Convert byte array to BigInteger incorrect-CodePudding

Since I tried to simulate the connection between my client and my server working on packet, I have been in the struggle with byte array and BigInteger.

When my client connected to the server, the server sent a response which include an RSA public key, then a packet in hex just like this:

C70001A100408031313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131E5AA194C3DBA71F9A38AF85D43C130A462BDCBACF85ED702B5E2FECB47197DAA433E7B5ACF5EF09A07C5DDE79B7A2EED76B91090CB981E13DBE316997FCF5DC51BE40B2D02D912457D97924B94094227F8BC65DD61FE78060B55BEAAA31C64E3B36863B407F7183DABA9D98F0C9061DED36AD16407F70C4925951BAA8807EC95

The 64 byte after C70001A1004080 is the RSA public exponent. The 128 byte next after RSA exponent is the modulus.

Then I tried to extract the exponent and the modulus to re-generate an RSA public key. My steps:

if (socket == null) socket = new Socket(loginHost, loginPort);
if (is == null) is = socket.getInputStream();
if (os == null) os = socket.getOutputStream();

int packageLength = 199;

byte[] response = IOUtils.toByteArray(is, packageLength); 

byte[] rsaPubExponentBytes = Arrays.copyOfRange(response, 7, 71);
byte[] rsaModuloBytes = Arrays.copyOfRange(response, 71, packageLength);

BigInteger rsaPubExponentNumber = new BigInteger(1, rsaPubExponentBytes);
BigInteger rsaModuloNumber = new BigInteger(1, rsaModuloBytes);

PublicKey pub = null;

try {
    RSAPublicKeySpec spec = new RSAPublicKeySpec(rsaModuloNumber, rsaPubExponentNumber);
    KeyFactory factory = KeyFactory.getInstance("RSA");
            
    pub = factory.generatePublic(spec);
} catch (NoSuchAlgorithmException | InvalidKeySpecException e) {
    e.printStackTrace();
}

Finally I had a public key:

Sun RSA public key, 1024 bits
  modulus: 161275860318613570660794349609651113455378591213521007305334206887210873414776462027746458127536797075994278751416175612148660222076731030937875746805281690156725876857482174279314968596913890067397869829419019179316569148699704292044128937649866682741942026327643537075317389490824101005022833230463069842581
  public exponent: 2576402308106616697565204803576809648025446765525597158856684355852417401857269811228595453373248109634555141377011045066015451991315223244608818828620081

Compare to the RSA from the server

Sun RSA public key, 1024 bits
  modulus: 105278801605955351183032861925660079240049371193037037019863031780531990060755731057393990664319512505978954889835933668032824049054190807125138251307247771506918060803959346902566451812689470408398611041302277800747341495594297701677567604614145074223483256879948522462707345079591319551080307454838134385381
  public exponent: 2576402308106616697565204803576809648025446765525597158856684355852417401857269811228595453373248109634555141377011045066015451991315223244608818828620081

Then the the modulus was wrong. I double checked by converting BigInteger to byte array and show it with hex

System.out.println(bytesToHex(rsaPubExponentNumber.toByteArray()));
System.out.println(bytesToHex(rsaModuloNumber.toByteArray()));

private String bytesToHex(byte[] bytes) {
    StringBuilder sb = new StringBuilder();
    for (byte b : bytes) {
       sb.append(String.format("X ", b));
    }
    return sb.toString().replaceAll(" ", "");
}

The result is:

Exponent: 31313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131

Modulus 00E5AA194C3DBA71F9A38AF85D43C130A462BDCBACF85ED702B5E2FECB47197DAA433E7B5ACF5EF09A07C5DDE79B7A2EED76B91090CB981E13DBE316997FCF5DC51BE40B2D02D912457D97924B94094227F8BC65DD61FE78060B55BEAAA31C64E3B36863B407F7183DABA9D98F0C9061DED36AD16407F70C4925951BAA8807EC95

The modulus now has 00 at the beginning and the public key was generated, but incorrect one.

I also tried:

BigInteger exponent = new BigInteger(exponentHexString, 16);
BigInteger modulus = new BigInteger(modulusHexString, 16);

However, the result still the same. How can I fix this?

CodePudding user response：

This code would not compile. You have the mistake here (rsaModuloNumber as an argument to create rsaModuloNumber):

BigInteger rsaModuloNumber = new BigInteger(1, rsaModuloNumber);

And you initiating two variables with same name:

PublicKey pub = null;

and

PublicKey pub = factory.generatePublic(spec);

CodePudding user response：

Lets go through your code and packet stream structure.

You have the following binary stream encoded as a hex string:

C70001A100408031313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131E5AA194C3DBA71F9A38AF85D43C130A462BDCBACF85ED702B5E2FECB47197DAA433E7B5ACF5EF09A07C5DDE79B7A2EED76B91090CB981E13DBE316997FCF5DC51BE40B2D02D912457D97924B94094227F8BC65DD61FE78060B55BEAAA31C64E3B36863B407F7183DABA9D98F0C9061DED36AD16407F70C4925951BAA8807EC95

According to your code:

bytes from index 7 to 71 are your exponent bytes,
bytes from index 71 till the end of the stream are your modulus bytes.

IIUC, you want to extract the exponent and the modulus from the above byte string.

The issue you are facing stems from the fact that in cryptography, the numbers are typically unsigned integers, with a protocol-defined byte order, whereas Java's BigIntegers are big-endian, signed integers.

In order to convert an arbitrary integer (signed/unsigned, big-endian/little-endian) into a BigInteger, one has to to perform some machinations.

In your case, it's enough to simply reverse the byte arrays, as suggested in the comments:

int packageLength = 199;

byte[] response = IOUtils.toByteArray(is, packageLength); 

byte[] rsaPubExponentBytes = Arrays.copyOfRange(response, 7, 71);
byte[] rsaModuloBytes = Arrays.copyOfRange(response, 71, packageLength);

// missing step!
reverse(rsaPubExponentBytes);
reverse(rsaModuloBytes);

BigInteger rsaPubExponentNumber = new BigInteger(1, rsaPubExponentBytes);
BigInteger rsaModuloNumber = new BigInteger(1, rsaModuloBytes);
// ...

public static void reverse(byte[] arr) {
    for (int i = 0; i < arr.length / 2) {
        int tmp = arr[i]
        arr[i] = arr[arr.length - 1 - i];
        arr[arr.length - 1 - i] = tmp;
    }
}

I've ran into a similar issue when working on a project of mine. You might find my library, SRP-6 Variables, helpful:

byte[] stream = new Hex("C70001A100408031313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131313131E5AA194C3DBA71F9A38AF85D43C130A462BDCBACF85ED702B5E2FECB47197DAA433E7B5ACF5EF09A07C5DDE79B7A2EED76B91090CB981E13DBE316997FCF5DC51BE40B2D02D912457D97924B94094227F8BC65DD61FE78060B55BEAAA31C64E3B36863B407F7183DABA9D98F0C9061DED36AD16407F70C4925951BAA8807EC95").asArray();

BigInteger exponent = 
    new SRP6CustomIntegerVariable(
        Bytes.wrapped(Arrays.copyOfRange(stream, 7, 71)),
        ByteOrder.LITTLE_ENDIAN
    ).asNonNegativeBigInteger();
BigInteger modulus = 
    new SRP6CustomIntegerVariable(
        Bytes.wrapped(Arrays.copyOfRange(stream, 71, stream.length)),
        ByteOrder.LITTLE_ENDIAN
    ).asNonNegativeBigInteger();