Using the RSA encryption algorithm let p 3 and q 5 Then n

Using the RSA encryption algorithm, let p = 3 and q = 5. Then n = 15, m = 8, and e = 11. Calculate the ciphertext code C for the plaintext value 3. Be sure to show your work!

Solution

Now as per RSA algorithm the formula to calculate plain text is

M = C^d mod n

Now here we know C = 3 and n = 15 , we need to find out d

We calculate d based on RSA key generation algorithm,
d e-1 mod f(n) which is equivalent to
ed 1 mod f(n)
or    ed mod f(n) = 1

Now we need to first calculate value of f(n) which can be calculated using formula
f(n) = (p-1)(q-1)
f(n) = (3-1) (5-1)
f(n) = 2*4
f(n) = 8
Now we alreday have e given which is 11, fit in the value to formula to calculate d
ed mod f(n) =1
11d mod 8 = 1
Here we if try putting 3 in place of d then it fulfills the condition
11*3 mod 8 = 1
Hence d = 3
Now

M = C^d mod n

M = 3³ mod 15

M = 27 mod 15

M = 12

Hence Plain text is 12