Cannot sign a JWT using Elliptic Curve (EC) cryptography

I have generated a private key using Elliptic Curve cryptography:

openssl ecparam -genkey -name secp521r1 -noout | openssl pkcs8 -topk8 -nocrypt

I have used the following Java code to sign a JWT:

    String privateKeyPEM = "MIHtAgEAMBAGByqGSM49AgEGBSuBBAAjBIHVMIHSAgEBBEEmSOGpmkjzKM+uWhya"
        + "Cl6sbSsmROUol4HaDbORnOI6klbEjbCkPEyxKRnrrtrGFShhu7TPPlGDK39f+K3G"
        + "IZhbYKGBiQOBhgAEAJQiOIKV7YmIVI30Y3y1UZIvgZFRviHFWvSiTXEG4IqzHKpF"
        + "jOIYs0rzn1F2zrFHKpmMtZ0Kh5OzyfJsGeu1GZPzANYLZQ9m13Joi3fhGFUgHLNL"
        + "0hsz/HQP89aTa9Qr8QqEP7r/vCvrcoKn9cKPGwRxOFkRgG4FWGv76F/hv+1Cj2Z7";

    byte[] encoded = Base64.decodeBase64(privateKeyPEM);
    KeyFactory keyFactory = KeyFactory.getInstance("EC");
    PKCS8EncodedKeySpec keySpec = new PKCS8EncodedKeySpec(encoded);
    ECPrivateKey privateKey = (ECPrivateKey) keyFactory.generatePrivate(keySpec);

    final JwtBuilder jwtBuilder = Jwts.builder()
        .setSubject("713f42c9-7df5-4271-8b53-112f30936c56")
        .signWith(SignatureAlgorithm.ES512, privateKey)
        .setHeaderParam("typ", "JWT");

    System.out.println(jwtBuilder.compact());

However, the resulting JWT always have an invalid signature:

eyJ0eXAiOiJKV1QiLCJhbGciOiJFUzUxMiJ9.eyJzdWIiOiI3MTNmNDJjOS03ZGY1LTQyNzEtOGI1My0xMTJmMzA5MzZjNTYifQ.MIGHAkFvCPq_BeXvATTN1duKjEf3K_Fja0ueoTuPQHC9kBc828wem7YO0vnlK6PVYXSkBk4gBaD0-OIMY_r-HS7-4-HaBwJCAMbj0k5YsBywMzme_adKTQq7YUsVvyZwGp8aVgX7vxsMhf-WNvQJSg7AG_zQiUaQ4jqtT9ZKzNoU4P5NZIGMDRCh

I can't figure out what's wrong with my code.

The posted private key is a PKCS#8 key. From this the following public X.509 key can be derived:

<!-- language: lang-none -->
-----BEGIN PUBLIC KEY-----
MIGbMBAGByqGSM49AgEGBSuBBAAjA4GGAAQAlCI4gpXtiYhUjfRjfLVRki+BkVG+
IcVa9KJNcQbgirMcqkWM4hizSvOfUXbOsUcqmYy1nQqHk7PJ8mwZ67UZk/MA1gtl
D2bXcmiLd+EYVSAcs0vSGzP8dA/z1pNr1CvxCoQ/uv+8K+tygqf1wo8bBHE4WRGA
bgVYa/voX+G/7UKPZns=
-----END PUBLIC KEY-----

If a JWT is created with the posted code, e.g.:

<!-- language: lang-none -->
eyJ0eXAiOiJKV1QiLCJhbGciOiJFUzUxMiJ9.eyJzdWIiOiI3MTNmNDJjOS03ZGY1LTQyNzEtOGI1My0xMTJmMzA5MzZjNTYifQ.AE0sx6wHk2xBPkbam24n8NE39qkB0YX4j65DhrWyBKtaQXRMZjuzV78vFir3scfXVolFOf2gpo2K6x_hu0jPz-0IAIMbYQsglePQHQ9OZMSb2XAxKCVXccdvW27QeBov-VGUxxlL-CFNviaPaAGbNny_sc8cRjIF97pDD4KjOPBKkZzt

then this can be verified without problems with this public key, check it e.g. here, i.e. the posted code produces a valid signature.

