1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
|
package org.spongycastle.crypto.examples;
import java.math.BigInteger;
import java.security.SecureRandom;
import org.spongycastle.crypto.CryptoException;
import org.spongycastle.crypto.Digest;
import org.spongycastle.crypto.agreement.jpake.JPAKEPrimeOrderGroup;
import org.spongycastle.crypto.agreement.jpake.JPAKEPrimeOrderGroups;
import org.spongycastle.crypto.agreement.jpake.JPAKEParticipant;
import org.spongycastle.crypto.agreement.jpake.JPAKERound1Payload;
import org.spongycastle.crypto.agreement.jpake.JPAKERound2Payload;
import org.spongycastle.crypto.agreement.jpake.JPAKERound3Payload;
import org.spongycastle.crypto.digests.SHA256Digest;
/**
* An example of a J-PAKE exchange.
* <p>
*
* In this example, both Alice and Bob are on the same computer (in the same JVM, in fact).
* In reality, Alice and Bob would be in different locations,
* and would be sending their generated payloads to each other.
*/
public class JPAKEExample
{
public static void main(String args[]) throws CryptoException
{
/*
* Initialization
*
* Pick an appropriate prime order group to use throughout the exchange.
* Note that both participants must use the same group.
*/
JPAKEPrimeOrderGroup group = JPAKEPrimeOrderGroups.NIST_3072;
BigInteger p = group.getP();
BigInteger q = group.getQ();
BigInteger g = group.getG();
String alicePassword = "password";
String bobPassword = "password";
System.out.println("********* Initialization **********");
System.out.println("Public parameters for the cyclic group:");
System.out.println("p (" + p.bitLength() + " bits): " + p.toString(16));
System.out.println("q (" + q.bitLength() + " bits): " + q.toString(16));
System.out.println("g (" + p.bitLength() + " bits): " + g.toString(16));
System.out.println("p mod q = " + p.mod(q).toString(16));
System.out.println("g^{q} mod p = " + g.modPow(q, p).toString(16));
System.out.println("");
System.out.println("(Secret passwords used by Alice and Bob: " +
"\"" + alicePassword + "\" and \"" + bobPassword + "\")\n");
/*
* Both participants must use the same hashing algorithm.
*/
Digest digest = new SHA256Digest();
SecureRandom random = new SecureRandom();
JPAKEParticipant alice = new JPAKEParticipant("alice", alicePassword.toCharArray(), group, digest, random);
JPAKEParticipant bob = new JPAKEParticipant("bob", bobPassword.toCharArray(), group, digest, random);
/*
* Round 1
*
* Alice and Bob each generate a round 1 payload, and send it to each other.
*/
JPAKERound1Payload aliceRound1Payload = alice.createRound1PayloadToSend();
JPAKERound1Payload bobRound1Payload = bob.createRound1PayloadToSend();
System.out.println("************ Round 1 **************");
System.out.println("Alice sends to Bob: ");
System.out.println("g^{x1}=" + aliceRound1Payload.getGx1().toString(16));
System.out.println("g^{x2}=" + aliceRound1Payload.getGx2().toString(16));
System.out.println("KP{x1}={" + aliceRound1Payload.getKnowledgeProofForX1()[0].toString(16) + "};{" + aliceRound1Payload.getKnowledgeProofForX1()[1].toString(16) + "}");
System.out.println("KP{x2}={" + aliceRound1Payload.getKnowledgeProofForX2()[0].toString(16) + "};{" + aliceRound1Payload.getKnowledgeProofForX2()[1].toString(16) + "}");
System.out.println("");
System.out.println("Bob sends to Alice: ");
System.out.println("g^{x3}=" + bobRound1Payload.getGx1().toString(16));
System.out.println("g^{x4}=" + bobRound1Payload.getGx2().toString(16));
System.out.println("KP{x3}={" + bobRound1Payload.getKnowledgeProofForX1()[0].toString(16) + "};{" + bobRound1Payload.getKnowledgeProofForX1()[1].toString(16) + "}");
System.out.println("KP{x4}={" + bobRound1Payload.getKnowledgeProofForX2()[0].toString(16) + "};{" + bobRound1Payload.getKnowledgeProofForX2()[1].toString(16) + "}");
System.out.println("");
/*
* Each participant must then validate the received payload for round 1
*/
alice.validateRound1PayloadReceived(bobRound1Payload);
System.out.println("Alice checks g^{x4}!=1: OK");
System.out.println("Alice checks KP{x3}: OK");
System.out.println("Alice checks KP{x4}: OK");
System.out.println("");
bob.validateRound1PayloadReceived(aliceRound1Payload);
System.out.println("Bob checks g^{x2}!=1: OK");
System.out.println("Bob checks KP{x1},: OK");
System.out.println("Bob checks KP{x2},: OK");
System.out.println("");
/*
* Round 2
*
* Alice and Bob each generate a round 2 payload, and send it to each other.
