RSA算法实验报告

1、精选优质文档-倾情为你奉上实验二 非对称密码算法RSA一、实验目的通过实际编程了解非对称密码算法RSA的加密和解密过程，加深对非对称密码算法的认识。二、实验环境运行Windows或Linux操作系统的PC机，具有JDK1.6版本的Java语言编译环境。三、实验内容和步骤1. 对RSA算法的理解RSA算法（公开密钥算法）的原理：(1) 选择两个大的素数p和q（典型情况下为1024位）(2) 计算n = p * q 和 z =（p-1）*（q-1）.(3) 选择一个与z互素的数，将它称为d(4) 找到e，使其满足e*d = 1 mod z提前计算出这些参数以后，我们就可以开始执行加密了。首先将明文

2、分成块，使得每个明文消息P落在间隔0*P<n中。为了做到这一点，只要将明文划分成k位的块即可，这里k是满足2k<n的最大整数。为了加密一个消息P，只要计算C=Pe(mod n) 即可。为了解密C，只要计算P=Cd(mod n)即可。可以证明，对于指定范围内的所有P，加密盒解密互为反函数。为了执行加密，你需要e和n；为了执行解密，你需要d和n。因此，公钥是有（e，n）对组成，而私钥是有（d，n）对组成。实例：根据已知参数：p=3，q=11，M=2，计算公私钥，并对明文进行加密，然后对密文进行解密。由题意知：n = p * q33，z =（p-1）*（q-1）20，选d7，计算得e=3

3、，所以C=Me(mod n)8M=Cd(mod n)22、RSA算法与DES算法的比较：运行附件的RSATool，输入一大段文字，记录运行时间。再使用DES算法加密相同的文字，记录运行时间，对比这两个时间发现，RSA算法比DES算法慢很多，因为RSA算法进行的是大数运算，所以程序运行的速度比DES慢很多。因此RSA算法只适合于少量数据加密，不适合于大量数据加密。3、算法设计主要的方法：（1）、public static void GetPrime()方法名称：产生大数的方法。说明：利用Java语言的中的java.math.BigInteger类的方法中随机产生大数。（2）、public sta

4、tic boolean MillerRobin(BigInteger num)方法名称：判断是否是素数的方法。参数说明：num是由GetPrime方法产生的大数。说明：这个方法判断GetPrime方法传过来的是否是一个素数，是就返回true,否就返回false。（3）、public static BigInteger powmod( BigInteger a, BigInteger t, BigInteger num )方法名称：大数的幂运算方法。说明：这个方法对传入的大数进行幂运算。（4）、public static BigInteger invmod(BigInteger a, BigIn

5、teger b)方法名称：大数的取模运算方法。说明：这个方法对大数进行取模运算。（5）、public static String Encode(String inStr,BigInteger PrimeP,BigInteger PrimeQ, BigInteger n,int nLen,int m,JTextField d)方法名称：加密算法。参数说明：inStr是从界面输入的明文。PrimeP和PrimeQ是由GetPrime方法产生的两个大素数。n是由PrimeP和PrimeQ得到的值。nLen为n的长度。d为公钥。（6）、public static String Decode(Strin

6、g inStr,BigInteger PrimeP,BigInteger PrimeQ, BigInteger n,int nLen,int m,JTextField e)方法名称：解密算法。参数说明：inStr是从界面输入的明文。PrimeP和PrimeQ是由GetPrime方法产生的两个大素数。n是由PrimeP和PrimeQ得到的值。nLen为n的长度。e为私钥。4、源程序：（RSA1.java文件）import javax.swing.*; import java.awt.event.*; import java.math.*; import java.util.*; import j

7、ava.awt.*; import java.io.*; public class RSA1 public static void main(String args) MyFrame frame = new MyFrame(); MyPanel_fbutton panel_fbutton = new MyPanel_fbutton(frame,frame.P,frame.Q,frame.d,frame.e); FlowLayout fl = new FlowLayout (FlowLayout.CENTER,0,0); frame.setLayout(fl); frame.add(panel_

