$($RSA Public Key Cryptosystem$)$ Let us pick two prime numbers $=41,=67.$ Then, $==4167=2747()=(1)(1)=4066=2640$ We pick a small prime number $,$ with gcd$(,())=1.=13.$ Then, $=1()=1312640=2437.($This inverse is computed by Euclid$$s algorithm.$)$ The public keys are $(,)$ and the private key $(,).($a$)$ Suppose a sender wants to send a number $=2169.$ Compute the encrypted message $.$ Make sure you perform a mod operation after each multiplication so the intermediate results does not become too large. Use the recursive algorithm Power to compute the exponentiation. $($You may use an Excel sheet to generate the data.$)$ Show the computation. $($b$)$ Compute the decrypted message $$ and verify that $=.$ Show the computation