You have found two plaintext-ciphertext pairs which you know are from an affine cipher based on...
- You have found two plaintext-ciphertext pairs which you know are from an affine cipher based on the English alphabet. The pairs are (1,7) and (0,2).
a. Find the equation of the cipher.
Homework Answers
Solution for the problem is provided below please comment if any doubts:
a.
Procedure:
- The affine cypher is of the form (ax+b) mod 26, where a and b are two numbers.
- “a” is relatively prime to 26 and b can be any number.
- “x” is the input or plain character.
- The cipher character y=(ax+b) mod 26.
- Here we have two plain cipher pairs.(1, 7) and (0, 2)
- Substitute to get two equations:
- 7 = (1*a + b) mod 26
- 2 = (0*a + b )mod 26
- Now from second equation,
- 2=b mod 26
- Thus b=2 (The smallest positive value)
- Substitute the value of “b” in first equation
- 7 = (a+2)mod 26
- 7 = a mod 26 + 2 mod 26
- 7 – 2 = a mod 26
- 5 = a mod 26
- a = 5
- since 5 is relatively prime to 26, a= 5.
- Now the equation is: (5x+2) mod 26
Thus the required solution is: (5x+2) mod 26
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