Caesar Cipher — Glossary

Caesar cipher is a substitution cipher that shifts every letter a fixed number of places along the alphabet, so a shift of 3 turns A into D and Attack into Dwwdfn. The shift is the whole key. It is named after Julius Caesar, who is reported to have used a shift of 3, and today it is a teaching example and puzzle staple, never a way to protect data.

How it works

Number the letters A=0 through Z=25. Encryption adds the shift k to each letter and wraps around modulo 26. Decryption subtracts k. Written as a formula, that is E(x) = (x + k) mod 26 and D(x) = (x - k) mod 26.

Key space: shifts 1 to 25 change the text, and shift 0 (or 26) leaves it unchanged. That leaves 25 useful keys.
Case and symbols: the classic version shifts only the 26 Latin letters. Spaces, digits and punctuation pass through unchanged, which leaks word lengths.
Decrypting: a message encrypted with shift k is decrypted with shift 26 - k. A shift of 13 is its own inverse, which is why ROT13 is the same operation both ways.
Non-ASCII: accented letters and other scripts fall outside A to Z and are normally left alone, so a Caesar implementation must say what it does with them.

The Python below encrypts with a shift of 3, then prints every candidate shift for a short ciphertext. Only one line reads as English.

def caesar(t, k):
    return ''.join(chr((ord(c) - 65 + k) % 26 + 65) if c.isupper()
                   else chr((ord(c) - 97 + k) % 26 + 97) if c.islower()
                   else c for c in t)

print(caesar("Attack at dawn", 3))
for k in (1, 2, 3, 4, 25):
    print(k, caesar("Dwwdfn dw gdzq", -k))

Dwwdfn dw gdzq
1 Cvvcem cv fcyp
2 Buubdl bu ebxo
3 Attack at dawn
4 Zsszbj zs czvm
25 Exxego ex hear

How many keys does the Caesar cipher have?

The Caesar cipher has 25 usable keys, one for each shift from 1 to 25. An attacker tries all 25 and reads the one that makes sense, which takes a fraction of a second by hand or by script. Even without brute force, counting letter frequencies finds the shift, because the most common ciphertext letter usually maps to E.

Common pitfalls

Treating it as encryption: with 25 keys and no secret beyond a small integer, the output is obfuscation. Do not use it for passwords, tokens or personal data.
Wrong direction: some tools shift forward to encrypt and others shift backward. If decrypting with shift 3 gives garbage, try 23, which is 26 - 3.
Forgetting case: lowercasing the input before shifting loses capitalization, and shifting only uppercase leaves lowercase letters readable. Handle both ranges.
Shifting digits and symbols: a variant that rotates all of ASCII, not only letters, is not the Caesar cipher and breaks interoperability with other tools.
Assuming word breaks hide anything: keeping spaces tells an attacker word lengths, and short words such as a and the give the shift away.

Related terms

ROT13 — the Caesar cipher with a fixed shift of 13, which is its own inverse.
Vigenere Cipher — uses a keyword of shifts, so each letter gets its own Caesar shift.
ASCII — the character codes that most code implementations shift to do the arithmetic.
Autokey Cipher — a Vigenere-style cipher whose key stream extends with the message.

How it works

How many keys does the Caesar cipher have?

Common pitfalls

Related terms

See also