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Wireshark'ed Firefox 3 request. Their names are nowhere documented.

Elliptic curve: secp256r1 (0x0017)
Elliptic curve: secp384r1 (0x0018)
Elliptic curve: secp521r1 (0x0019)

What are the supported curves for other browsers? Does someone want to extend this list?

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I recommend using an RSA certificate together with ECDH on P256 for key exchange. That way a single certificate works in all browsers, but you get most of the benefit of ECC. The security level required for authentication is lower than what's required for confidentiality, since you only need to protect against current but not future attacks. –  CodesInChaos Mar 1 '13 at 16:14
    
RSA is not an option for slow devices like soho routers and smaller. For this case it also doesn't matter that there is no ECC CA. And your answer is a little bit offtopic here. –  Smit Johnth Mar 1 '13 at 19:58
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When software (browsers, Web servers...) supports elliptic curves at all, you can more or less expect support for the two curves given in NSA suite B, i.e. the P-256 and P-384 curves which are specified in FIPS 186-3. These are the same curves as the "secp256r1" and "secp384r1" which you list. The 15 standard NIST curves (from FIPS 186-3) are actually a subset of the curves specified by Certicom in SEC 2.

Some software implementations go further and support other curves. For instance, OpenSSL supports all 15 NIST curves (code was contributed by Sun and is believed not to infringe on any patent -- which explains why OpenSSL does not implement acceleration of Koblitz curves through the Frobenius endomorphism). But if you want to maximize interoperability with existing browsers and servers, stick to P-256 and P-384 (I think these are the only two which will work with Internet Explorer, for instance).

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IE8 doesn't support ECC at all. Should we make a list of browsers which support ECC? –  Smit Johnth Mar 1 '13 at 15:35
    
Such a list would be useful, but would have to be maintained. The situation is made more complex because the OS version may matter; I suspect IE 8.0 could support ECC if used on a recent enough OS, e.g. Windows 7. Also, processing of X.509 certificates and usage of elliptic curves as part of an ECHDE cipher suite are usually distinct software elements, which need not support the exact same set of curves. –  Tom Leek Mar 1 '13 at 15:47
    
It should only matter on IE, which uses OS built-in crypto, the rest should use built-in. The reason for this list is which curves may be used for certificate generation. So if someone can extend these data - please do it! –  Smit Johnth Mar 1 '13 at 16:04
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