If an attacker has an unlimited physical access to CPU, but does not have access to memory, including RAM, can he attack and gain access to the user's data?

I heard the opinion that this is impossible according to the laws of physics, even with an electron microscope. It's true?

  • $\begingroup$ This seems more appropriate for Cryptography. $\endgroup$ – Yuval Filmus Jul 27 '18 at 17:38
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    $\begingroup$ I don't see what the laws of physics have to do with this question. $\endgroup$ – Yuval Filmus Jul 27 '18 at 17:39
  • $\begingroup$ What's the basis for that opinion? Have you asked them why they said that? $\endgroup$ – D.W. Jul 27 '18 at 18:48
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    $\begingroup$ The title question seems different from the body question… $\endgroup$ – Draconis Jul 27 '18 at 20:04
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    $\begingroup$ This seems largely hypothetical. The CPU and RAM are in the same box. How can I have physical access to one but not the other? $\endgroup$ – David Richerby Jul 31 '18 at 12:42

If you have unlimited physical access to the CPU, then you can send your own instructions into it, including instructions to read from arbitrary memory addresses. Looking at the voltages on the data bus then shows you exactly what's in that word of memory.

Remember, any data the computer is able to use, has to be accessible by at least one CPU. That's just how it works. So access to the CPU gives you theoretical access to everything else.

(Note: this is an answer to the question in the body, not the question in the title.)

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