Verifying JWT signed with the RS256 algorithm using public key in C#

Question

Ok, I understand that the question I am asking may be pretty obvious, but unfortunately I lack the knowledge on this subject and this task seems to be quite tricky for me.

I have an id token (JWT) returned by OpenID Connect Provider. Here it is:

eyJraWQiOiIxZTlnZGs3IiwiYWxnIjoiUlMyNTYifQ.ewogImlzcyI6ICJodHRwOi8vc2VydmVyLmV4YW1wbGUuY29tIiwKICJzdWIiOiAiMjQ4Mjg5NzYxMDAxIiwKICJhdWQiOiAiczZCaGRSa3F0MyIsCiAibm9uY2UiOiAibi0wUzZfV3pBMk1qIiwKICJleHAiOiAxMzExMjgxOTcwLAogImlhdCI6IDEzMTEyODA5NzAsCiAiY19oYXNoIjogIkxEa3RLZG9RYWszUGswY25YeENsdEEiCn0.XW6uhdrkBgcGx6zVIrCiROpWURs-4goO1sKA4m9jhJIImiGg5muPUcNegx6sSv43c5DSn37sxCRrDZZm4ZPBKKgtYASMcE20SDgvYJdJS0cyuFw7Ijp_7WnIjcrl6B5cmoM6ylCvsLMwkoQAxVublMwH10oAxjzD6NEFsu9nipkszWhsPePf_rM4eMpkmCbTzume-fzZIi5VjdWGGEmzTg32h3jiex-r5WTHbj-u5HL7u_KP3rmbdYNzlzd1xWRYTUs4E8nOTgzAUwvwXkIQhOh5TPcSMBYy6X3E7-_gr9Ue6n4ND7hTFhtjYs3cjNKIA08qm5cpVYFMFMG6PkhzLQ

Its header and payload are decoded as this:

{
 "kid":"1e9gdk7",
 "alg":"RS256"
}.
{
 "iss": "http://server.example.com",
 "sub": "248289761001",
 "aud": "s6BhdRkqt3",
 "nonce": "n-0S6_WzA2Mj",
 "exp": 1311281970,
 "iat": 1311280970,
 "c_hash": "LDktKdoQak3Pk0cnXxCltA"
}

From the OIDC provider's discovery, I've got the public key (JWK):

{
 "kty":"RSA",
 "kid":"1e9gdk7",
 "n":"w7Zdfmece8iaB0kiTY8pCtiBtzbptJmP28nSWwtdjRu0f2GFpajvWE4VhfJAjEsOcwYzay7XGN0b-X84BfC8hmCTOj2b2eHT7NsZegFPKRUQzJ9wW8ipn_aDJWMGDuB1XyqT1E7DYqjUCEOD1b4FLpy_xPn6oV_TYOfQ9fZdbE5HGxJUzekuGcOKqOQ8M7wfYHhHHLxGpQVgL0apWuP2gDDOdTtpuld4D2LK1MZK99s9gaSjRHE8JDb1Z4IGhEcEyzkxswVdPndUWzfvWBBWXWxtSUvQGBRkuy1BHOa4sP6FKjWEeeF7gm7UMs2Nm2QUgNZw6xvEDGaLk4KASdIxRQ",
 "e":"AQAB"
}

So, the question is how exactly in C# can I verify this JWT using the public key for the RS256 algorithm I've got? It would be awesome if there is a good tutorial describing this procedure explicitly. However, an example of how to do this using System.IdentityModel.Tokens.Jwt will also work fine.

UPDATE: I understand, that I need to do something like the code below, but I have no idea where to get 'key' for calculating SHA256 hash.

  string tokenStr = "eyJraWQiOiIxZTlnZGs3IiwiYWxnIjoiUlMyNTYifQ.ewogImlzcyI6ICJodHRwOi8vc2VydmVyLmV4YW1wbGUuY29tIiwKICJzdWIiOiAiMjQ4Mjg5NzYxMDAxIiwKICJhdWQiOiAiczZCaGRSa3F0MyIsCiAibm9uY2UiOiAibi0wUzZfV3pBMk1qIiwKICJleHAiOiAxMzExMjgxOTcwLAogImlhdCI6IDEzMTEyODA5NzAsCiAiY19oYXNoIjogIkxEa3RLZG9RYWszUGswY25YeENsdEEiCn0.XW6uhdrkBgcGx6zVIrCiROpWURs-4goO1sKA4m9jhJIImiGg5muPUcNegx6sSv43c5DSn37sxCRrDZZm4ZPBKKgtYASMcE20SDgvYJdJS0cyuFw7Ijp_7WnIjcrl6B5cmoM6ylCvsLMwkoQAxVublMwH10oAxjzD6NEFsu9nipkszWhsPePf_rM4eMpkmCbTzume-fzZIi5VjdWGGEmzTg32h3jiex-r5WTHbj-u5HL7u_KP3rmbdYNzlzd1xWRYTUs4E8nOTgzAUwvwXkIQhOh5TPcSMBYy6X3E7-_gr9Ue6n4ND7hTFhtjYs3cjNKIA08qm5cpVYFMFMG6PkhzLQ";
  string[] tokenParts = tokenStr.Split('.');

