Discrete Maths . [n this exercise, we work through the REA encryption algorithm as done in lectures, using the same notation. The numbers we use are too small to he used in a reallife application, hut we are attempting only to see how the method works. We choose prime numhers p = 23 and q = 4?. {a} Find n = pq. [h] The encryption exponent e must he coprime to {p 1:}(q I]. 1Verify that e = 3 has this property. {c} The plaintext message is \"MIT", which we encode using the scheme A H '01, B IJ- [12, etc. 1What is the numher m that results? [d] The numher n has 4 digits, so we write m in two hlocks of 3 digits. The rst block is El = 131]. "What is the second Hg? {e} Calculate Bf mod n and 3; mod n and hence write down the numher c that is the ciphertext. You may use technology such as a calculator, Excel, Wolfram Alpha, lvlatlah, etc, hut you must sayr what you used. Now suppose that you are the receiver, and that you receive the IDES sage 2219. Since you know 11, and hence that it has 4 digits, you hrealc this into two numhers 22d and 195., each of which is the encoded form of parts of the plain text. {f} Find 11' = s'1 mod [p 1}[q 1}, explaining how you did this. {5} Calculate 22E\"! mod n and 195': mod n and use the results to decrypt the message, giving your answer in the form of a numher. You might again need to use teclmology for these calculations. {h} I[l'z-nimnert your number in [g]: into the plaintext memage