On the other hand, the JWT posted in the question:

<!-- language: lang-none -->
eyJ0eXAiOiJKV1QiLCJhbGciOiJFUzUxMiJ9.eyJzdWIiOiI3MTNmNDJjOS03ZGY1LTQyNzEtOGI1My0xMTJmMzA5MzZjNTYifQ.MIGHAkFvCPq_BeXvATTN1duKjEf3K_Fja0ueoTuPQHC9kBc828wem7YO0vnlK6PVYXSkBk4gBaD0-OIMY_r-HS7-4-HaBwJCAMbj0k5YsBywMzme_adKTQq7YUsVvyZwGp8aVgX7vxsMhf-WNvQJSg7AG_zQiUaQ4jqtT9ZKzNoU4P5NZIGMDRCh

can indeed not be verified. The signature of this JWT is Base64url decoded:

<!-- language: lang-none -->
30818702416f08fabf05e5ef0134cdd5db8a8c47f72bf1636b4b9ea13b8f4070bd90173cdbcc1e9bb60ed2f9e52ba3d56174a4064e2005a0f4f8e20c63fafe1d2efee3e1da07024200c6e3d24e58b01cb033399efda74a4d0abb614b15bf26701a9f1a5605fbbf1b0c85ff9636f4094a0ec01bfcd0894690e23aad4fd64accda14e0fe4d64818c0d10a1

and thus ASN.1 encoded, s. here and here. However, JWTs use a signature encoded as r|s, see e.g. here. If the signature is converted to this encoding, the result is:

<!-- language: lang-none -->
6f08fabf05e5ef0134cdd5db8a8c47f72bf1636b4b9ea13b8f4070bd90173cdbcc1e9bb60ed2f9e52ba3d56174a4064e2005a0f4f8e20c63fafe1d2efee3e1da07c6e3d24e58b01cb033399efda74a4d0abb614b15bf26701a9f1a5605fbbf1b0c85ff9636f4094a0ec01bfcd0894690e23aad4fd64accda14e0fe4d64818c0d10a1

If this is Base64url encoded and used in the posted JWT (instead of the old signature), that is:

<!-- language: lang-none -->
eyJ0eXAiOiJKV1QiLCJhbGciOiJFUzUxMiJ9.eyJzdWIiOiI3MTNmNDJjOS03ZGY1LTQyNzEtOGI1My0xMTJmMzA5MzZjNTYifQ.bwj6vwXl7wE0zdXbioxH9yvxY2tLnqE7j0BwvZAXPNvMHpu2DtL55Suj1WF0pAZOIAWg9PjiDGP6_h0u_uPh2gfG49JOWLAcsDM5nv2nSk0Ku2FLFb8mcBqfGlYF-78bDIX_ljb0CUoOwBv80IlGkOI6rU_WSszaFOD-TWSBjA0QoQ

the JWT can be successfully validated.

Since the posted code generates an RFC compliant JWT (with r|s signature), the JWT posted in the question was probably not generated with the posted code (because of the ASN.1 signature).

Update: According to the jjwt bugtracker there is a bug (#125) that causes the signature to be signed incorrectly with ASN.1. This bug should be fixed with jjwt 0.7 and would be a plausible explanation for your issue, provided you are working with an affected version (the bug is from 05.2016).<br>I have tested your code with jjwt 0.9.1 (from 07.2018), which generates a valid signature, meaning it works.<br>The current version is jjwt 0.11.2 (from 06.2020), which also works according to the other answer.<br>So if you are working with an affected version, it would be best to use a newer / the current jjwt version. If this is not possible for some reason you can of course convert the signature manually from ASN.1 to r|s encoding.

My IntelliJ is claiming that the "signWith"-line is deprecated.

So changing your code

final JwtBuilder jwtBuilder = Jwts.builder()
  .setSubject("713f42c9-7df5-4271-8b53-112f30936c56")
  .signWith(SignatureAlgorithm.ES512, privateKey)
  .setHeaderParam("typ", "JWT");

to

final JwtBuilder jwtBuilder = Jwts.builder()
  .setSubject("713f42c9-7df5-4271-8b53-112f30936c56")
  .signWith(privateKey, SignatureAlgorithm.ES512)
  .setHeaderParam("typ", "JWT");

is giving this JWT:

eyJ0eXAiOiJKV1QiLCJhbGciOiJFUzUxMiJ9.eyJzdWIiOiI3MTNmNDJjOS03ZGY1LTQyNzEtOGI1My0xMTJmMzA5MzZjNTYifQ.ALFk_BGerAstughF4ssl5eGQmx0mu5jvWb13QB228hAD5g8dwM-NvBsyevCuYUXLBJKzIUdPL-LVwQoPkwIbYrKhACzKwUwRN_v3IX2GIPW2ctTcRGPwA7gUaDWrOtwqcHALSfk20QZXT2TQfOnXX8tv0vhXLK_SnnHH5o1b96sa_HSR

As you only provided the ec private key I used OpenSSL to generate the EC Public key and passed the JWT and public key to the Online JWT verifier https://jwt.io/
and got the result "Signature verified".