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Exercise Sheet 6
Assignment 6: Protocols
(!This is a graded assignment and is worth 25% of final grade)
1. Design a secure mutual authentication protocol based on a shared symmetric key. The
protocol must establish a session key, and to ensure perfect forward secrecy.
a. Design such a protocol that uses three messages. [3marks]
b. Design such a protocol that uses two messages. [2 marks]
[5 marks]
2. Consider the following mutual authentication and key establishment protocol, where
the session key is given by K = gab mod p
Suppose that Alice attempts to initiate a connection with Bob using
this protocol.
a. Show that Trudy can attack the protocol so that both of the following
will occur.
i. Alice and Bob authenticate each other.
ii. Trudy knows Alice's session key.
Hint: Consider a man-in-the-middle attack. [8 marks]
b. Is this attack of any use to Trudy? [2 marks]
[10 marks]
“I am Alice”, Na
Nb, {Na}KbPriv,{gb Alice mod p}KaPub
{Nb}KaPriv, {ga mod p}KbPub

Exercise Sheet 6
Dr. Anca Jurcut Page 2
3. Suppose that in the Fiat-Shamir protocol, as illustrated below, we have N = 27,331 and
v = 7339.
a. In the first iteration, Alice sends x = 21,684 in message one, Bob sends e = 0 in
message two, and Alice sends y = 657 in the third message. Show that Bob verifies
Alice's response in this case. [1 marks]
b. At the next iteration, Alice again sends x = 21,684 in message one, but Bob sends
e = 1 in message two, and Alice responds with y = 26,938 in message three. Show
that Bob again verifies Alice's response. [1 marks]
c. Determine Alice's secret S. Hint: 657- 1 = 208 mod 27,331. [3 marks]
[5 marks]
4. Give a secure two-message protocol that prevents cell phone cloning, prevents a fake
base station attack, and establishes a shared session key. Mimic the GSM protocol.
[5 marks]

x = r2 mod N
Alice e ∈ {0, 1}
y = r *Se mod N