Looking at the question “ECDSA vs ECIES vs ECDH” it appears that you can either have a tool that can derive keys or bits, or can be used to sign and verify something. Is there an EC way to do both with the same keypair?

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    $\begingroup$ The algorithms for key exchange and signing are different, but the algorithm for generating key-pairs is the same for both. So you certainly can use a key-pair for both, but if done incorrectly it might harm security. See Using same keypair for Diffie-Hellman and signing $\endgroup$ – CodesInChaos Nov 3 '15 at 22:49
  • $\begingroup$ I've voted as dupe, but note that ECIES is basically ephemeral-static ECDH + symmetric encryption, something that may not be directly clear from the other question. $\endgroup$ – Maarten Bodewes Nov 4 '15 at 9:32