Let p = 47 and q = 59, n = p . q, and e = 157. Compute a multiplicative inverse of d, modulo (n).

 Let p = 47 and q = 59, n = p . q, and e = 157.

a. Compute a multiplicative inverse of d, modulo φ(n).

b. Every two-letter string (including A-Z and spaces) can be converted to a number-message between 0 and 2626, by replacing a space by 00, 'A' by 01, 'B' by 02, etc.. For example. 'ME' becomes 1305. Encrypt the two-letter string 'HI' by computing its number-message m, and the ciphertext me mod n.

c. Decrypt the sequence of ciphertexts 0802, 2179, 2276, 1024 to find a message.