8、fbutton); frame.setBounds( 150, 100, 500, 480 ); frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE); frame.setVisible(true); class MyFrame extends JFrame public MyFrame() setTitle("RSA算法"); add(wel); MyPanel_p panel_p = new MyPanel_p(P); add(panel_p); MyPanel_q panel_q = new MyPanel_q(Q)

9、; add(panel_q); MyPanel_d panel_d = new MyPanel_d(d); add(panel_d); MyPanel_e panel_e = new MyPanel_e(e); add(panel_e); MyPanel_in panel_in = new MyPanel_in(input); add(panel_in); MyPanel_out panel_out = new MyPanel_out(output); add(panel_out); MyPanel_out1 panel_out1 = new MyPanel_out1(output1); ad

10、d(panel_out1); MyPanel_button panel_button = new MyPanel_button(P,Q,d,e,input,output,output1); add(panel_button); private JLabel wel = new JLabel(" RSA算法演示 "); protected JTextField P = new JTextField(35); protected JTextField Q = new JTextField(35); protected JTextField d = new JTextField(

11、35); protected JTextField e = new JTextField(35); protected JTextArea input = new JTextArea(4,35); protected JTextArea output = new JTextArea(4,35); protected JTextArea output1 = new JTextArea(4,35); class MyPanel_fbutton extends JPanel public MyPanel_fbutton(Frame aframe,JTextField aP, JTextField a

12、Q, JTextField ad, JTextField ae) frame = aframe; P = aP; Q = aQ; e = ae; d = ad; private Frame frame; private JTextField P; private JTextField Q; private JTextField d; private JTextField e; class MyPanel_p extends JPanel public MyPanel_p(JTextField aP) P=aP; add(new JLabel(" 质数 P:"); add(P

13、); private JTextField P; class MyPanel_q extends JPanel public MyPanel_q(JTextField aQ) Q=aQ; add(new JLabel(" 质数 Q:"); add(Q); private JTextField Q; class MyPanel_d extends JPanel public MyPanel_d(JTextField ad) d=ad; add(new JLabel(" 公 钥:"); add(d); private JTextField d; class

14、MyPanel_e extends JPanel public MyPanel_e(JTextField ae) e=ae; add(new JLabel(" 私 钥:"); add(e); private JTextField e; class MyPanel_in extends JPanel public MyPanel_in(JTextArea ainput) input = ainput; add(new JLabel(" 输入明文:"); JScrollPane jsp1 = new JScrollPane (input,v,h); add(

15、jsp1); private JTextArea input; int v=JScrollPane.VERTICAL_SCROLLBAR_AS_NEEDED; int h=JScrollPane.HORIZONTAL_SCROLLBAR_AS_NEEDED; class MyPanel_out extends JPanel public MyPanel_out(JTextArea aoutput) output = aoutput; add(new JLabel(" 生成的密文:"); JScrollPane jsp = new JScrollPane (output,v,

16、h); add(jsp); private JTextArea output; int v=JScrollPane.VERTICAL_SCROLLBAR_AS_NEEDED; int h=JScrollPane.HORIZONTAL_SCROLLBAR_NEVER; class MyPanel_out1 extends JPanel public MyPanel_out1(JTextArea aoutput1) output1 = aoutput1; add(new JLabel("解密后的明文:"); JScrollPane jsp = new JScrollPane (

17、output1,v,h); add(jsp); private JTextArea output1; int v=JScrollPane.VERTICAL_SCROLLBAR_AS_NEEDED; int h=JScrollPane.HORIZONTAL_SCROLLBAR_AS_NEEDED; class MyPanel_button extends JPanel public MyPanel_button(JTextField aP,JTextField aQ,JTextField ad,JTextField ae, JTextArea ainput,JTextArea aoutput,J

18、TextArea aoutput1) P = aP; Q = aQ; e = ae; d = ad; input = ainput ; output = aoutput ; output1 = aoutput1 ; randProduce.addActionListener(new RandListener( P, Q ); add(randProduce); randD.addActionListener(new RandDListener( P, Q, d, e ); add(randD); encode.addActionListener(new EncodeListener( P, Q

