Виженер шифрі: тарихы мен қағидалары

Simple type of polyalphabetic encryption system

The Vigenère cipher (viʒnɛːʁ) is a method of encrypting alphabetic text where each letter of the plaintext is encoded with a different Caesar cipher, whose increment is determined by the corresponding letter of another text, the key. For example, if the plaintext is attacking tonight and the key is OCULORHINOLARINGOLOGY, then
the first letter a of the plaintext is shifted by 14 positions in the alphabet (because the first letter O of the key is the 14th letter of the alphabet, counting from 0), yielding o;
the second letter t is shifted by 2 (because the second letter C of the key means 2) yielding v;
the third letter t is shifted by 20 (U) yielding n, with wrap around;
and so on; yielding the message ovnlqbpvt hznzouz. If the recipient of the message knows the key, they can recover the plaintext by reversing this process. The Vigenère cipher is therefore a special case of a polyalphabetic substitution. First described by Giovan Battista Bellaso in 1553, the cipher is easy to understand and implement, but it resisted all attempts to break it until 1863, three centuries later. This earned it the description le chiffrage indéchiffrable (French for 'the indecipherable cipher'). Many people have tried to implement encryption schemes that are essentially Vigenère ciphers. In 1863, Friedrich Kasiski was the first to publish a general method of deciphering Vigenère ciphers. In the 19th century, the scheme was misattributed to Blaise de Vigenère (1523–1596) and so acquired its present name.

The very first well documented description of a polyalphabetic cipher was by Leon Battista Alberti around 1467 and used a metal cipher disk to switch between cipher alphabets. Alberti's system only switched alphabets after several words, and switches were indicated by writing the letter of the corresponding alphabet in the ciphertext. Later, Johannes Trithemius, in his work Polygraphiae (which was completed in manuscript form in 1508 but first published in 1518), invented the tabula recta, a critical component of the Vigenère cipher. The Trithemius cipher, however, provided a progressive, rather rigid and predictable system for switching between cipher alphabets. In 1586 Blaise de Vigenère published a type of polyalphabetic cipher called an autokey cipher – because its key is based on the original plaintext – before the court of Henry III of France. The cipher now known as the Vigenère cipher, however, is based on that originally described by Giovan Battista Bellaso in his 1553 book La cifra del Sig. Giovan Battista Bellaso. He built upon the tabula recta of Trithemius but added a repeating "countersign" (a key) to switch cipher alphabets every letter. Whereas Alberti and Trithemius used a fixed pattern of substitutions, Bellaso's scheme meant the pattern of substitutions could be easily changed, simply by selecting a new key. Keys were typically single words or short phrases, known to both parties in advance, or transmitted "out of band" along with the message, Bellaso's method thus required strong security for only the key. As it is relatively easy to secure a short key phrase, such as by a previous private conversation, Bellaso's system was considerably more secure. Note, however, as opposed to the modern Vigenère cipher, Bellaso's cipher didn't have 26 different "shifts" (different Caesar's ciphers) for every letter, instead having 13 shifts for pairs of letters. In the 19th century, the invention of this cipher, essentially designed by Bellaso, was misattributed to Vigenère. David Kahn, in his book, The Codebreakers lamented this misattribution, saying that history had "ignored this important contribution and instead named a regressive and elementary cipher for him [Vigenère] though he had nothing to do with it". The Vigenère cipher gained a reputation for being exceptionally strong. Noted author and mathematician Charles Lutwidge Dodgson (Lewis Carroll) called the Vigenère cipher unbreakable in his 1868 piece "The Alphabet Cipher" in a children's magazine. In 1917, Scientific American described the Vigenère cipher as "impossible of translation". That reputation was not deserved. Charles Babbage is known to have broken a variant of the cipher as early as 1854 but did not publish his work. Kasiski entirely broke the cipher and published the technique in the 19th century, but even in the 16th century, some skilled cryptanalysts could occasionally break the cipher. The Confederate States of America, for example, used a brass cipher disk to implement the Vigenère cipher during the American Civil War. The Confederacy's messages were far from secret, and the Union regularly cracked its messages. Throughout the war, the Confederate leadership primarily relied upon three key phrases: "Manchester Bluff", "Complete Victory" and, as the war came to a close, "Come Retribution". A Vigenère cipher with a completely random (and non reusable) key which is as long as the message becomes a one time pad, a theoretically unbreakable cipher. Gilbert Vernam tried to repair the broken cipher (creating the Vernam–Vigenère cipher in 1918), but the technology he used was so cumbersome as to be impracticable.

The idea behind the Vigenère cipher, like all other polyalphabetic ciphers, is to disguise the plaintext letter frequency to interfere with a straightforward application of frequency analysis. For instance, if P is the most frequent letter in a ciphertext whose plaintext is in English, one might suspect that P corresponds to e since e is the most frequently used letter in English. However, by using the Vigenère cipher, e can be enciphered as different ciphertext letters at different points in the message, which defeats simple frequency analysis. The primary weakness of the Vigenère cipher is the repeating nature of its key. If a cryptanalyst correctly guesses the key's length n, the cipher text can be treated as n interleaved Caesar ciphers, which can easily be broken individually. The key length may be discovered by brute force testing each possible value of n, or Kasiski examination and the Friedman test can help to determine the key length (see below: and ).

Once the length of the key is known, the ciphertext can be rewritten into that many columns, with each column corresponding to a single letter of the key. Each column consists of plaintext that has been encrypted by a single Caesar cipher. The Caesar key (shift) is just the letter of the Vigenère key that was used for that column. Using methods similar to those used to break the Caesar cipher, the letters in the ciphertext can be discovered. An improvement to the Kasiski examination, known as Kerckhoffs' method, matches each column's letter frequencies to shifted plaintext frequencies to discover the key letter (Caesar shift) for that column. Once every letter in the key is known, all the cryptanalyst has to do is to decrypt the ciphertext and reveal the plaintext. Kerckhoffs' method is not applicable if the Vigenère table has been scrambled, rather than using normal alphabetic sequences, but Kasiski examination and coincidence tests can still be used to determine key length.

A simple variant is to encrypt by using the Vigenère decryption method and to decrypt by using Vigenère encryption. That method is sometimes referred to as "Variant Beaufort". It is different from the Beaufort cipher, created by Francis Beaufort, which is similar to Vigenère but uses a slightly modified enciphering mechanism and tableau. The Beaufort cipher is a reciprocal cipher.

Despite the Vigenère cipher's apparent strength, it never became widely used throughout Europe. The Gronsfeld cipher is a variant attributed by Gaspar Schott to Count Gronsfeld (Josse Maximilaan van Gronsveld né van Bronckhorst) but was actually used much earlier by an ambassador of Duke of Mantua in 1560s 1570s. It is identical to the Vigenère cipher except that it uses just 10 different cipher alphabets, corresponding to the digits 0 to 9: a Gronsfeld key of 0123 is the same as a Vigenere key of ABCD. The Gronsfeld cipher is strengthened because its key is not a word, but it is weakened because it has just 10 cipher alphabets. It is Gronsfeld's cipher that became widely used throughout Germany and Europe, despite its weaknesses.

Vigenère actually invented a stronger cipher, an autokey cipher. The name "Vigenère cipher" became associated with a simpler polyalphabetic cipher instead. In fact, the two ciphers were often confused, and both were sometimes called le chiffre indéchiffrable. Babbage actually broke the much stronger autokey cipher, but Kasiski is generally credited with the first published solution to the fixed key polyalphabetic ciphers.