to frame people.
Maybe DNA from blood is a different matter, but when it comes to hair samples I don't think we can trust the FBI.
"The Justice Department and FBI have formally acknowledged that nearly every examiner in an elite FBI forensic unit gave flawed testimony in almost all trials in which they offered evidence against criminal defendants over more than a two-decade period before 2000."[1]
1. https://www.washingtonpost.com/local/crime/fbi-overstated-fo...