encryption - Using SHA1 and RSA with java.security.Signature vs. MessageDigest and Cipher

Question

I'm trying to understand what the Java java.security.Signature class does. If I compute an SHA1 message digest, and then encrypt that digest using RSA, I get a different result to asking the Signature class to sign the same thing:

// Generate new key
KeyPair keyPair = KeyPairGenerator.getInstance("RSA").generateKeyPair();
PrivateKey privateKey = keyPair.getPrivate();
String plaintext = "This is the message being signed";

// Compute signature
Signature instance = Signature.getInstance("SHA1withRSA");
instance.initSign(privateKey);
instance.update((plaintext).getBytes());
byte[] signature = instance.sign();

// Compute digest
MessageDigest sha1 = MessageDigest.getInstance("SHA1");
byte[] digest = sha1.digest((plaintext).getBytes());

// Encrypt digest
Cipher cipher = Cipher.getInstance("RSA");
cipher.init(Cipher.ENCRYPT_MODE, privateKey);
byte[] cipherText = cipher.doFinal(digest);

// Display results
System.out.println("Input data: " + plaintext);
System.out.println("Digest: " + bytes2String(digest));
System.out.println("Cipher text: " + bytes2String(cipherText));
System.out.println("Signature: " + bytes2String(signature));

Results in (for example):

Input data: This is the message being signed
Digest: 62b0a9ef15461c82766fb5bdaae9edbe4ac2e067
Cipher text: 057dc0d2f7f54acc95d3cf5cba9f944619394711003bdd12...
Signature: 7177c74bbbb871cc0af92e30d2808ebae146f25d3fd8ba1622...

I must have a fundamental misunderstanding of what Signature is doing - I've traced through it, and it appears to be calling update on a MessageDigest object, with the algorithm set to SHA1 as I would expect, then getting the digest, then doing the encryption. What's making the results differ?

EDIT:

Leonidas made me check whether the signature scheme is supposed to do what I think it does. There are two types of signature defined in the RFC:

• RSASSA-PKCS1-v1_5
• RSASSA-PSS

The first of these (PKCS1) is the one I describe above. It uses a hash function to create a digest, and then encrypts the result with a private key.

The second algorithm uses a random salt value, and is more secure but non-deterministic. The signature produced from the code above does not change if the same key is used repeatedly, so I don't think it can be PSS.

EDIT:

Here's the bytes2string method I was using:

private static String bytes2String(byte[] bytes) {
    StringBuilder string = new StringBuilder();
    for (byte b : bytes) {
        String hexString = Integer.toHexString(0x00FF & b);
        string.append(hexString.length() == 1 ? "0" + hexString : hexString);
    }
    return string.toString();
}

Answer 1

OK, I've worked out what's going on. Leonidas is right, it's not just the hash that gets encrypted (in the case of the Cipher class method), it's the ID of the hash algorithm concatenated with the digest:

  DigestInfo ::= SEQUENCE {
      digestAlgorithm AlgorithmIdentifier,
      digest OCTET STRING
  }

Which is why the encryption by the Cipher and Signature are different.