Question

4. You are part of the Cryptographic Security Team at a military facility, tasked with decoding messages as required. A message has come in from HQ, as an ordered collection of numbers, which is personalised for yourself and aimed at testing aspects of your decoding skills 375611, 125336, 421644, 325129, 125442, 180232, 48609, 269786, 326504, 164977, 236038, 206659 These numbers (above) have each been encoded using RSA with a modulus of m-pq = 520229 (with p and q being primes) and encoding exponent of 217939 You are advised that(25397, 120989) is a valid encoding-decoding pair for the same modulus. m (a) Use this information to determine y(m) for this modulus (Using software to directly factorise m is not a valid option for doing this part.) (b) Verify your answer by determining the primes p and q Show how these combine to give both rn and 'p(m) (c) Calculate the decoding exponent for 217939 (as encoding exponent) using the extended Euclidean algorithm. (Again, using software to directly obtain this is not a valid option, though you are welcome to use software to confirm your answer.) d) For each of the 12 numbers in your message, verify they have no prime factors in common with m (It is OK to use software for this task, provided you have answered the previous part.)

Answer 1

4) Sokdron Soen bat Nou t tcphgrplic seuhy tem.at 683 부43 (r) 506044 504469 By.foemzda γη medr ジ1

506094 mod 506044 252463 i lepa ng compoet e=84939 bard on extended Euelm t to tnd 4 legie dj.factou tor 25 63 are ''s.n. 28 609,s5eal, 2544. 2-6548 954134, 41666, 220 303, 3636, 33650, 1619,303*