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ASSIGNMENT
METHOD OF SUBMISSION: Complete the cover sheet with your unit code, your
full name, campus enrolled at (B, G or X) and ID; please underline your family name
as recorded with Deakin.
1. Alice and Bob want to establish a common key pair using the Diffie-Hellman key
exchange protocol and then use it in to send each other messages using a symmetric
cipher. They agree by email on a prime p=877 and a primitive root (generator) a=
453; these are public knowledge). Then Alice chooses secret x=25 while Bob chooses
secret y=13.
Alice is in Australia while Bob is in Brazil. Carl, a Canadian friend of Alice, has been
tracking the email received and sent by Alice and decides that he wants to listen in on
conversations between Alice and Bob. Carl therefore sets up a man-in-the-middle
attack as follows.
Carl sees the set-up agreed to by Alice and Bob and he chooses secret z = 17.
Using the primitive root and her secret, Alice computes 45325 (mod 877) and sends it
to Bob; however, Carl intercepts this email (which Bob never receives). Similarly,
Carl intercepts Bob’s e-mail containing 45313 (mod 877) (which Alice never
receives).
Determine what common key Carl sets up with Bob, and his common key with Alice.
4 marks
2. Tony selects the prime p = 2357 and a primitive root g = 2 (mod 2357). Tony also
chooses the private key a = 1751 and computes ga
mod p which is 21751 (mod 2357) ≡
1185. Now Tony’s public key is (p = 2357; g = 2; ga
= 1185).
To encrypt a message m = 2035 to send to Tony, Bai selects a random integer k =
1520 and computes u = 21520 (mod 2357) ≡ 1430 and v = 2035 * 11851520 (mod
2357) ≡ 697, and sends the pair ( 1430, 697) to Tony. Tony decrypts to retrieve the
message 2035.
Bai then sends a second message m’ = 1339 to Tony, using the same value of random
integer k: he computes u = 21520
(mod 2357) ≡ 1430 and v = 1339 * 11851520 (mod
2357) ≡ 2145, and send the pair (1430, 2145) to Tony.
Oscar, works with Tony and has seen the pair (1430, 697) and m = 2035. Oscar is
now keen to obtain m' without Tony knowing. He sees the second pair (1430, 2145)
on Tony’s laptop. Show how he derives m’. 4 marks