Caesar Cipher

The Caesar cipher (or Caesar code) is a monoalphabetic substitution cipher in which each letter is replaced by another letter located a fixed number of positions further along the alphabet.

The shift distance is defined by a number called the shift or offset, which can be to the right (A to B) or to the left (B to A).

For every shift to the right (by +N), there is an equivalent shift to the left (by 26-N), because the alphabet wraps around. The Caesar cipher is therefore sometimes called a rotation cipher.

The Caesar cipher is based on an alphabet shift. The most commonly used shift is 3 letters, so that A becomes D.

Another, more mathematical way to encrypt is to encode any letter x using (x+3) mod 26.

Assign the values A=0, B=1, …, Z=25, add a constant (the shift), and take the result modulo 26 (the length of the alphabet) to obtain the encrypted text.

Decryption with the Caesar cipher replaces each letter with another letter located earlier in the alphabet, according to the shift used.

Another, more mathematical way to decrypt is to assign the values A=0, B=1, …, Z=25, subtract a constant (the shift), and take the result modulo 26 (the length of the alphabet) to obtain the plaintext.

A message encrypted with the Caesar cipher has the same shift applied to every letter. Its letter-frequency distribution is therefore shifted by the same number of positions.

The index of coincidence is identical to that of the plaintext (as with any monoalphabetic substitution cipher).

References to Caesar, the Roman general and emperor, his contemporaries (Cicero, Brutus, Cleopatra), or more generally to antiquity and the Roman Empire may provide clues.

Keywords such as Julius (Iulius/Ivlivs), Ave, Augustus, or even Caesar salad may also evoke the Roman emperor.

The English pronunciation of Caesar is close to seizure.

It is possible to decrypt a text encrypted with the Caesar cipher even without knowing the shift used. The main methods are:

— Brute-force attack (trying all possible keys): there are only 25 non-trivial shifts (since a shift of 26 returns the original text). The correct shift can be identified by testing each possibility until a meaningful text is obtained.

— Frequency analysis (identifying the most common letters): languages have characteristic letter frequencies. In English, the letter E is the most common. If another letter appears very frequently in the ciphertext, it may represent a shifted E. Calculating the difference between this letter and E makes it possible to estimate the shift.

— Use dCode, which applies these methods automatically.

No, the Caesar cipher is not secure. It is an easy cipher to break. With a 26-letter alphabet, there are only 25 non-trivial keys, making brute-force attacks very easy. dCode can automatically decrypt a message encrypted with the Caesar cipher in less than a second.

The Caesar cipher is best known for its shift of 3, but all other shifts are possible. Some shifts are known by other cipher names.

Another variant consists of modifying the original alphabet, for example by introducing digits.

A Caesar cipher with a shift of N corresponds to an affine cipher of the form (A×x+B) mod 26, with A=1 and B=N.

Caesar is sometimes written César (in French) or Ceaser (a misspelling).

The Caesar cipher applies only to letters in the chosen alphabet. However, there are several ways to handle numbers:

— Write numbers using Roman numerals: numbers then become letters and can be encrypted normally.

— Shift digits using the same shift as the letters.

— Include digits in the alphabet.

Julius Caesar (Gaius Iulius Caesar) used this technique for some of his correspondence, particularly military communications, as reported by Suetonius. The shift of 3 is traditionally associated with him.

However, other civilizations may also have used this type of cipher independently.

The Augustan cipher is a variant of the Caesar cipher attributed to Emperor Augustus. According to Suetonius (Life of Augustus, 88), each letter is replaced by the next letter in the alphabet: A becomes B, B becomes C, etc. Unlike the standard Caesar cipher, the encryption does not wrap around the alphabet: Z is replaced by AA.

The Caesar cipher is also known as a shift cipher. The shift can be hidden in the name of variants or mnemonic codes, for example:

CD code, C = D, the shift is 1.

Hello (LO) code, L = O, the shift is 3.

Jail (JL) code, J = L, the shift is 2.

Ellen (LN) code, L = N, the shift is 2.

Cutie (QT) code, Q = T, the shift is 3.

Eiffel (FL) code, F = L, the shift is 6.

WC code, W = C, the shift is 6.

Empty (MT) code, M = T, the shift is 7.

Baden Powell (founder of the Scout movement), B = P, the shift is 14.

Any (NE) code, N = E, the shift is 17.

See You (CU) code, C = U, the shift is 18.

I See (IC) code, I = C, the shift is 20.

Easy (EZ) code, E = Z, the shift is 21.

CEASAR (a misspelling of CAESAR), where E = A or A = E, corresponds to a shift of either +22 or +4.

Any two-letter code can represent an association between an encrypted letter and its plaintext equivalent (see gramograms).

ROT13 uses a shift of 13 and is reversible.

ROT5 applies a shift of 5 to digits and is reversible.

ROT47 applies a shift of 47 to printable ASCII characters and is reversible.

More generally, ROT-N denotes a shift of N positions. If N is less than 26, the Latin alphabet can be used; otherwise, a larger or custom alphabet is required.

The 25 ways to encrypt CAESAR using the Caesar cipher (shifts from 1 to 25): DBFTBS, ECGUCT, FDHVDU, GEIWEV, HFJXFW, IGKYGX, JHLZHY, KIMAIZ, LJNBJA, MKOCKB, NLPDLC, OMQEMD, PNRFNE, QOSGOF, RPTHPG, SQUIQH, TRVJRI, USWKSJ, VTXLTK, WUYMUL, XVZNVM, YWAOWN, ZXBPXO, AYCQYP, BZDRZQ.

For N from 1 to Text Length Do

Set C = the Nth character of the Text

If C is a letter in the alphabet Then

Calculate R = the position of C in the alphabet (A=0, B=1, …, Z=25)

Calculate R2 = (R + Shift) Modulo 26

Write the letter at position R2 in the alphabet

Else

Keep C unchanged

End If

End For

The cipher was named after Julius Caesar, who was born in 100 BCE. Ancient accounts, notably that of Suetonius, indicate that he used this type of substitution to protect some communications, particularly military messages.

The exact date when the cipher was created and the identity of its actual inventor remain unknown.