The long awaited crypto problem Alice wants to use the RSA

The long - awaited crypto problem: Alice wants to use the RSA public key encryption system to send a message to Bob. Assume the message, M has already been converted to a numerical format: M = 6588973. a) Bob\'s public key pair as (n = 6015727, e = 3674911). Use the necessary information to encrypt the message M so that it can be sent from Alice to Bob. b) Assume that Bob\'s private decryption key d = 674883. Show the math required to recover the original message M.

Solution

Encrypted message C,is calculated using the formula

C=M^e mod n

I.e., 6588973 to the power of 3674911

So by calculating the above with scientific calculator cipher text that is encrypted message generated is

5555858

So the message M is encrypted as 5555858

At the receiver side the above encrypted message is decrypted using the formula below

M=C ^ d mod n