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They have been. Through years of use, independent auditing, industry and government certification processes, and their Apple Security Research program.
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They've published several whitepapers and technical documentation on how the secure enclave works and it's been poked at by security researchers for years.
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If it's not open source (with open hardware), you cannot trust it. Whitepapers are great, but who knows what's actually implemented.
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Apple can’t prove a negative. You have to prove they’re lying.
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You can. They do all the time in math and programming.
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You don't have to prove anything. You need to asses your risk profile and decide if you want to expose yourself to Apple or not.
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