(i) Find Bezouts Identity for 53 and 61. Using RSA, you send Alice the modulus m = 3233 (= 53 61) and

the encrypting exponent e = 7. Alice has a two-letter message that she turns into a number 2626 and encrypts and sends you. You receive c = 1067. You have already determined that the decrypting exponent is d = 1783.

(ii) Find c^d (mod 53) and c^d (mod 61).

(iii) Then use Bezouts identity from (i) to find Alices plaintext message.