Question

any encrypted message

Look in section 8.4 for help in doing this. Your first post will be a message (at least a sentence) encrypted by the RSA code using p = 5,9 = 11 and e = 3 (follow example in book). Use 1 = A, 2 =B, ... 26 = Z, 27 = (space) 28 =. 29 = ! and 30 = ?

Answer 1

Given,

=>RSA encryption algorithm is used.

=>p = 5,q = 11 and e = 3

Explanation:

Calculating value of n:

=>n = p*q

=>n = 5*11

=>n = 55

Calculating value of $\phi$ (n)(Euler totient function):

=>$\phi$(n) = $\phi$ (p)*$\phi$(q)

=>$\phi$(n) = (5-1)*(11-1)

=>$\phi$(n) = 4*10

=>$\phi$(n) = 40

Calculating value of d:

=>Choosing d such that e*d mod $\phi$ (n) = 1

=>3*d mod 40 = 1

=>d = 27 as 3*27 mod 40 = 1

Calculating encrypted message:

=>Let say message = "YOU ARE GREAT!"

Applying encryption:

=>Y = 25, O = 15, U = 21, space = 27, A = 1, R = 18, E = 5, G = 7, T = 20, ! = 29

=>We know that, ciphertext(C) = (M)^e mod n where M is plain text.

Calculating values:

=>Ciphertext of Y = (25)^3 mod 55

=>Ciphertext of Y = 5

=>Ciphertext of O =(15)^3 mod 55

=>Ciphertext of O = 30

=>Ciphertext of U = (21)^3 mod 55

=>Ciphertext of U = 21

=>Ciphertext of sapce = (27)^3 mod 55

=>Ciphertext of space = 48

=>Ciphertext of A = (1)^3 mod 55

=>Ciphertext of A = 1

=>Ciphertext of R = (18)^3 mod 55

=>Ciphertext of R = 2

=>Ciphertext of E = (5)^3 mod 55

=>Ciphertext of E = 15

=>Ciphertext of G = (7)^3 mod 55

=>Ciphertext of G = 13

=>Ciphertext of T = (20)^3 mod 55

=>Ciphertext of T = 25

=>Ciphertext of ! = (29)^3 mod 55

=>Ciphertext of ! = 24

=>Hence the encrypted message of message "YOU ARE GREAT!" = "53021481215481321512524"

I have explained each and every part with the help of statements attached to it.