JWTs can be "successfully" encoded and decoded even when algorithm does not match the EC curve type

[DavidBuchanan314]

You can generate a SECP256K1 keypair and then tell pyjwt to sign a message using algorithm "ES256".

Expected Result

An exception should be raised, because the SECP256K1 curve is not compatible with the ES256 algorithm (it wants ES256K).

Actual Result

An invalid JWT is encoded (signature will not verify against declared algorithm).

Subsequently, the invalid JWT can be decoded "successfully" without error.

This is arguably a security issue, but it only arises if you use the API "wrong". Nonetheless, I think the API should try to guard against such incorrect uses.

Reproduction Steps

from cryptography.hazmat.primitives.asymmetric import ec
import jwt

#KEY_TYPE = ec.SECP256R1()
KEY_TYPE = ec.SECP256K1()

privkey = ec.generate_private_key(KEY_TYPE)

my_jwt = jwt.encode(
	{ "hello": "world" },
	privkey,
	algorithm="ES256", # nistp256 aka ec.SECP256R1()
)

print(my_jwt) # I think this should raise an exception!

decoded = jwt.decode(my_jwt, key=privkey.public_key(), algorithms=["ES256"])

print(decoded) # This should raise an exception even more so!

System Information

$ python -m jwt.help

{
  "cryptography": {
    "version": "41.0.7"
  },
  "implementation": {
    "name": "CPython",
    "version": "3.12.7"
  },
  "platform": {
    "release": "6.11.0-400.asahi.fc40.aarch64+16k",
    "system": "Linux"
  },
  "pyjwt": {
    "version": "2.10.0"
  }
}

[DavidBuchanan314]

p.s. it would be nice if I didn't have to pass algorithm explicitly, since the correct algorithm to use can be inferred from the passed key type, assuming the passed key is an object (and not just a string or whatever).