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# Efficient And Secure Star Topology Based Multicast Key Management Algorithm

1470 words - 6 pages

For example , Assume that there are three members U1, U2, U3 in the group .
U1 selects p1=11, q1=17 computes X1=11*17= 187
U2 selects p2=31, q2=47 computes X2=31*47= 1457
U3 selects p3=17, q3=47 computes X3=17*47= 799
X1≠X2 ≠X3, so all the three members are registered in multicast group. Let us say, U3 leaves the group. Therefore, the modulus operation in cipher text computation is performed with respect to X1 and X2. Although member U3 has left the group, but both his factors p3 and q3 of X3 are already present in X1 and X2 respectively. Therefore, he can decrypt the future cipher text to obtain the original confidential message M using secret information X3 and private key d3. Hence, ...view middle of the document...

2. The individual member Ui chooses two prime number pi and qi randomly and also compute the product Xi and Ф(Xi)
Where, Xi = pi × qi and Ф(Xi)=(pi-1) × (qi-1)
3. The member calculates the private key by applying the extended Euclidean algorithm, computing a unique integer di, such that
e×di ≡ 1 mod (Ф(Xi))
4. The authenticated members deliver their Xi value to the key server.
5. The server registers the member if and only if
gcd (Z, Xi) = 1 and keeps Xi as secret. Then, the server stores product of Xi values in Z.

3.1.2 Message encryption phase

The steps to be performed by server for message encryption are described as follows:-

1. After determining the set of registered users, the server uses e as well as secret values of message xi to encrypt a message M by using the following formulae [5]:-
C = (M)e mod Π Xi; i=1 to n
where, n is the no. of selected members to whom secret message is to be sent.
2. After computing the cipher text C by the key server , the server sends a broadcast message to all the registered member of the group..

3.1.3Message decryption phase
The steps to be performed by the member for message decryption are described as follows:-

1.After the cipher text C is received, the individual member Ui can decrypt C, using his private key di and secret information Xi, to obtain the confidential message M as follows [5]:-
Ui → M = (C mod Xi)di mod Xi
The proposed scheme ensures that only the members whose Xi values are used to encrypt the message are able to decrypt it.

3.2 Member joining and leaving the group

3.2.1 Member joining the group

Whenever a new member Ui+1 wants to join the group , the server repeats the same procedure as that of key assignment. The rekeying process for existing members is eliminated because their secret information Xi and private key di remains unaffected.

3.2.2 Member leaving the group
Whenever a member Ui wants to leave the group, the remaining members do not need to modify the secret information X and private key d. The key server deletes the secret value Xi from the active list.
In the cipher text computation, the modulus operation is performed with the subset of Xk values of the remaining members Uk. For example, if the key server sends a message to the remaining group members, the encryption is performed as:
C=Me mod(X1 × X2 × …× Xi-1 × Xi+1 ×… ×Xn )
Thus, Ui cannot decrypt the message.

4. AN EXAMPLE

In this section, a simple example is discussed to illustrate our scheme for group communication.

Key assignment phase
Suppose that there are six members U1, U2, U3, U4, U5 and U6 who want to join the group. Then the following steps are performed for key assignment:-
1. The server declares the parameter e=101 to the members and also authenticates the member who wants to join the group.
2. The individual member Ui chooses two prime number pi and qi randomly and also compute the product Xi and Ф(Xi)
Where, Xi = pi × qi and Ф(Xi) = (pi-1) × (qi-1)
U1 chooses p1 = 283 and q1...

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