The Caesar cipher

Shifting the alphabet modulo 26: encrypting, decrypting, finding the key from a plaintext and ciphertext pair, the key space and exhaustive search.

The outline, topic by topic

Each topic is weighted the way the exam weighs it.

Caesar cipher: what is it?
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A substitution where each letter is replaced by the one k places further along the alphabet, wrapping round after Z (addition modulo 26).
With k = 3, A becomes D and X becomes A. The whole key fits in this single number k, which is the cipher's weakness.
With key 5, what does the word MATHS become?
- RFYMX
- HVOCN
- RFYNX
- QEXLW
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RFYMX
M→R, A→F, T→Y, H→M, S→X, giving RFYMX. HVOCN is the result of a shift in the wrong direction (−5), QEXLW that of key 4.
With key 3, the encryption of letter number x (A = 0) is letter number ….
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With key 3, the encryption of letter number x (A = 0) is letter number (x + 3) mod 26.
The "mod 26" brings the result back into the alphabet: X (23) gives 26 mod 26 = 0, that is A.
Symmetric encryption: what is it?
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Encryption where the same secret key is used to encrypt and decrypt, or where one is immediately derived from the other.
In Caesar, whoever knows the encryption shift also knows the decryption shift. The problem is getting the key to the recipient without interception.