19、, d, e, input, output ); add(encode); decode.addActionListener(new DecodeListener( P, Q, d, e, output, output1 ); add(decode); private JTextField P; private JTextField Q; private JTextField d; private JTextField e; private JTextArea input; private JTextArea output; private JTextArea output1; private

20、 JButton randProduce = new JButton("生成质数P和Q"); private JButton randD = new JButton("生成公钥和私钥"); private JButton encode = new JButton("加密"); private JButton decode = new JButton("解密"); class FileEncodeListener implements ActionListener public FileEncodeListener(

21、Frame f,JTextField ap, JTextField aq,JTextField ae,JTextField ad) P = ap; Q = aq; E = ae; D = ad; fr = f; public void actionPerformed(ActionEvent ee) FileDialog fd = new FileDialog(fr); fd.setVisible(true); String infileName =fd.getDirectory()+fd.getFile(); String inStr = new String(); inStr = Publi

22、cMethod.read(infileName); BigInteger PrimeP = new BigInteger(P.getText(); BigInteger PrimeQ = new BigInteger(Q.getText(); BigInteger n =PrimeP.multiply(PrimeQ); int nLen = n.bitLength(); int m=(int)(Math.ceil(double)(nLen)/16.0); nLen = (nLen-1) / 16; String outStr = new String(); outStr = PublicMet

23、hod.Encode(inStr,PrimeP,PrimeQ,n,nLen,m,D); for(i=infileName.length()-1;i>=0;-i) if(infileName.charAt(i)='.') break; String outfileName = infileName.substring(0,i); outfileName = outfileName + new String(".EncodeRsa") + infileName.substring(i,infileName.length(); PublicMethod.ou

24、tput(outfileName,outStr); private JTextField P; private JTextField Q; private JTextField E; private JTextField D; private Frame fr; int i; class FileDecodeListener implements ActionListener public FileDecodeListener(Frame f,JTextField ap, JTextField aq,JTextField ae,JTextField ad) P = ap; Q = aq; E

25、= ae; D = ad; fr = f; public void actionPerformed(ActionEvent ee) FileDialog fd = new FileDialog(fr); fd.setVisible(true); String infileName =fd.getDirectory()+fd.getFile(); String inStr = new String(); inStr = PublicMethod.input(infileName); System.out.println(inStr); BigInteger PrimeP = new BigInt

26、eger(P.getText(); BigInteger PrimeQ = new BigInteger(Q.getText(); BigInteger n =PrimeP.multiply(PrimeQ); int nLen = n.bitLength(); int m=(int)(Math.ceil(double)(nLen)/16.0); nLen = (nLen-1) / 16; String outStr = new String(); outStr = PublicMethod.Decode(inStr,PrimeP,PrimeQ,n,nLen,m,E); for(i=infile

27、Name.length()-1;i>=0;-i) if(infileName.charAt(i)='.') break; String outfileName = infileName.substring(0,i); outfileName = outfileName + new String(".DecodeRsa") + infileName.substring(i,infileName.length(); PublicMethod.write(outfileName,outStr); private JTextField P; private J

28、TextField Q; private JTextField E; private JTextField D; private Frame fr; int i; class RandListener implements ActionListener public RandListener(JTextField aP, JTextField aQ) P = aP; Q = aQ; public void actionPerformed(ActionEvent e) PublicMethod.GetPrime( P ); PublicMethod.GetPrime( Q ); private

29、JTextField P; private JTextField Q; class RandDListener implements ActionListener public RandDListener(JTextField aP, JTextField aQ, JTextField ad, JTextField ae) P = aP; Q = aQ; d = ad; e = ae; public void actionPerformed(ActionEvent ee) BigInteger PP = new BigInteger(P.getText(); BigInteger QQ = n

30、ew BigInteger(Q.getText(); BigInteger temp = (PP.subtract(new BigInteger("1").multiply(QQ.subtract(new BigInteger("1"); BigInteger temp1; do temp1=new BigInteger(100, new Random().mod(temp); while(PublicMethod.MillerRobin(temp1)=false); d.setText(temp1.toString(); e.setText(Publi

