Cryptography - Alice And Bob - Tony - Cryptography Assignment Writing Help

Internal Code : 2ADHE

Cryptography Assignment Writing Help

TASK1 Alice and Bob want to establish a common key pair using the Diffie-Hellman key exchangeprotocol and then use it in to send each other messages using a symmetric cipher. Theyagree by email on a prime p=877 and a primitive root (generator) a= 453; these are publicknowledge). Then Alice chooses secret x=25 while Bob chooses secret y=13. Alice is inAustralia while Bob is in Brazil. Carl, a Canadian friend of Alice, has been tracking the emailreceived and sent by Alice and decides that he wants to listen in on conversations betweenAlice and Bob. Carl therefore sets up a man-in-the-middle attack as follows. Carl sees theset-up agreed to by Alice and Bob and he chooses secret z = 17. Using the primitive root andher secret, Alice computes 45325 (mod 877) and sends it to Bob; however, Carl interceptsthis email (which Bob never receives). Similarly, Carl intercepts Bob’s e-mail containing 5313 (mod 877) (which Alice never receives). TASK2 Tony selects the prime p = 2357 and a primitive root g = 2 (mod 2357). Tony also chooses theprivate key a = 1751 and computes ga mod p which is 21751 (mod 2357) ? 1185. Now Tony’spublic key is (p = 2357; g = 2; ga = 1185). To encrypt a message m = 2035 to send to Tony, Baiselects 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 toetrieve the message 2035. Bai then sends a second message m’ = 1339 to Tony, using thesame 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 withTony 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.