破解 RSA 的有效方法？

Question

我正在尝试找到一种更有效的方法来破解 RSA 密码。 下面的非常非优化的小程序使用公共指数和模数破解了简单的 RSA 密码。请记住，这是暴力攻击，因此破解时间取决于您的机器。

编辑：我正在寻找基于代码的解决方案，而不是寻找有关如何解决问题的理论。

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

public class RSACracker extends JApplet implements ActionListener {
    private static final long serialVersionUID = 1 L;
    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());
    }
}