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勺加密和解密过程，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d⑷. 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2A k<n的最大整数。

为了加密一个消息P,只要计算C=P A e(mod n)即可。

为了解密C,只要计算P=C A d(modn)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 * q = 33, z = (p-1 ) * (q-1 )= 20,选 d = 7，计算得e=3,所以C=MAe(mod n) = 8M=CAd(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语言的中的类的方法中随机产生大数。

(2)、public static 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, BigInteger 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(String 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：(文件) import .*;import import .*;import .*;import .*;import .*; public class RSA1{public static void main(String[] args) {MyFrame frame = new MyFrame();MyPanel_fbutton panel_fbutton = new MyPanel_fbutton(frame,,,,; FlowLayout fl = newFlowLayout ,0,0);(fl); (panel_fbutton);( 150, 100, 500, 480 );J(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); 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); add(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(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 aQ, JTextField 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);}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 JPanelpublic MyPanel_d(JTextField ad)d=ad;add(new JLabel("公 钥 :")); ad,{{add(d);}private JTextField d;}class 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(jsp1);}private JTextArea input;int v=;int h=;}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,h); add(jsp);}private JTextArea output;int v=;int h=;}class MyPanel_out1 extends JPanelpublic MyPanel_out1(JTextArea aoutput1)output1 = aoutput1;add(new JLabel(" 解密后的明文:"));JScrollPane jsp = new JScrollPane (output1,v,h); add(jsp);}private JTextArea output1;int v=;int h=;}class MyPanel_button extends JPanel{public MyPanel_button(JTextField aP,JTextField aQ,JTextField ad,JTextField ae, JTextArea ainput,JTextArea aoutput,JTextArea aoutput1) {P = aP;Q = aQ;e = ae;d = ad;input = ainput ;output = aoutput ; output1 = aoutput1 ;(new RandListener( P, Q )); add(randProduce);(new RandDListener( P, Q, d, e )); add(randD);(new EncodeListener( P, Q, d, e, input, output )); add(encode);(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 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(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);(true);String infileName =()+();String inStr = new String();inStr = (infileName);BigInteger PrimeP = new BigInteger());BigInteger PrimeQ = new BigInteger());BigInteger n =(PrimeQ);int nLen = ();int m=(int)((double)(nLen)/);nLen = (nLen-1) / 16;String outStr = new String();outStr = (inStr,PrimeP,PrimeQ,n,nLen,m,D); for(i=()-1;i>=0;--i){if(i)=='.') break;}String outfileName = (0,i);outfileName = outfileName + new String(".EncodeRsa") + (i,()); (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 = ae; D = ad; fr = f;} public void actionPerformed(ActionEvent ee){FileDialog fd = new FileDialog(fr);(true);String infileName =()+();String inStr = new String(); inStr = (infileName);BigInteger PrimeP = new BigInteger());BigInteger PrimeQ = new BigInteger()); BigInteger n =(PrimeQ); int nLen = ();int m=(int)((double)(nLen)/); nLen = (nLen-1) / 16; String outStr = new String(); outStr =(inStr,PrimeP,PrimeQ,n,nLen,m,E); for(i=()-1;i>=0;--i){ if(i)=='.') break;}String outfileName = (0,i); outfileName = outfileName + new String(".DecodeRsa") +(i,()); (outfileName,outStr);}private JTextField P;private JTextField 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) {( P );( Q );}private 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());BigInteger QQ = new BigInteger());BigInteger temp = (new BigInteger("1"))).multiply(new BigInteger("1")));BigInteger temp1;do{temp1=new BigInteger(100, new Random()).mod(temp);}while(temp1)==false);());(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;d = ad;e = ae;{input = in;output = out;}public void actionPerformed(ActionEvent ee){BigInteger PrimeP = new BigInteger());BigInteger PrimeQ = new BigInteger());BigInteger n =(PrimeQ);int nLen = ();int m=(int)((double)(nLen)/);nLen = (nLen-1) / 16;String inStr = (); (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{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());BigInteger