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Im currently experimenting setting up my first SSL server and don't understand the following scenario: My server has a generated ECC keypair with group identifier $A$ (e.g Brainpool256r1).

During TLS negotiation the ClientHello extension contains multiple curves $B, C, D$.

Is my server capable to support those curves $B, C$, or $D$, or would it only be capable to support curve $A$?

If I want my server to work with multiple curves as well, do I need to have a keypair + certificate for all curve types? Cipher Suite for my specific case would be ECDHE_ECDSA.

What I like to know is the connection between the curve I used during keypair generation and the requested curve list from ClientHello message.

RFC 8422 specifies: If a server does not understand the Supported Elliptic Curves Extension,(...) it MUST NOT negotiate the use of an ECC cipher suite. Depending on what other cipher suites are proposed by the client and supported by the server, this may result in a fatal handshake failure alert due to the lack of common cipher suites.

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