What curves can be used with what algorithms?

Asked Jan 27 '22 at 21:51

Active Jan 27 '22 at 21:51

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I've been trying to improve my understanding of elliptic-curve cryptography; I'm currently trying to understand the extent to which curves are interchangeable.

Examples of curves: P-256, Curve25519
Examples of algorithms: ECDH, ECDSA, EdDSA

Of the curves I listed, I've read that both are used with ECDH, but I've only read of P-256 being used with ECDSA and Curve25519 being used with EdDSA. Why can both curves be used with ECDH, but only one can be used with each signing algorithm? Or can ECDSA and EdDSA be used with both of those curves, but there just aren't any implementations of that?

asked Jan 27 '22 at 21:51

Billy

2

Welcome to Cryptography.SE This is a too broad question and indeed there is a simple answer; Every curve can be used with DHKE, EdDSA needs Edward Curve, ECDSA is free for every curve. The matter is the speed and the additional securities. – kelalaka Jan 27 '22 at 22:00
First dupe of many questions Curve25519 over Ed25519 for key exchange? Why? 2) Note the recommended word What the X stands for in the front of Elliptic curve names like X25519 3) ECDSA, EdDSA and ed25519 relationship / compatibility 4) Which curve is used for ECDH – kelalaka Jan 27 '22 at 22:01
There are more, left to Billy... – kelalaka Jan 27 '22 at 22:13

What curves can be used with what algorithms?

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