Question

Using RSA Implementation:

1. Alice's RSA public key is given by (e, n) = (59, 1189). = (a) Determine Alice's private key (d, n). (b) Bob sends his first message Mi 67 to Alice, encrypting it with RSA using Alice's public key. He obtains a cypher text Cị that gets forwarded to Alice. What is Cį? (c) Bob sends his second message M2 to Alice, encrypting it with RSA using Alice's public key. Eve, who was eavesdropping on the commu- nication between Alice and Bob, intercepted the cipher text C2 = 631 that originated from M2. What is M2?

Answer 1

2 59 Now, n = 1189 = 29x41 & (n) = 1189 (-a)(1-7) = 1120 @=59, 4 (n) = 1120. 120=59(18) +58 58 (0) + 1 = 59 -58(1) (from ② 59 - [1120 - 59 (18)](!) [from 59(19) +11201-1) » 1 - 59 (19) + 1120 (1) 3 59(19) =. (mod 1120) =) 19 = 1 (mod &(n)). -> d=19 :: (din) = (19,1189). M. e (modn) 67 (mod 1189) = 1077 (mod on) (mod 1189) b ci 59 d C M2 2 C 631 19 = 100 key RSA Algooithm Generation : Select biq -þ&q both poime; þ#q Calculate n=pxq Calculode $(n) = ($0)(9- Select integer e ged(4cm),e)-!; i<e<$(n) Calculated de mod($(n)) = 1 Private { din} Public key Wey 2) Encryption c'me (modn) 3) Decryption M = cd (modn)