Editing Vigenère cipher (section)

==History==
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 [[Polygraphia (book)|''Polygraphia'']] (which was completed in manuscript form in 1508 but first published in 1518),<ref>{{cite book |last1=Gamer |first1=Maximilian |editor1-last=Baier |editor1-first=Thomas |editor2-last=Schultheiß |editor2-first=Jochen |title=Würzburger Humanismus |trans-title=The Humanism of Würzburg |date=2015 |publisher=Narr Verlag |location=Tübingen, Germany |pages=121–141 |language=de |chapter=Die Polygraphia des Johannes Trithemius. Zwei Fassungen eines frühneuzeitlichen Handbuchs zur Geheimschrift [The Polygraphia of Johannes Trithemius. Two editions of an early modern handbook on cryptography]}} See pp. 121–122.</ref> invented the [[tabula recta]], a critical component of the Vigenère cipher.<ref>{{cite book |last1=Trithemius |first1=Joannis |title=Polygraphiae, libri sex … |trans-title=Cryptography, in six books … |date=1518 |publisher=Johann Haselberg |location=Reichenau, (Germany) |chapter=Liber quintus exordium capit (Book 5, Ch. 1) |pages=471 |language=la}}  Available at: [http://lcweb2.loc.gov/cgi-bin/ampage?collId=rbc3&fileName=rbc0001_2009fabyan12345page.db&recNum=470 George Fabyan Collection (Library of Congress; Washington, D.C., U.S.A.)] (Note: The pages of this book are not numbered.)</ref> The [[Trithemius cipher]], however, provided a progressive, rather rigid and predictable system for switching between cipher alphabets.<ref group=note>In a separate manuscript that Trithemius called the ''Clavis Polygraphiae'' (The Key to the Polygraphia), he explained (among other things) how to encipher messages by using a polyalphabetic cipher and how to decipher such messages.  The ''Clavis Polygraphiae'' was not always included in the original 1518 printed copies, and even when it was included, it wasn't always inserted in the same location in the ''Polygraphiae''.  From (Gamer, 2015), p. 129:  ''"Eine eigene Stellung innerhalb … in den Ausführungen zu Buch VI."''  (The ''Clavis'' occupies a peculiar place within the text that's been passed down only in print.  Trithemius alludes several times in other places to the existence of a ''Clavis Polygraphiae'' as a separate work, contemporaneous with the manuscript of 1508.  However, we know only the edition that is bound with the printed version, which was sporadically adapted to changes during printing, as often as not – as, for example, in the case of the shifted chapter on alphanumeric number notation. The ''Clavis'' didn't accompany this relocation: the explanations of the representations of numbers remained in the remarks on Book VI.)

The ''Clavis'' explains how to encipher and decipher messages by using polyalphabetic ciphers.  In Trithemius' examples, he decoded a message by using two Vigenere tables – one in which the letters are in normal alphabetical order and the other in which the letters are in reversed order (see (Gamer, 2015), p. 128).  From [https://www.digitale-sammlungen.de/de/view/bsb11200432?page=19 (Trithemius, 1518), pp. 19–20]:

