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I want to prevent others from reverse-engineering the on-die ROM, using X-ray, microscope, etc..

I think it's best to inject some substance between chip and packag and when the chip package is tempered or the radiation comes through the chip, that substance explodes or do someways to destroy the chip(at least ROM structure).

Is there any research doing this kind of things to prevent reverse-engineering of chip or at least, on-die ROM structure?

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    \$\begingroup\$ If you want to stop reverse engineering attempts backed by state-level funding then you will need state-level funding of your own. \$\endgroup\$ – DKNguyen Jan 8 '20 at 6:29
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    \$\begingroup\$ As an IC designer I can guarantee you that with the right equipment and enough samples I can always reverse engineer your chip's design. There's nothing you can do to stop that. It will be a destructive analysis of course. To protect the contents of your ROM probably the best way is to encrypt its contents. \$\endgroup\$ – Bimpelrekkie Jan 8 '20 at 7:19
  • \$\begingroup\$ There is no perfectly secure method (apart from a one time pad) in the commercial sector (military equipment often has small detonators to destroy hardware, at least in some older equipment). Encrypting the content is the way to go. In cryptography, the name of the game is to make the value of the information less than the cost of decrypting it and there are numerous products available to implement such protections. \$\endgroup\$ – Peter Smith Jan 8 '20 at 10:47
  • \$\begingroup\$ What if I want to have private key on the ROM? Beyond that, doesn't it have to put decrpytion key to else where on that chip to decrypt it anyway? \$\endgroup\$ – user3498780 Jan 8 '20 at 13:25
  • \$\begingroup\$ @Bimplerekkie I don't think encryption can solve anything here. Where are you going to put the key for decrypting? In ROM? \$\endgroup\$ – dim Jan 8 '20 at 17:33
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Brief answer is "no", at least at the chip level.

At board level there are a number of solutions but they all involve techniques that are probably illegal, since they amount to creating a booby trap which is at the vey least capable of destroying most of the board. And also likely corroding or setting fire to its surroundings. IIRC a military technique has been to use a thermite charge packaged with equipment.

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To answer your actual question, "is there research", the answer is yes. However, the research itself and any techniques developed will be classified as state secrets. If you have to ask in a public forum then you are already off on the wrong foot.

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