  RSACryptoServiceProvider rsa = new RSACryptoServiceProvider();
  rsa.ImportParameters(
    new RSAParameters() {
      Modulus = FromBase64Url("w7Zdfmece8iaB0kiTY8pCtiBtzbptJmP28nSWwtdjRu0f2GFpajvWE4VhfJAjEsOcwYzay7XGN0b-X84BfC8hmCTOj2b2eHT7NsZegFPKRUQzJ9wW8ipn_aDJWMGDuB1XyqT1E7DYqjUCEOD1b4FLpy_xPn6oV_TYOfQ9fZdbE5HGxJUzekuGcOKqOQ8M7wfYHhHHLxGpQVgL0apWuP2gDDOdTtpuld4D2LK1MZK99s9gaSjRHE8JDb1Z4IGhEcEyzkxswVdPndUWzfvWBBWXWxtSUvQGBRkuy1BHOa4sP6FKjWEeeF7gm7UMs2Nm2QUgNZw6xvEDGaLk4KASdIxRQ"),
      Exponent = FromBase64Url("AQAB")
    });

  HMACSHA256 sha = new HMACSHA256(key);
  byte[] hash = sha.ComputeHash(Encoding.UTF8.GetBytes(tokenParts[0] + '.' + tokenParts[1]));
  byte[] signature = rsa.Encrypt(hash, false);
  string strSignature = Base64UrlEncode(signature);
  if (String.Compare(strSignature, tokenParts[2], false) == 0)
    return true;

Answer 1

Thanks to jwilleke, I have got a solution. To verify the RS256 signature of a JWT, it is needed to use the RSAPKCS1SignatureDeformatter class and its VerifySignature method.

Here is the exact code for my sample data:

  string tokenStr = "eyJraWQiOiIxZTlnZGs3IiwiYWxnIjoiUlMyNTYifQ.ewogImlzcyI6ICJodHRwOi8vc2VydmVyLmV4YW1wbGUuY29tIiwKICJzdWIiOiAiMjQ4Mjg5NzYxMDAxIiwKICJhdWQiOiAiczZCaGRSa3F0MyIsCiAibm9uY2UiOiAibi0wUzZfV3pBMk1qIiwKICJleHAiOiAxMzExMjgxOTcwLAogImlhdCI6IDEzMTEyODA5NzAsCiAiY19oYXNoIjogIkxEa3RLZG9RYWszUGswY25YeENsdEEiCn0.XW6uhdrkBgcGx6zVIrCiROpWURs-4goO1sKA4m9jhJIImiGg5muPUcNegx6sSv43c5DSn37sxCRrDZZm4ZPBKKgtYASMcE20SDgvYJdJS0cyuFw7Ijp_7WnIjcrl6B5cmoM6ylCvsLMwkoQAxVublMwH10oAxjzD6NEFsu9nipkszWhsPePf_rM4eMpkmCbTzume-fzZIi5VjdWGGEmzTg32h3jiex-r5WTHbj-u5HL7u_KP3rmbdYNzlzd1xWRYTUs4E8nOTgzAUwvwXkIQhOh5TPcSMBYy6X3E7-_gr9Ue6n4ND7hTFhtjYs3cjNKIA08qm5cpVYFMFMG6PkhzLQ";
  string[] tokenParts = tokenStr.Split('.');

  RSACryptoServiceProvider rsa = new RSACryptoServiceProvider();
  rsa.ImportParameters(
    new RSAParameters() {
      Modulus = FromBase64Url("w7Zdfmece8iaB0kiTY8pCtiBtzbptJmP28nSWwtdjRu0f2GFpajvWE4VhfJAjEsOcwYzay7XGN0b-X84BfC8hmCTOj2b2eHT7NsZegFPKRUQzJ9wW8ipn_aDJWMGDuB1XyqT1E7DYqjUCEOD1b4FLpy_xPn6oV_TYOfQ9fZdbE5HGxJUzekuGcOKqOQ8M7wfYHhHHLxGpQVgL0apWuP2gDDOdTtpuld4D2LK1MZK99s9gaSjRHE8JDb1Z4IGhEcEyzkxswVdPndUWzfvWBBWXWxtSUvQGBRkuy1BHOa4sP6FKjWEeeF7gm7UMs2Nm2QUgNZw6xvEDGaLk4KASdIxRQ"),
      Exponent = FromBase64Url("AQAB")
    });

  SHA256 sha256 = SHA256.Create();
  byte[] hash = sha256.ComputeHash(Encoding.UTF8.GetBytes(tokenParts[0] + '.' + tokenParts[1]));

  RSAPKCS1SignatureDeformatter rsaDeformatter = new RSAPKCS1SignatureDeformatter(rsa);
  rsaDeformatter.SetHashAlgorithm("SHA256");
  if (rsaDeformatter.VerifySignature(hash, FromBase64Url(tokenParts[2])))
    MessageBox.Show("Signature is verified");

//...
  static byte[] FromBase64Url(string base64Url)
  {
    string padded = base64Url.Length % 4 == 0
        ? base64Url : base64Url + "====".Substring(base64Url.Length % 4);
    string base64 = padded.Replace("_", "/")
                          .Replace("-", "+");
    return Convert.FromBase64String(base64);
  }