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’.

Answer rating: 100% (QA)

Oscar knows i Public of tony iep23578 2 emd i a mod p 14 30 omd Vm ngkmodp 697 omd m 20... View the full answer