JOptionPane causes Java Plug-in to hang

When an applet is signed with RSA, Java Plug-in will popup a security dialog using the modal JOptionPane:

JDialog dialog = pane.createDialog(null, title);
dialog.setResizeable(false);
dialog.setModal(true);
dialog.show(); <-- hang
dialog.toFront();

The bug can be demonstrated at http://javaweb.eng/~sridhare/tests/RSA/st13Veri.html.

Notice that the same plug-in using Kestrel/Firefly/Ladybird do not have this problem, so this problem is probably on the Swing side.

This bug occurs on all platforms - Windows/Solaris/Linux.