打破RSA需要什么？

Question

如果我们捕获公共指数和模数（即使用中间人攻击），许多人会问如何破解RSA密码。 Bellow I我提出了非压缩密码的强力解决方案。可能有人会分享其他解决方案吗？

import javax.swing.*;
import javax.swing.text.*;
import java.awt.*;
import java.awt.event.*;
import java.math.BigInteger;

/**
 * Applet break simple RSA cipher using public exponent and modulus.
 * Remember that it is brute-force attack, so breaking time depend on your machine.
 * 
 * @author Tomasz Kanik [yetiicom(at)wp(dot)eu]
 * @see {@link http://en.wikipedia.org/wiki/RSA} for details about RSA algorithm
 */
public class RSACracker extends JApplet implements ActionListener {
 private static final long serialVersionUID = 1L;
 String[] fieldNames = { "Modulus(n):", "Public exponent(e):", "Cipher(c):", "Message(m):" };
 JComponent[] jca = new JComponent[fieldNames.length];
 int[][] fs = { { 16, 1 }, { 16, 1 }, { 16, 1 }, { 16, 10 } };
 Container cp;

 @Override
 public void init() {
  cp = getContentPane();
  cp.setLayout(new GridBagLayout());
  GridBagConstraints gbc = new GridBagConstraints();
  gbc.anchor = GridBagConstraints.WEST;
  gbc.insets = new Insets(5, 10, 5, 5);
  for (int i = 0; i < fieldNames.length; ++i) {
   gbc.gridwidth = GridBagConstraints.RELATIVE;
   cp.add(new JLabel(fieldNames[i]), gbc);
   gbc.gridwidth = GridBagConstraints.REMAINDER;
   if (fs[i][1] == 1) {
    JTextField tf = new JTextField(fs[i][0]);
    jca[i] = tf;
    cp.add(tf, gbc);
   } else {
    JTextArea ta = new JTextArea(fs[i][1], fs[i][0]);
    ta.setLineWrap(true);
    ta.setWrapStyleWord(true);
    JScrollPane jsp = new JScrollPane(ta,
      JScrollPane.VERTICAL_SCROLLBAR_ALWAYS,
      JScrollPane.HORIZONTAL_SCROLLBAR_NEVER);
    jca[i] = ta;
    cp.add(jsp, gbc);
   }
  }
  JButton b = new JButton("Calculate");
  b.addActionListener(this);
  gbc.anchor = GridBagConstraints.EAST;
  cp.add(b, gbc);
  cp.setSize(400, 400);

  //My Test: p=51407, q=63667, message=123456
  ((JTextComponent) jca[0]).setText("1760806643"); //n - modulus
  ((JTextComponent) jca[1]).setText("65537"); //e - public exponent
  ((JTextComponent) jca[2]).setText("818474911"); //c - cipher

  //Wiki Test: p = 61 and q = 53, message = 65
//  ((JTextComponent) jca[0]).setText("3233"); //n - modulus
//  ((JTextComponent) jca[1]).setText("17"); //e - public exponent
//  ((JTextComponent) jca[2]).setText("2790"); //c - cipher
 }

 @Override
 public void start() {
  setSize(450, 450);
  repaint();
 }

 public void actionPerformed(ActionEvent evt) {
  BigInteger n = new BigInteger(((JTextComponent) jca[0]).getText());
  BigInteger e = new BigInteger(((JTextComponent) jca[1]).getText());
  BigInteger c = new BigInteger(((JTextComponent) jca[2]).getText());

  BigInteger p = BigInteger.ONE;
  BigInteger q = BigInteger.ZERO;

  while(true)
  {
   p = p.add(BigInteger.ONE);
            if (n.mod(p).compareTo(BigInteger.ZERO) == 0)
            {
             q = n.divide(p);
                if (p.multiply(q).compareTo(n) == 0)
                    break;
            }
        }
  BigInteger totient=p.subtract(BigInteger.ONE).multiply(q.subtract(BigInteger.ONE));
//  System.out.println("p="+p+"\n"+"q="+q+"\n"+"totient="+totient);

  BigInteger d = e.modInverse(totient);
  BigInteger m = c.modPow(d, n);

  ((JTextComponent) jca[fieldNames.length-1]).setText(m.toString());
 }
}