You and your friend agree to communicate using affine enciphering transformations c congruent ap + b mod n (see examples 3 and 4 in sec iii.1, where lowercase letters a and b were used for the coefficients of transformation). your message units are single letters in the 31 - letter alphabet with a-z corresponding to 0-25, blank = 26, =27, ? = 28, ! = 29, ' = 30. you regard the key k_e = (a, b) as an element a + bi in the field of 31^2 elements (where i denotes a squareroot of -1 that field). you also agree to exchange keys using the diffie-hellman system, and to choose g = 4 + i. then you randomly choose a secret integer a = 209. your friend sends you her g^b = 1 + 19i. find the enciphering key. what element of f_961 must you send your friend in order that she can also find the key? find the deciphering transformation. read the message "buvcfiwoujtz! h."