The Caesar cipher

What just happened?

We replace each letter with the letter $k$ positions away in the alphabet. The bottom strip is simply the alphabet rotated by $k$ — which is why it “rotates” when you move the slider.

The Caesar cipher (modular arithmetic):

Number the letters: $A=0,\ B=1,\ \dots,\ Z=25$. Then encryption and decryption are addition modulo 26:

— $x$ is the number of the plaintext letter, $k$ is the key (the shift), $c$ is the number of the ciphertext letter. “mod 26” wraps the alphabet, so after $Z$ we return to $A$.

Why is it a weak cipher?

The whole secret is a single number $k \in \{0,1,\dots,25\}$. The shift $k=0$ changes nothing, so only 25 meaningful keys remain. To break the cipher by “brute force”, it is enough to check all 25 shifts and see which gives readable text.

Why you need this for the exam:

It is the simplest example that a cipher = a function on numbers, and that security depends on the size of the key space. By understanding $c=(x+k)\bmod 26$, you practise congruences and the $\bmod$ operation — tools from the number-theory topic.

Remember: the Caesar cipher is $c=(x+k)\bmod 26$, and its key space has only 25 elements — trivially small, so brute-force breaking is instant.