As of today, there's no way to prove the security of any available cryptosystem. Let me say that differently: for all we know, ALL currently available cryptosystems can be easily cracked by some unpublished techniques. The only sort-of exception to that requires quantum communication, which is nowhere near practicability on the scale required. 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.
On the other hand, some popular cryptosystems that were more common in the past have been significantly weakened over the years by mathematical advances. Those were also based on math problems that were believed to be "hard." (They're still very hard actually, but less so than we thought.)
What I'm getting at is that if you have some extremely sensitive data that could still be valuable to an adversary after decades, you know, the type of stuff the government of a developed nation might be holding, you probably shouldn't let it get into the hands of an adversarial nation-state even encrypted.