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    $\begingroup$ @ErikAronesty AES-GCM uses AES. My point is not that this specific paper demonstrates an attack on your specific application. Your specific application doesn't matter enough for anyone to publish a paper at a reputable cryptography conference demonstrating an attack. My point is that you have violated the security contract of AES (and anything built out of it like AES-GCM), and the paper shows an example of what goes wrong when you skimp on your contractual obligations. $\endgroup$ Commented Jul 17, 2018 at 22:03
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    $\begingroup$ @ErikAronesty The IV does not serve a similar purpose to the KDF. If you use a nonuniform key, you have voided the contract of AES. Don't play with it. $\endgroup$ Commented Jul 17, 2018 at 22:12
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    $\begingroup$ @ErikAronesty NOOOOOOOOOO! EFAIL! $\endgroup$ Commented Jul 17, 2018 at 22:14
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    $\begingroup$ @ErikAronesty If you violate the security contract of the primitive or invent a bespoke composition of it, you are asking for a shot in the foot. If you want public-key encryption, you should use an existing construction that is credibly advertised to guarantee IND-CCA2/NM-CCA2. Tweaking it to replace a MAC of the message by a hash of the key is asking for trouble. $\endgroup$ Commented Jul 17, 2018 at 22:17
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    $\begingroup$ I'm not sure what @ErikAronesty means by "SHA3 on the key", but shouldn't it be OK (or even better) to use AES-GMAC with the key derived by the KDF, instead of using separated encryption and MAC schemes as specified by ECIES? $\endgroup$ Commented Jul 18, 2018 at 11:53