'''Original Latin text''':  ''"In primis tabulam descripsimus rectam, alphabeta quatuor & viginti continentem, per cuius intelligentiam tot poterunt alphabeta componi, quot stellae numerantur in firmamento caeli.  Quot enim in ipsa tabula sunt grammata, totiens consurgunt ex arte decies centena milia per ordinem alphabeta.  Post haec tabulam distribuimus aversam, quae totiens consurget in aliam, quotiens literam mutaveris a capite primam.  Est autem litera prima in tabula recta b, & in aversa z.  In quarum locum quotiens reposueris quamlibet aliam variatam totiens invenies tabulam per omnia novam, & ita usque ad infinitum.  Deinde primam tabulam rectam expandimus, unicuique literae transpositae nigrae illam quam repraesentat ad caput eius cum minio collocantes, ut modum scribendi faciliorem lectori praeberemus.  Est autem modus iste scribendi, ut in primo alphabeto nigro, capias occultae sententiae literam unam, de secundo aliam, de tertio tertiam, & sic consequenter usque ad finem.  Quo cum perveneris, totiens ad ordinem primum redeundum memineris, quousque mentis tuae secretum mysterium occultando compleveris.  Verum ut ordinem videas, ponamus exemplum.  Hxpf gfbmcz fueib gmbt gxhsr ege rbd qopmauwu. wfxegk ak tnrqxyx.  Huius mystici sermonis sententia est.  Hunc caveto virum, quia malus est, fur, deceptor, mendax & iniquus.  Cernis iam nunc lector quam mirabilem transpositionem literarum alphabeti haec tabula reddat, cum sit nemo qui sine noticia eius hoc valeat penetrare secretum.  Exedit enim modus iste scribendi omnem transpositionem literarum communem, cum unaquaeque litera semper de una serie alphabeti mutetur in aliam.  Ex tabula quoque aversa quam simili distributione per ordinem expandimus, pro introductione tale ponamus exemplum.  Rdkt, stznyb, tevqz, fnzf, fdrgh, vfd.  Cuius arcani sensus est talis, Hunc caveto virum, quia malus [est]. Et nota quod sub exemplo tabulae recte iam posito seriem occultam a principio per totum eius deduximus, & deinceps continuando similiter per aversam, rursusque circulum facimus, ut cernis ad principium tabulae rectae."''<br>
'''English translation''':  In the first [illustration], we have transcribed a regular table [i.e., ''tabula recta'', a table in which the letters of alphabet are listed in their normal order; see [http://lcweb2.loc.gov/cgi-bin/ampage?collId=rbc3&fileName=rbc0001_2009fabyan12345page.db&recNum=470 (Trithemius, 1518), p. 471.]) containing 24 alphabets [Note: Trithemius used alphabets containing only 24 letters by setting j=i and v=u.], by which knowledge they will be able to compose as many alphabets as stars are numbered in the firmament of heaven.  For in the table itself there are as many letters as arise by [applying] skill – a million per alphabetical row. [That is, the letters in the table need not be listed in alphabetical order, so many enciphering tables can be created.]  After this, we arrange [the alphabets in] the reverse table [i.e., ''tabula aversa'', a table in which the letters of the alphabet are listed in reverse order; see [http://lcweb2.loc.gov/cgi-bin/ampage?collId=rbc3&fileName=rbc0001_2009fabyan12345page.db&recNum=471 (Trithemius, 1518), p. 472.]), which will arise in the other [reversed table] as many times as you will have changed [i.e., permuted] the first letter of the top [of the regular table].  And so the first letter in the regular table is b, and z in the reverse [table].  As often as you will have put in its place another changed [table], you will find a new table for everything, and so on indefinitely.  [That is, again, many enciphering tables can be created.]  Next we explain the first regular table: it shows how it is assigning, to each transposed black letter, [a letter] in red [ink along] its [i.e., the table's] top [border], in order to show to the reader an easier way of writing [i.e., of deciphering messages].  And that is a way of writing so that in the first black alphabet [i.e., an alphabet printed in the table using black, not red, ink], you will get one letter of the hidden sentence [i.e., the deciphered message]; from the second [black alphabet], another [deciphered letter]; from the third [black alphabet], a third [deciphered letter]; and thus accordingly until the end.  You will have arrived there [i.e., at the end] when you will have recalled returning many times to the first row, until you will have completed concealing the secret mystery of your thought. [That is, the message is deciphered by deciphering its first 24 letters by using the ''tabula recta'', then repeating the procedure by using the same ''tabula recta'' to decipher the next 24 letters of the message, and so on.]  However, so that you [can] see the sequence [i.e., procedure], we present an example:  ''Hxpf gfbmcz fueib gmbt gxhsr ege rbd qopmauwu wfxegk ak tnrqxyx.''  The meaning of this mystical sentence is:  ''Hunc caveto virum, quia malus est, fur, deceptor, mendax et iniquus.'' (Beware of this man, who is bad, a thief, a deceiver, a liar, and unjust.)  You already discern now, reader, how this table renders an astonishing transposition of the letters of the alphabet, because there is no one who, without acquaintance of this, can penetrate the secret.  For that method of writing corrodes every transposition of common letters, because each and every letter of one sequence of the alphabet is always changed into another [letter].  Likewise, we explain how [to decipher a message], by means of the sequence [i.e., the deciphering procedure], from the reverse table with a similar arrangement [of letters]; as an introduction, we present such an example:  ''Rdkt, stznyb, tevqz, fnzf, fdrgh, vfd.'' The secret meaning of which is such:  ''Hunc caveto virum, quia malus [est].'' (Beware of this man, who is bad.)  And note about the example of the regular table [that was] already presented [i.e., the example that began with ''Hxpf''], that we derived the secret series [i.e., the deciphered message] from the beginning through all of it [i.e., of the regular table], and thereafter by continuing similarly by means of the reverse [table], and again we make a circle, so that you are looking at the beginning of the regular table. [That is, the message is deciphered by using the regular table, but if the message is longer than 24 characters, then the decipherment continues by using the reverse table, and if necessary, one continues to decipher by returning to the regular table – and so forth.]</ref>