PrimeQ = new BigInteger());BigInteger n =(PrimeQ);int nLen = ();int m=(int)((double)(nLen)/);nLen = (nLen-1) / 16;String inStr = (); (inStr,PrimeP,PrimeQ,n,nLen,m,d));}private JTextField P;private JTextField Q;private JTextField 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)()*20+100);num = new BigInteger( length, 5 , rand );());} while(MillerRobin(num)==false);}public static boolean MillerRobin(BigInteger num){int time = 1000;BigInteger mod = (new BigInteger("2"));if(new BigInteger("0"))){return false;}int s = 0, j=0;BigInteger t=(new BigInteger("1"));while( (new BigInteger("2")).equals("0") ){(new BigInteger("2"));++s;}for(int i=0; i<time; ++i){BigInteger a = new BigInteger(100, newRandom()).mod(new BigInteger("3"))).add(new BigInteger("2"));BigInteger y = powmod(a, t, num); if(new BigInteger("1"))==false&& (new BigInteger("1")))==false){j=1;while(j==s&&(new BigInteger("1")))==false){y = (y).mod(num);if(new BigInteger("1"))){return false;}++j;}if(new BigInteger("1")))==false){return false;}}}return true;}public static BigInteger powmod( BigInteger a, BigInteger t, BigInteger num ) {BigInteger A = new BigInteger("1");while(new BigInteger("0"))==false){if(new BigInteger("2")).equals(new BigInteger("1"))){A = (a).mod(num);}a = (a).mod(num);t=(new BigInteger("2"));}return A;}public static BigInteger invmod(BigInteger a, BigInteger b){" "+b);BigInteger s0=new BigInteger("1"), s1=new BigInteger("0"), s2, q, t, b0=b; while(new BigInteger("0"))==false){q=(b);s2=( (s1) );if(new BigInteger("0"))!=-1){s2=(b0);}else{s2=( (new BigInteger("-1")).mod(b0) );}s0=s1;s1=s2;t=b;b=(b);a=t;}if(new BigInteger("1"))){return s0;}else{return new BigInteger("0");}}public static String Encode(String inStr,BigInteger PrimeP,BigInteger PrimeQ, BigInteger n,intnLen,int m,JTextField d){BigInteger res = new BigInteger("0");StringBuffer outBuf = new StringBuffer();int i,k,j;for(i=0;i<();i=j){BigInteger t = new BigInteger("0");for(j=i;j<i+nLen&&j<();j++){t=(16);long num = (j);t=(num));}res = (t,new BigInteger()),n);String buf = new String();for(k=0;k<m;++k){long num = (65535))).longValue(); res = (16);buf = (char)(num)+buf;} outBuf = (buf);}return ();}public static String Decode(String inStr,BigInteger PrimeP,BigInteger PrimeQ,BigInteger n,int nLen,int m,JTextField e){StringBuffer outBuf = new StringBuffer();BigInteger res = new BigInteger("0"); int i,j;for(i=0;i<();i+=j){BigInteger t = new BigInteger("0"); for(j=0;j<m&&j+i<();j++) {t = (16);long num =(long) (j+i)); t=(num));}res = (t,new BigInteger()),n);String buf = new String(); while(new BigInteger("0"))>0) {long num =(65535))).longV alue(); buf = (char)(num) + buf; res = (16) ;}outBuf = (buf);}return ();}public static String read(String infileName){String ans = new String ();try{FileInputStream fis = new FileInputStream(infileName); InputStreamReader isr =new InputStreamReader(fis); BufferedReader br = new BufferedReader (isr);int t; while(true) {t= (); if(t==-1) break; ans = ans + (char)(t);}();();();}catch(FileNotFoundException e){"FileStreamsTest: "+e);} catch(IOException e){"FileStreamsTest: "+e);}"READSTR="+());return ans;}public static void write(String outfileName,String outStr){try{FileOutputStream fos = new FileOutputStream(outfileName);OutputStreamWriter osw = new OutputStreamWriter(fos,"UNICODE");BufferedWriter out = new BufferedWriter (osw);int c;for(int i=0;i<();i++){c=(int)(i);(c);}();();();}catch(FileNotFoundException e){"FileStreamsTest: "+e);}catch(IOException e)"FileStreamsTest: "+e);}"WRITE="+());return ;}public static String input(String infileName){String ans = new String();try{FileInputStream in = new FileInputStream(infileName); ObjectInputStream s = newObjectInputStream(in); ans = (String)();();();}catch(FileNotFoundException e){{"FileStreamsTest: "+e);} catch(IOException e){"FileStreamsTest: "+e);}catch(ClassNotFoundException e){"FileStreamsTest: "+e);}return ans;}public static void output(String outfileName,String outStr){try{FileOutputStream f = new FileOutputStream(outfileName); ObjectOutputStream s =new ObjectOutputStream(f); (outStr);();();}catch(FileNotFoundException e){"FileStreamsTest: "+e);}catch(IOExcepti on e){"FileStreamsTest: "+e);}}}四、实验结果运行程序，弹出的对话框如上图所示。