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 372133, 493011, 229391, 92386, 254934, 496676, 220303, 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, ma (a) Use this information to determine p(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 m and φ(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) Soudron Encnelfng component. 오홀1991 p= 683 Y: 부43 hou e .fotai pe tactos, thografe 520229, 낙4' 3,G83. I, (m)= 506044

So lefUs-lake 역외93 3921弓ろ劢6044 no Comer72386, , 4A6646, 220 305, 269164 ,326504 ,%גา29 肪4斤34 36638, 2066 S9· ớne no com 69