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I'm using secp256k1; in normal scenario alice.privateKey and bob.publicKey (or vice versa) is used to derive the same secret.

Is it safe to use alice.privateKey and alice.publicKey to derive secret as a key for encryption for alice's personal information - where alice.publicKey and encrypted blob is publicly available?

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Yes, recovering the computed secret is as hard as doing it for conventional Diffie-Hellman and thus infeasible for any secure groups.

This is known as Square-Diffie-Hellman problem, the reduction to the computational Diffie-Hellman problem (CDH) can be found in this Q&A.

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  • $\begingroup$ It does however seem unwise. In addition to whatever cipher you use you now also introduce the additional attack surface of ECC. $\endgroup$ – user10653 Dec 1 '17 at 21:07
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    $\begingroup$ @dingrite Actually I can see the point of doing this. For example consider a smartcard / HSM with an ECDH engine (which would provide you with eg a CDH oracle) but without a symmetric keystore. You can then use this HW device to hardware-enforce your "symmetric" key(s). $\endgroup$ – SEJPM Dec 1 '17 at 21:31
  • $\begingroup$ Is it required to input a salt or something similar as used in static-static DH key agreement? It seems to me that you would otherwise always derive the same secret. $\endgroup$ – Maarten Bodewes Dec 2 '17 at 0:41

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