# 5th - CSci 5471 Modern Cryptography Spring 2010 Homework#5...

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CSci 5471: Modern Cryptography, Spring 2010 Homework #5 Yongdae Kim Due: Apr 6th. 9:00 AM. Show all steps. Please ask any questions, if the problems are not clear. Total 2 pages, 160 possible points. Problem 4 could be subject to change. Check class web site frequently. Please ask questions if you need clariﬁca- tion. 1. Group Key Agreement (20 pt total) In general, Difﬁe-Hellman protocol allows two parties share a common key (that’s why it is called two party Difﬁe-Hellman key agreement). The following natural extensions of two party Difﬁe-Hellman protocol allows n parties to share a common key. (And it is called group key agreement protocol.) – Step 1: Each member M i selects random r i Z p * , computes Z i = g r i mod p and broadcasts the message to the group. – Step 2: Each member M i , after receiving Z i - 1 and Z i +1 , computes X i = ( Z i +1 /Z i - 1 ) r i = g r i +1 r i - r i r i - 1 mod p and broadcasts it to the group. – Step 3: Each member M j , after receiving all X i ,i 6 = j , computes K = K j = ( Z j - 1 ) nr j X j n - 1 ...X j +( n - 2) . Prove that

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5th - CSci 5471 Modern Cryptography Spring 2010 Homework#5...

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