Question
Let f(a;b) & f(c;d) be two affine ciphers s/t
f(a;b)(x) (a:x + b) mod 26
f(c;d)(x) (c:x + d) mod 26
Is f(c;d) f(a;b) a stronger encryption scheme than f(a;b)?
(10)
Using Affine Cipher Theory and given;a=9 and b=4, Encrpt the word "MAZERAS" and show the resulting cipher text.
f(a;b)(x) (a:x + b) mod 26
f(c;d)(x) (c:x + d) mod 26
Is f(c;d) f(a;b) a stronger encryption scheme than f(a;b)?
(10)
Using Affine Cipher Theory and given;a=9 and b=4, Encrpt the word "MAZERAS" and show the resulting cipher text.
Answers
Answered by
GPT 3.5
To encrypt the word "MAZERAS" using the affine cipher, we need to apply the encryption function f(a;b)(x) = (ax + b) mod 26.
Given a = 9 and b = 4, we can substitute these values into the encryption function.
For the letter 'M':
Using the numerical representation of the alphabet (A = 0, B = 1, ..., Z = 25), 'M' is represented by the number 12.
The cipher equation becomes: f(9;4)(12) = (9*12 + 4) mod 26 = 109 mod 26 = 3.
So, the encrypted letter for 'M' is 'C'.
Similarly, we can encrypt the remaining letters:
'A' -> f(9;4)(0) = (9*0 + 4) mod 26 = 4 mod 26 = 4 -> 'E'
'Z' -> f(9;4)(25) = (9*25 + 4) mod 26 = 229 mod 26 = 21 -> 'V'
'E' -> f(9;4)(4) = (9*4 + 4) mod 26 = 40 mod 26 = 14 -> 'O'
'R' -> f(9;4)(17) = (9*17 + 4) mod 26 = 157 mod 26 = 5 -> 'F'
'A' -> f(9;4)(0) = (9*0 + 4) mod 26 = 4 mod 26 = 4 -> 'E'
'S' -> f(9;4)(18) = (9*18 + 4) mod 26 = 166 mod 26 = 14 -> 'O'
So, the resulting ciphertext for the word "MAZERAS" is "CEVOFE".
To answer the second part of your question, whether f(c;d) is a stronger encryption scheme than f(a;b), we would need the values of c and d for a proper comparison. Without these values, it is not possible to determine the strength of one encryption scheme over the other.
Given a = 9 and b = 4, we can substitute these values into the encryption function.
For the letter 'M':
Using the numerical representation of the alphabet (A = 0, B = 1, ..., Z = 25), 'M' is represented by the number 12.
The cipher equation becomes: f(9;4)(12) = (9*12 + 4) mod 26 = 109 mod 26 = 3.
So, the encrypted letter for 'M' is 'C'.
Similarly, we can encrypt the remaining letters:
'A' -> f(9;4)(0) = (9*0 + 4) mod 26 = 4 mod 26 = 4 -> 'E'
'Z' -> f(9;4)(25) = (9*25 + 4) mod 26 = 229 mod 26 = 21 -> 'V'
'E' -> f(9;4)(4) = (9*4 + 4) mod 26 = 40 mod 26 = 14 -> 'O'
'R' -> f(9;4)(17) = (9*17 + 4) mod 26 = 157 mod 26 = 5 -> 'F'
'A' -> f(9;4)(0) = (9*0 + 4) mod 26 = 4 mod 26 = 4 -> 'E'
'S' -> f(9;4)(18) = (9*18 + 4) mod 26 = 166 mod 26 = 14 -> 'O'
So, the resulting ciphertext for the word "MAZERAS" is "CEVOFE".
To answer the second part of your question, whether f(c;d) is a stronger encryption scheme than f(a;b), we would need the values of c and d for a proper comparison. Without these values, it is not possible to determine the strength of one encryption scheme over the other.