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, DifﬁeHellman protocol allows two parties share a common key
(that’s why it is called two party DifﬁeHellman key agreement). The following natural extensions of two party
DifﬁeHellman 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)
.
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 Spring '08
 Staff
 Cryptography, group key agreement, Handbook of Applied Cryptography, b1 b2 mod

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