[jwt] RS256 vs HS256: What's the difference?

I'm using Auth0 to handle authentication in my web app. I'm using ASP.NET Core v1.0.0 and Angular 2 rc5 and I don't know much about authentication/security in general.

In the Auth0 docs for ASP.NET Core Web Api, there are two choices for the JWT algorithm being RS256 and HS256. This may be a dumb question but:

What's the difference between RS256 and HS256? What are some use cases (if applicable)?

There is a difference in performance.

Simply put HS256 is about 1 order of magnitude faster than RS256 for verification but about 2 orders of magnitude faster than RS256 for issuing (signing).

 640,251  91,464.3 ops/s
  86,123  12,303.3 ops/s (RS256 verify)
   7,046   1,006.5 ops/s (RS256 sign)

Don't get hung up on the actual numbers, just think of them with respect of each other.

[Program.cs]

class Program
{
    static void Main(string[] args)
    {
        foreach (var duration in new[] { 1, 3, 5, 7 })
        {
            var t = TimeSpan.FromSeconds(duration);

            byte[] publicKey, privateKey;

            using (var rsa = new RSACryptoServiceProvider())
            {
                publicKey = rsa.ExportCspBlob(false);
                privateKey = rsa.ExportCspBlob(true);
            }

            byte[] key = new byte[64];

            using (var rng = new RNGCryptoServiceProvider())
            {
                rng.GetBytes(key);
            }

            var s1 = new Stopwatch();
            var n1 = 0;

            using (var hs256 = new HMACSHA256(key))
            {
                while (s1.Elapsed < t)
                {
                    s1.Start();
                    var hash = hs256.ComputeHash(privateKey);
                    s1.Stop();
                    n1++;
                }
            }

            byte[] sign;

            using (var rsa = new RSACryptoServiceProvider())
            {
                rsa.ImportCspBlob(privateKey);

                sign = rsa.SignData(privateKey, "SHA256");
            }

            var s2 = new Stopwatch();
            var n2 = 0;

            using (var rsa = new RSACryptoServiceProvider())
            {
                rsa.ImportCspBlob(publicKey);

                while (s2.Elapsed < t)
                {
                    s2.Start();
                    var success = rsa.VerifyData(privateKey, "SHA256", sign);
                    s2.Stop();
                    n2++;
                }
            }

            var s3 = new Stopwatch();
            var n3 = 0;

            using (var rsa = new RSACryptoServiceProvider())
            {
                rsa.ImportCspBlob(privateKey);

                while (s3.Elapsed < t)
                {
                    s3.Start();
                    rsa.SignData(privateKey, "SHA256");
                    s3.Stop();
                    n3++;
                }
            }

            Console.WriteLine($"{s1.Elapsed.TotalSeconds:0} {n1,7:N0} {n1 / s1.Elapsed.TotalSeconds,9:N1} ops/s");
            Console.WriteLine($"{s2.Elapsed.TotalSeconds:0} {n2,7:N0} {n2 / s2.Elapsed.TotalSeconds,9:N1} ops/s");
            Console.WriteLine($"{s3.Elapsed.TotalSeconds:0} {n3,7:N0} {n3 / s3.Elapsed.TotalSeconds,9:N1} ops/s");

            Console.WriteLine($"RS256 is {(n1 / s1.Elapsed.TotalSeconds) / (n2 / s2.Elapsed.TotalSeconds),9:N1}x slower (verify)");
            Console.WriteLine($"RS256 is {(n1 / s1.Elapsed.TotalSeconds) / (n3 / s3.Elapsed.TotalSeconds),9:N1}x slower (issue)");

            // RS256 is about 7.5x slower, but it can still do over 10K ops per sec.
        }
    }
}

short answer, specific to OAuth2,

• HS256 user client secret to generate the token signature and same secret is required to validate the token in back-end. So you should have a copy of that secret in your back-end server to verify the signature.
• RS256 use public key encryption to sign the token.Signature(hash) will create using private key and it can verify using public key. So, no need of private key or client secret to store in back-end server, but back-end server will fetch the public key from openid configuration url in your tenant (https://[tenant]/.well-known/openid-configuration) to verify the token. KID parameter inside the access_toekn will use to detect the correct key(public) from openid-configuration.

In cryptography there are two types of algorithms used:

Symmetric algorithms

A single key is used to encrypt data. When encrypted with the key, the data can be decrypted using the same key. If, for example, Mary encrypts a message using the key "my-secret" and sends it to John, he will be able to decrypt the message correctly with the same key "my-secret".

Asymmetric algorithms

Two keys are used to encrypt and decrypt messages. While one key(public) is used to encrypt the message, the other key(private) can only be used to decrypt it. So, John can generate both public and private keys, then send only the public key to Mary to encrypt her message. The message can only be decrypted using the private key.

HS256 and RS256 Scenario

These algorithms are NOT used to encrypt/decryt data. Rather they are used to verify the origin or the authenticity of the data. When Mary needs to send an open message to Jhon and he needs to verify that the message is surely from Mary, HS256 or RS256 can be used.

HS256 can create a signature for a given sample of data using a single key. When the message is transmitted along with the signature, the receiving party can use the same key to verify that the signature matches the message.

RS256 uses pair of keys to do the same. A signature can only be generated using the private key. And the public key has to be used to verify the signature. In this scenario, even if Jack finds the public key, he cannot create a spoof message with a signature to impersonate Mary.