import java.math.BigInteger;
import java.util.Random;

public class AuthDHKeyAgree {
 private static final int securityParam = 1023;
 public static BigInteger p;
 public static BigInteger q;
 public static BigInteger g;
 
 //生成安全素數p,p=2q+1,q為一個1023 bits的大素數
 public static void safePGen() {
 BigInteger one = new BigInteger("1",10);
 BigInteger two = new BigInteger("2",10);
 do {
 p = new BigInteger("0",10);
 q = new BigInteger(securityParam, 100, new Random());
 p = p.add(q.multiply(two).add(one));
 }while( p.isProbablePrime(100) == false );
 }
 
 //選取隨機生成元g,通過隨機選擇[2,p-2]之間的數g,然后判斷g^q mod p是否等于1,如果不等于1,則g為生成元
 public static void generatorGGen() {
 BigInteger one = new BigInteger("1",10);
 BigInteger two = new BigInteger("2",10);
 BigInteger result;
 do {
 g = new BigInteger(securityParam, new Random());
 g = g.mod(p.subtract(one));
 result = g.modPow(q, p);
 }while( g.compareTo(two) < 0 || result.compareTo(one) == 0 );
 }
 
 public static void main(String[] args) {
 System.out.println("系統初始化,生成安全素數p,選取隨機生成元g...");
 safePGen();
 System.out.println("p: "+p.toString(16));
 System.out.println("q: "+q.toString(16));
 generatorGGen();
 System.out.println("g: "+g.toString(16));
 
 //Alice選擇隨機秘密值 0<=r1<=p-1
 BigInteger r1 = new BigInteger(securityParam, new Random());
 BigInteger A;
 r1 = r1.mod(p);
 //Alice計算g^r1 mod p
 A = g.modPow(r1, p);
 //Bob選擇隨機秘密值0<=r2<=p-1
 BigInteger r2 = new BigInteger(securityParam, new Random());
 BigInteger B;
 //Bob計算g^r2 mod p
 B = g.modPow(r2, p);
 //Bob初始化一個RSA簽名算法對象
 RSASignatureAlgorithm BobRSA = new RSASignatureAlgorithm();
 BobRSA.initKeys();
 byte[] BobM = (A.toString()+B.toString()+"Alice"+"Bob").getBytes();
 //Bob生成簽名
 BigInteger BobSig = BobRSA.signature(BobM);
 //Alice驗證簽名
 BobM = (A.toString()+B.toString()+"Alice"+"Bob").getBytes();
 boolean result = BobRSA.verify(BobM, BobSig);
 if( result == true ) System.out.println("Alice驗證簽名通過。");
 else System.out.println("Alice驗證簽名不通過。");
 //Alice計算會話密鑰
 BigInteger sessionKey = (A.multiply(B)).mod(p);
 System.out.println("Alice計算得到的會話密鑰為:"+sessionKey.toString(16));
 //Alice初始化一個RSA簽名算法對象
 RSASignatureAlgorithm AliceRSA = new RSASignatureAlgorithm();
 AliceRSA.initKeys();
 byte[] AliceM = (A.toString()+B.toString()+"Alice"+"Bob").getBytes();
 //Alice生成簽名
 BigInteger AliceSig = AliceRSA.signature(AliceM);
 //Bob驗證簽名
 AliceM = (A.toString()+B.toString()+"Alice"+"Bob").getBytes();
 result = AliceRSA.verify(AliceM, AliceSig);
 if ( result == true ) System.out.println("Bob驗證簽名通過。");
 else System.out.println("Bob驗證簽名不通過");
 //Bob計算會話密鑰
 sessionKey = (B.multiply(A)).mod(p);
 System.out.println("Bob計算得到的會話密鑰為:"+sessionKey.toString(16));
 }

}

import java.math.BigInteger;
import java.math.BigInteger;
import java.security.MessageDigest;
import java.security.NoSuchAlgorithmException;
import java.util.Random;

public class RSASignatureAlgorithm {
 BigInteger n;
 BigInteger e;
 BigInteger d;
 public BigInteger __hash(byte m[]) {
 MessageDigest md;
 try {
 md = MessageDigest.getInstance("SHA-256");
 md.update(m);
 byte b[] = new byte[33];
 System.arraycopy(md.digest(), 0, b, 1, 32);
 return new BigInteger(b);
 } catch (NoSuchAlgorithmException e) {
 System.out.println("this cannot happen.");
 }
 return null;
 }
 public void initKeys() {
 BigInteger p = new BigInteger(1024, 500, new Random());
 BigInteger q = new BigInteger(1024, 500, new Random());
 assert(p.compareTo(q) != 0);
 n = p.multiply(q);
 BigInteger fi_n = p.subtract(BigInteger.ONE)
 .multiply(q.subtract(BigInteger.ONE));
 e = new BigInteger(512, 100, new Random());
 d = e.modInverse(fi_n);
 
 System.out.println("n : " + n.toString(16));
 System.out.println("e : " + e.toString(16));
 System.out.println("d : " + d.toString(16));
 }
 public BigInteger signature(byte m[]) {
 BigInteger s = __hash(m).modPow(d, n);
 System.out.println("s : " + s);
 return s;
 }
 public boolean verify(byte m[], BigInteger s) {
 BigInteger left = __hash(m).mod(n);
 BigInteger right = s.modPow(e, n);
 return left.compareTo(right) == 0;
 }
}