当软件（浏览器、Web 服务器...）完全支持椭圆曲线时，您可以或多或少地期望支持NSA 套件 B中给出的两条曲线，即FIPS 186中指定的 P-256 和 P-384 曲线-3。这些曲线与您列出的“secp256r1”和“secp384r1”相同。15 条标准 NIST 曲线（来自 FIPS 186-3）实际上是 Certicom 在SEC 2中指定的曲线的子集。

一些软件实现更进一步并支持其他曲线。例如，OpenSSL支持所有 15 条 NIST 曲线（代码由 Sun 提供，据信不侵犯任何专利——这解释了为什么 OpenSSL 没有通过 Frobenius 内同态实现 Koblitz 曲线的加速）。但是，如果您想最大限度地提高与现有浏览器和服务器的互操作性，请坚持使用 P-256 和 P-384（例如，我认为只有这两个可以与 Internet Explorer 一起使用）。

就像@Tom Leek 所说的那样secp256r1，是 P-256、secp384r1P-384 和secp521r1P-521。它们都是NSA 套件 B的一部分。

维基百科文章列出了曲线的所有实现。所以最常见的客户是：

OpenSSL/LibreSSL

• 支持 28 条曲线
• 包括 P-256、P-384 和 P-521
• 它们不支持 IETF 新标准化的 Curve25519 和 (Ed448-)Goldilocks。

由于Chrome/Chromium使用 BoringSSL - OpenSSL 的一个分支 - 它应该支持相同的。

火狐 (NSS)

Firefox 使用 NSS（网络安全服务）进行 HTTPS 连接。NSS 支持：

• 25 条曲线（与 OpenSSL 相比，缺少 3 条脑池曲线）
• 包括 P-256、P-384 和 P-521
• 他们也不支持 Curve25519 和 (Ed448-)Goldilocks

然而...

...这只是理论部分，许多实现可能只在服务器端生效。实际上，您可以像您一样使用 Wireshark 分析流量，并查看它提供的曲线。

• 你是对的：Firefox 支持 P-256、P-384 和 P-521。
• 我用 Chromium 对其进行了测试，得到：P-256、P-384。

更新：2016-07-03

请注意，您还可以在SSLLabs上查看哪些浏览器支持哪些椭圆曲线。在那里，您还可以看到Chrome 50 支持 X25519。

Firefox（以及palemoon和waterfox）声称支持secp256r1、secp384r1和secp521r1，但是当使用由secp521r1 CA签署的secp384r1证书连接到网络服务器时，我收到一个错误：（错误代码：sec_error_bad_signature）。

IE 和 Chrome 成功连接到这个服务器，他们似乎已经正确地实现了 EC。

IE（和 Edge）的椭圆密码曲线 - ECDH 密钥交换

实际上还有一些 ECC 曲线可以被调用（“命名”）以用于 IE 或 Edge，这意味着与它挂钩的浏览器的系统端。

我已将以下内容导入我的 Windows 10 系统（同时也可能适用于 Windows 8.1，因为这些也支持密钥交换上的椭圆曲线参数，Windows 7 似乎只有两条默认曲线，并且只是忽略了粘贴到该注册表分支） ：

Windows 注册表编辑器版本 5.00

[HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Cryptography\Configuration\Local\SSL\00010002]
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