DqKQznh4

1public class ThresholdElGamal extends ElGamal
2{
3    // comments to this code will be presented during the lecture
4    
5    public static ElGamalSK Setup(ElGamalSK SK) {
6        
7        SecureRandom sc=new SecureRandom();
8        BigInteger s=new BigInteger(SK.PK.securityparameter,sc);
9        BigInteger h=SK.PK.g.modPow(s, SK.PK.p);
10        
11        ElGamalPK PK=new ElGamalPK(SK.PK.p,SK.PK.q,SK.PK.g,h,SK.PK.securityparameter);
12        return new ElGamalSK(s,PK);
13    }
14    
15    public static ElGamalSK SetupParameters(int securityparameter) {
16        BigInteger p,q,g,h,s;
17        
18        SecureRandom sc=new SecureRandom();
19        
20        while(true) {
21            q = BigInteger.probablePrime(securityparameter, sc);
22            
23            p=q.multiply(BigInteger.TWO);
24            p=p.add(BigInteger.ONE);
25            
26            if (p.isProbablePrime(50)==true) break;
27            
28        }
29        
30        
31        
32        g=new BigInteger("2");
33        
34        while(true) {
35            
36            if (isqr(g,p)==1)break;
37            g=g.add(BigInteger.ONE);
38        }
39        
40        s=BigInteger.ZERO;
41        h=BigInteger.ZERO;
42        
43        ElGamalPK PK=new ElGamalPK(p,q,g,h,securityparameter);
44        
45        return new ElGamalSK(s,PK);
46    }
47    
48    
49    
50    public static ElGamalPK AggregatePartialPublicKeys(ElGamalPK PK[]) {
51        BigInteger tmp=BigInteger.ONE;
52        for (int i=0;i<PK.length;i++)tmp=tmp.multiply(PK[i].h).mod(PK[0].p);
53        return new ElGamalPK(PK[0].p,PK[0].q,PK[0].g,tmp,PK[0].securityparameter);
54        
55    }
56    
57    
58    
59    public static ElGamalCT PartialDecrypt(ElGamalCT CT,ElGamalSK SK)
60    {
61        
62        BigInteger tmp = CT.C2.modPow(SK.s, SK.PK.p);
63        tmp=tmp.modInverse(SK.PK.p);
64        BigInteger newC = tmp.multiply(CT.C).mod(SK.PK.p);
65        return new ElGamalCT(newC,CT.C2);
66    }
67    
68    
69    
70    
71    public static void main(String[] args) throws IOException
72    {
73        
74        
75        SecureRandom sc = new SecureRandom();
76        
77        ElGamalSK Params=SetupParameters(64);
78        ElGamalSK []SK=new ElGamalSK[3];
79        
80        for (int i=0;i<3;i++) {
81            SK[i]=Setup(Params);
82            
83            System.out.println("Setup for "+i+"-th authority:");
84            System.out.println("partial secret-key = " + SK[i].s);
85            System.out.println("partial public-key = " + SK[i].PK.h);
86            System.out.println("p = " + SK[i].PK.p);
87            System.out.println("q = " + SK[i].PK.q);
88            System.out.println("g = " + SK[i].PK.g);
89        }
90        
91        
92        ElGamalPK []PartialPK=new ElGamalPK[3];
93        
94        for (int i=0;i<3;i++) 	  PartialPK[i]=SK[i].PK;
95        ElGamalPK PK=	  AggregatePartialPublicKeys(PartialPK);
96        
97        
98        BigInteger M;
99        while(true) {
100            M=new BigInteger(Params.PK.securityparameter,sc);
101            if (isqr(M,Params.PK.p)==1) break;
102        }
103        System.out.println("plaintext to encrypt with threshold El Gamal = " + M);
104        ElGamalCT CT=Encrypt(PK,M);
105        
106        ElGamalCT PartialDecCT=CT;
107        for (int i=0;i<2;i++) PartialDecCT=PartialDecrypt(PartialDecCT,SK[i]);
108        BigInteger D=Decrypt(PartialDecCT,SK[2]);
109        System.out.println("decrypted plaintext with threshold El Gamal = " + D+"\n"); // it should print the same integer as before
110        
111        
112        
113    }
114}