Question

3.) Alice reflects on the situation and realizes this is a situation where asymmetric encryption could be used as long as she and Bob arrange to exchange their public keys in a secure fashion. If Bob and Alice agree to use the F₃ Fermat number as their exponent demonstrate the computation of an RSA public/private keypair if Alice selects 59 and 67 as the prime factors for her composite modulus. Indicate what number Alice needs to retain privately and what number she needs to securely convey to Bob.

Answer 1

e = 257

p = 59

q = 67

n = p * q = 3953

phi = (p-1) * (q-1) = 58 * 66 = 3828

find d= e^-1 mod phi = 257^-1 mod 3828 = 3545

alice need to keep (3545,3953)

alice need send (257,3953) to bob