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]].<ref>{{cite book|last1=Vigenère|first1=Blaise de|title=Traicté des Chiffres, ou Secretes Manieres d'Escrire|trans-title=Treatise on ciphers, or secret ways of writing|date=1586|publisher=Abel l'Angelier|location=Paris, France|url=http://gallica.bnf.fr/ark:/12148/bpt6k94009991.image|language=fr}}</ref> 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''.<ref>{{cite book|last1=Bellaso|first1=Giovan Battista|title=La Cifra del Sig. Giovan Battista Belaso …|date=1553|location=Venice, (Italy)|language=it}}  Available at: [https://bibdig.museogalileo.it/Teca/Viewer;jsessionid=E02FA6976F859981BC4EC1DF5CC3B240?an=976325&vis=D#page/1/mode/2up Museo Galileo (Florence (Firenze), Italy)]</ref> He built upon the tabula recta of Trithemius but added a repeating "countersign" (a [[Key (cryptography)|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.{{Citation needed|date=April 2012}}

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".<ref name="KahnOrigin">{{cite book|first=Kahn|last=David|year=1999|title=The Codebreakers: The Story of Secret Writing|chapter=On the Origin of a Species|publisher=Simon & Schuster|isbn=0-684-83130-9}}</ref>

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".<ref>{{cite journal|last1=(Anon.)|title=A new cipher code|journal=Scientific American Supplement|date=27 January 1917|volume=83|issue=2143|page=61|doi=10.1038/scientificamerican01271917-61csupp|url=https://babel.hathitrust.org/cgi/pt?id=uc1.31210000211050;view=1up;seq=69}}<br>
However, see also:
*  {{cite journal|last1=Borden|first1=Howard A.|title=Letter to the Editor: Cipher codes|journal=Scientific American Supplement|date=3 March 1917|volume=83|issue=2148|page=139|doi=10.1038/scientificamerican03031917-139csupp|url=https://babel.hathitrust.org/cgi/pt?id=uc1.31210000211050;view=1up;seq=147}}
*  {{cite journal|last1=Holstein|first1=Otto|title=Letter to the Editor: A new cipher|journal=Scientific American Supplement|date=14 April 1917|volume=83|issue=2154|page=235|url=https://babel.hathitrust.org/cgi/pt?id=uc1.31210000211050;view=1up;seq=243}}
*  {{cite journal|last1=Holstein|first1=Otto|title=The ciphers of Porta and Vigenère: The original undecipherable code, and how to decipher it|journal=Scientific American Monthly|date=October 1921|volume=4|pages=332–334|url=https://babel.hathitrust.org/cgi/pt?id=pst.000018628043;view=1up;seq=338}}</ref><ref>{{cite book|first=Lars R.|last=Knudsen|year=1998|title=State of the Art in Applied Cryptography: Course on Computer Security and Industrial Cryptograph Leuven Belgium, June 1997 Revised Lectures |url=https://archive.org/details/stateartappliedc00pren|url-access=limited|chapter=Block Ciphers—a survey|editor=Bart Preneel and Vincent Rijmen|pages=[https://archive.org/details/stateartappliedc00pren/page/n35 29]|publisher=Springer|isbn=3-540-65474-7|location=Berlin; London}}</ref> 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.<ref name="Singh">{{cite book|first=Simon|last=Singh|year=1999|title=The Code Book|chapter=Chapter 2: Le Chiffre Indéchiffrable|pages=[https://archive.org/details/codebook00simo/page/63 63–78]|publisher=[[Anchor Books#Divisions and imprints|Anchor Books]], [[Random House]]|isbn=0-385-49532-3|chapter-url-access=registration|chapter-url=https://archive.org/details/codebook00simo/page/63}}</ref> 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.<ref name="KahnOrigin" />

[[File:Cryptographic sliding rule-IMG 0533.jpg|thumb|Cryptographic slide rule used as a calculation aid by the Swiss Army between 1914 and 1940.]]
The Vigenère cipher is simple enough to be a field cipher if it is used in conjunction with cipher disks.<ref>{{usurped|1=[https://web.archive.org/web/20051205013154/http://www.vectorsite.net/ttcode_03.html#m2 Codes, Ciphers, & Codebreaking]}} (The Rise Of Field Ciphers)</ref> 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".<ref>{{cite book|first=Kahn|last=David|year=1999|title=The Codebreakers: The Story of Secret Writing|chapter=Crises of the Union|pages=217–221|publisher=Simon & Schuster|isbn=0-684-83130-9}}</ref>

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.<ref>Stanislaw Jarecki, [http://www.ics.uci.edu/~stasio/fall04/lect1.pdf "Crypto Overview, Perfect Secrecy, One-time Pad"], ''University of California'', September 28, 2004, Retrieved November 20, 2016</ref> [[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.<ref>{{Citation |last= Simmons |first= Gustavus J. |author-link= Gustavus J. Simmons |title= Vernam-Vigenère cipher |publisher= Encyclopedia Britannica |url= https://www.britannica.com/topic/Vernam-Vigenere-cipher }}</ref>