*/
JPAKERound2Payload aliceRound2Payload = alice.createRound2PayloadToSend();
JPAKERound2Payload bobRound2Payload = bob.createRound2PayloadToSend();
System.out.println("************ Round 2 **************");
System.out.println("Alice sends to Bob: ");
System.out.println("A=" + aliceRound2Payload.getA().toString(16));
System.out.println("KP{x2*s}={" + aliceRound2Payload.getKnowledgeProofForX2s()[0].toString(16) + "},{" + aliceRound2Payload.getKnowledgeProofForX2s()[1].toString(16) + "}");
System.out.println("");
System.out.println("Bob sends to Alice");
System.out.println("B=" + bobRound2Payload.getA().toString(16));
System.out.println("KP{x4*s}={" + bobRound2Payload.getKnowledgeProofForX2s()[0].toString(16) + "},{" + bobRound2Payload.getKnowledgeProofForX2s()[1].toString(16) + "}");
System.out.println("");
/*
* Each participant must then validate the received payload for round 2
*/
alice.validateRound2PayloadReceived(bobRound2Payload);
System.out.println("Alice checks KP{x4*s}: OK\n");
bob.validateRound2PayloadReceived(aliceRound2Payload);
System.out.println("Bob checks KP{x2*s}: OK\n");
/*
* After round 2, each participant computes the keying material.
*/
BigInteger aliceKeyingMaterial = alice.calculateKeyingMaterial();
BigInteger bobKeyingMaterial = bob.calculateKeyingMaterial();
System.out.println("********* After round 2 ***********");
System.out.println("Alice computes key material \t K=" + aliceKeyingMaterial.toString(16));
System.out.println("Bob computes key material \t K=" + bobKeyingMaterial.toString(16));
System.out.println();
/*
* You must derive a session key from the keying material applicable
* to whatever encryption algorithm you want to use.
*/
BigInteger aliceKey = deriveSessionKey(aliceKeyingMaterial);
BigInteger bobKey = deriveSessionKey(bobKeyingMaterial);
/*
* At this point, you can stop and use the session keys if you want.
* This is implicit key confirmation.
*
* If you want to explicitly confirm that the key material matches,
* you can continue on and perform round 3.
*/
/*
* Round 3
*
* Alice and Bob each generate a round 3 payload, and send it to each other.
*/
JPAKERound3Payload aliceRound3Payload = alice.createRound3PayloadToSend(aliceKeyingMaterial);
JPAKERound3Payload bobRound3Payload = bob.createRound3PayloadToSend(bobKeyingMaterial);
System.out.println("************ Round 3 **************");
System.out.println("Alice sends to Bob: ");
System.out.println("MacTag=" + aliceRound3Payload.getMacTag().toString(16));
System.out.println("");
System.out.println("Bob sends to Alice: ");
System.out.println("MacTag=" + bobRound3Payload.getMacTag().toString(16));
System.out.println("");
/*
* Each participant must then validate the received payload for round 3
*/
alice.validateRound3PayloadReceived(bobRound3Payload, aliceKeyingMaterial);
System.out.println("Alice checks MacTag: OK\n");
bob.validateRound3PayloadReceived(aliceRound3Payload, bobKeyingMaterial);
System.out.println("Bob checks MacTag: OK\n");
System.out.println();
System.out.println("MacTags validated, therefore the keying material matches.");
}
private static BigInteger deriveSessionKey(BigInteger keyingMaterial)
{
/*
* You should use a secure key derivation function (KDF) to derive the session key.
*
* For the purposes of this example, I'm just going to use a hash of the keying material.
*/
SHA256Digest digest = new SHA256Digest();
byte[] keyByteArray = keyingMaterial.toByteArray();
byte[] output = new byte[digest.getDigestSize()];
digest.update(keyByteArray, 0, keyByteArray.length);
digest.doFinal(output, 0);
return new BigInteger(output);
}
}
|
