Vigenère cipher

The Vigenère cipher was described by Giovan Battista Bellaso in 1553, then wrongly attributed to the French diplomat Blaise de Vigenère, who published his version in 1586. For nearly three centuries it was considered the indecipherable cipher — until Friedrich Kasiski broke it in 1863.

Principle

Vigenère is a polyalphabetic cipher: a Caesar whose shift changes at every letter, driven by a key repeated cyclically beneath the plaintext.

Formally, for plaintext P, cycled key K, ciphertext C:

C_i = (P_i + K_i) mod 26
D_i = (C_i − K_i) mod 26

Each key letter picks a row of the Vigenère table (26 alphabets shifted against one another). Security comes from the fact that the same plaintext letter may be enciphered differently depending on its position.

Example

Plaintext CIPHERCHRONICLE with key KEY (cycled KEYKEYKEYKEYKEY):

C + K → M    I + E → M    P + Y → N
H + K → R    E + E → I    R + Y → P
C + K → M    H + E → L    R + Y → P
O + K → Y    N + E → R    I + Y → G
C + K → M    L + E → L    E + Y → P

Result: MMNRIPMLPYRGMLP. The same plain letter (C, three occurrences) maps to three different ciphers depending on position.

Close variants

• Beaufort — an involutive variant: C = (K − P) mod 26 instead of addition.
• Autokey — the key is extended with the plaintext itself, removing periodicity.
• Gronsfeld — numeric key (0-9 digits) instead of alphabetic.
• Vernam (One-Time Pad) — Vigenère with a random key as long as the message, never reused: the only provably unbreakable cipher.

Weaknesses

Vigenère’s strength collapses the moment you know the key length:

• Kasiski method (1863): repeating patterns at regular intervals reveal the key period.
• Index of coincidence (Friedman): a statistical measure that estimates key length from the letter distribution.

Once length n is known, split the ciphertext into n columns, and each column is a Caesar you attack with frequency analysis.

In CipherChronicle

Vigenère is the step from teaching to genuine logic puzzle. Its grids ask the player to guess the period before attacking column by column — a mechanic that rewards observation over brute force.