31、cMethod.invmod(temp1, temp).toString(); private JTextField P; private JTextField Q; private JTextField d; private JTextField e; class EncodeListener implements ActionListener public EncodeListener(JTextField aP, JTextField aQ, JTextField ad, JTextField ae, JTextArea in, JTextArea out) P = aP; Q = aQ

32、; d = ad; e = ae; input = in; output = out; public void actionPerformed(ActionEvent ee) BigInteger PrimeP = new BigInteger(P.getText(); BigInteger PrimeQ = new BigInteger(Q.getText(); BigInteger n =PrimeP.multiply(PrimeQ); int nLen = n.bitLength(); int m=(int)(Math.ceil(double)(nLen)/16.0); nLen = (

33、nLen-1) / 16; String inStr = input.getText(); output.setText(PublicMethod.Encode(inStr,PrimeP,PrimeQ,n,nLen,m,e); private JTextField P; private JTextField Q; private JTextField d; private JTextField e; private JTextArea input; private JTextArea output; class DecodeListener implements ActionListener

34、public DecodeListener(JTextField aP, JTextField aQ, JTextField ad, JTextField ae, JTextArea out, JTextArea out1) P = aP; Q = aQ; d = ad; e = ae; output = out; output1 = out1; public void actionPerformed(ActionEvent ee) BigInteger PrimeP = new BigInteger(P.getText(); BigInteger PrimeQ = new BigIntege

35、r(Q.getText(); BigInteger n =PrimeP.multiply(PrimeQ); int nLen = n.bitLength(); int m=(int)(Math.ceil(double)(nLen)/16.0); nLen = (nLen-1) / 16; String inStr = output.getText(); output1.setText(PublicMethod.Decode(inStr,PrimeP,PrimeQ,n,nLen,m,d); private JTextField P; private JTextField Q; private J

36、TextField d; private JTextField e; private JTextArea output; private JTextArea output1; class PublicMethod public static void GetPrime( JTextField prime ) BigInteger num = new BigInteger("0"); Random rand = new Random(); do int length = (int)(Math.random()*20+100); System.out.println(lengt

37、h); num = new BigInteger( length, 5 , rand ); prime.setText(num.toString(); while(MillerRobin(num)=false); public static boolean MillerRobin(BigInteger num) int time = 1000; BigInteger mod = num.mod(new BigInteger("2"); if(mod.equals(new BigInteger("0") return false; int s = 0, j

38、=0; BigInteger t=num.subtract(new BigInteger("1"); while( t.mod(new BigInteger("2").equals("0") ) t.divide(new BigInteger("2"); +s; for(int i=0; i<time; +i) BigInteger a = new BigInteger(100, new Random().mod(num.subtract(new BigInteger("3").add(n

39、ew BigInteger("2"); BigInteger y = powmod(a, t, num); if(y.equals(new BigInteger("1")=false && y.equals(num.subtract(new BigInteger("1")=false) j=1; while(j=s&&y.equals(num.subtract(new BigInteger("1")=false) y = y.multiply(y).mod(num); if(y.eq

40、uals(new BigInteger("1") return false; +j; if(y.equals(num.subtract(new BigInteger("1")=false) return false; return true; public static BigInteger powmod( BigInteger a, BigInteger t, BigInteger num ) BigInteger A = new BigInteger("1"); while(t.equals(new BigInteger(&quo

41、t;0")=false) if(t.mod(new BigInteger("2").equals(new BigInteger("1") A = A.multiply(a).mod(num); a = a.multiply(a).mod(num); t=t.divide(new BigInteger("2"); return A; public static BigInteger invmod(BigInteger a, BigInteger b) System.out.println(a+" "+b);

42、 BigInteger s0=new BigInteger("1"), s1=new BigInteger("0"), s2, q, t, b0=b; while(b.equals(new BigInteger("0")=false) q=a.divide(b); s2=s0.subtract( q.multiply(s1) ); if(pareTo(new BigInteger("0")!=-1) s2=s2.mod(b0); else s2=b0.subtract( s2.multiply(new BigInte