Your best bet is probably to get the Mac address of the network card (one of them, at least).
I suggest to google for java get mac address or similar, to see if it is possible easily.

Hey, thanks for having done the research. Conversion to Processing code is pretty straightforward:

1. import java.net.InetAddress;
2. import java.net.NetworkInterface;
3. import java.net.SocketException;
4. import java.net.UnknownHostException;
5.  
6. void start()
7. {
8.   InetAddress ip;
9.   try
10.   {
11.     ip = InetAddress.getLocalHost();
12.     println("Current IP address: " + ip.getHostAddress());
13.  
14.     NetworkInterface network = NetworkInterface.getByInetAddress(ip);
15.  
16.     byte[] mac = network.getHardwareAddress();
17.  
18.     print("Current MAC address: ");
19.  
20.     StringBuilder sb = new StringBuilder();
21.     for (int i = 0; i < mac.length; i++)
22.     {
23.       sb.append(String.format("%02X%s", mac[i], (i < mac.length - 1) ? "-" : ""));
24.     }
25.     println(sb.toString());
26.   }
27.   catch (UnknownHostException e)
28.   {
29.     e.printStackTrace();
30.   }
31.   catch (SocketException e)
32.   {
33.     e.printStackTrace();
34.   }
35. }

Thanks PhiLo