Task Five: Symmetric Cryptosystem Analysis $(3$ marks$)$

Alice and Bob use a cryptosystem in which their private key is a $($large$)$ prime k and their plain$-$ texts

and ciphertexts are integers. Bob encrypts a message m by computing the product

c $=$ km

The enemy, Eve, intercepts two ciphertexts c$1$ and c$2.$

$$ Can you help Eve to find Bob and Alice$$s private key? Show the mathematics formula to

demonstrate this. $(1$ mark$)$

$$ Write a program to implement your method in the earlier part of this question. Then, enter

the following ciphertexts:

and

c$1=12849217045006222$

c$2=6485880443666222$

Can you find the private key? $(2$ marks$)$

Write your report for this section in Task$5.$pdf$.$