Please give me help on this question Post an answer ONLY if

Please give me help on this question. Post an answer ONLY if you can do all (a), (b) parts.

6. Using RSA Kevin and Bob decide to apply the RSA cryptography so that Kevin can send a secret message to Bob. (a) Assuming p 3, q 11, and e 37, what is d? Calculate the exact value (b) Following Part (a), what is the original message if Bob receives 4? Calculate the exact value.

Solution

(a)   GIven p =3, q=11 and e=7
(p-1)*(q-1) = (3-1)*(11-1) = 20
Hence, d is the multiplicative inverse of 7 mod 20. Also, gcd(7,20) =
Which implies, 1 = (-1)*(20) + (3)*(7). Therefore d = 3

(b) Now N = p*q = 3*11 = 33
   given bob recieves 4 implies 4^d = 4³ = 64
   Which will be equivalent to 31 (mod 33)