Vigenere Tableau

IPhenomenon

The Vigenere is a Caesar cipher whose shift changes on every letter, driven by a repeating keyword.

Plaintext: LOOM NEVER STOPS

Key: BRASSBRASSBRA

Convert both to numbers with A = 0. Add them position by position, take the result modulo 26, convert back.

The same plaintext letter produces a different ciphertext letter at every position. The letter E appeared at positions 6 and 8 and left as F and E. That single fact is what defeats frequency counting, and it is the whole point of the design.

IIKey space

For a keyword of length k the number of distinct keys is 26^k. That sounds enormous, and for k = 12 it is: 9.5 x 10^16, comfortably beyond manual search and beyond 1930s machinery.

The gap between the arithmetic and the reality is the key length. 26^k assumes the attacker does not know k. In practice cryptanalysts find k first, using an observation published in 1863 by Friedrich Kasiski: repeated sequences in the ciphertext occur at distances that are multiples of the key length.

Once k is known, the cipher collapses. Take every k-th letter, and you are holding k separate Caesar ciphers, each with 25 keys, each readable by frequency analysis on its own. A 12-letter key reduces to 12 small homework problems.

The Vigenere is not weak because 26^12 is small. It is weak because the key repeats, and repetition is measurable.

IIIEnciphering

• Agree on a keyword and strip its spaces: BRASS.
• Strip the plaintext to capitals and remove spaces.
• Write the keyword above the plaintext, repeating it as many times as needed.
• Convert plaintext and key letters to numbers, A = 0 through Z = 25.
• Add each pair, take the result modulo 26.
• Convert back to letters. Group the output in fives.
• Alternatively use the 26 x 26 tableau: find the plaintext letter along the top, the key letter down the left, and read the intersection.

IVDeciphering

• Find the key length k with Kasiski examination: locate repeated three-letter sequences in the ciphertext, record the distances between them, and take the greatest common divisor of the distances.
• Split the ciphertext into k streams by taking every k-th letter.
• Run frequency analysis on each stream separately. Each stream is a Caesar cipher with a constant shift.
• Recover the k shift amounts; those shifts are the numeric key.
• Convert the numbers back to letters to read the keyword, then decrypt the whole message in one pass.
• If Kasiski gives several candidate lengths, try the shortest first: a credible short key is far more likely than a long one.

VWeakness

Key repetition. Every weakness in this cipher descends from it. A key as long as the message, used once, is unbreakable in principle — and that cipher (Vernam) is later on this loom.

Kasiski examination. Any plaintext word that repeats at a distance divisible by the key length produces an identical ciphertext sequence at that distance. Find those repeats, take the greatest common divisor of the gaps, and you have a shortlist of key lengths.

Index of coincidence. Even without repeated words, the statistical texture of the text reveals the period: if you slice the ciphertext into k streams and each stream looks like natural language, you have the right k.

Probable words. A known phrase — 'DEAR SIR', a signature block, a standard opening — pins down the key letters at those positions. Two or three known phrases and the key falls out.

Key management. The keyword had to be remembered and shared. In practice eighteenth- and nineteenth-century users picked memorable words, and a dictionary attack against candidate keywords is far cheaper than 26^k suggests.

VIPractice

·History note

Giovan Battista Bellaso published the tableau in 1553 in La cifra del Sig. Giovan Battista Bellaso. Blaise de Vigenere published a different and more cumbersome autokey system in 1586, and through a seventeenth-century misattribution the cipher acquired his name permanently. It resisted attack for centuries despite being published; Charles Babbage broke a version in 1854 but never published the method, and Friedrich Kasiski published an independent solution in 1863. The first recorded field use against a live Vigenere was by the Union during the American Civil War, followed by the British in the Boer War.

·Further reading

The Vigenere's failure is more instructive than its success. It shows that a large keyspace is necessary but not sufficient: what matters is whether the key material is used differently at each position, and a repeating key is by definition used the same way over and over.

That insight produced the one-time pad, the only cipher with a formal proof of perfect secrecy, and it also produced rotor machines that changed the effective key on every character without a repeating pattern — the next entry on this loom.

Next: playfair-square attacks the problem from the other end, encrypting two letters at a time.

+Weave into