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<title>Polyalphabetic cipher</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Polyalphabetic cipher</span></span>

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<p>A <b>polyalphabetic cipher</b> is a <a href="Substitution_cipher" title="Substitution cipher">substitution</a>, using multiple substitution alphabets. The <a href="Vigen%C3%A8re_cipher" title="Vigenère cipher">Vigenère cipher</a> is probably the best-known example of a polyalphabetic cipher, though it is a simplified special case. The <a href="Enigma_machine" title="Enigma machine">Enigma machine</a> is more complex but is still fundamentally a polyalphabetic substitution cipher.

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<div class="mw-heading mw-heading2"><h2 id="History">History</h2></div>

<p>The work of <a href="Al-Qalqashandi" title="Al-Qalqashandi">Al-Qalqashandi</a> (1355–1418), based on the earlier work of <a href="Ibn_al-Durayhim" title="Ibn al-Durayhim">Ibn al-Durayhim</a> (1312–1359), contained the first published discussion of the substitution and transposition of ciphers, as well as the first description of a polyalphabetic cipher, in which each plaintext letter is assigned more than one substitute.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> However, it has been claimed that polyalphabetic ciphers may have been developed by the Arab cryptologist <a href="Al_Kindi" class="mw-redirect" title="Al Kindi">Al Kindi</a> (801–873) centuries earlier.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

</p><p>The <a href="Alberti_cipher" title="Alberti cipher">Alberti cipher</a> by <a href="Leon_Battista_Alberti" title="Leon Battista Alberti">Leon Battista Alberti</a> around 1467 was an early polyalphabetic cipher. Alberti used a mixed alphabet to encrypt a message, but whenever he wanted to, he would switch to a different alphabet, indicating that he had done so by including an uppercase letter or a number in the cryptogram. For this encipherment Alberti used a decoder device, his <i><a href="Cipher_disk" title="Cipher disk">cipher disk</a></i>, which implemented a polyalphabetic substitution with mixed alphabets.

</p><p><a href="Johannes_Trithemius" title="Johannes Trithemius">Johannes Trithemius</a>—in his book <i>Polygraphiae libri sex</i> (Six books of polygraphia), which was published in 1518 after his death—invented a <i>progressive key</i> polyalphabetic cipher called the <a href="Trithemius_cipher" class="mw-redirect" title="Trithemius cipher">Trithemius cipher</a>.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Unlike Alberti's cipher, which switched alphabets at random intervals, Trithemius switched alphabets for each letter of the message. He started with a <a href="Tabula_recta" title="Tabula recta">tabula recta</a>, a square with 26 letters in it (although Trithemius, writing in <a href="Latin" title="Latin">Latin</a>, used 24 letters). Each alphabet was shifted one letter to the left from the one above it, and started again with A after reaching Z (see table).

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<p>Trithemius's idea was to encipher the first letter of the message using the first shifted alphabet, so A became B, B became C, etc. The second letter of the message was enciphered using the second shifted alphabet, etc. Alberti's cipher disk implemented the same scheme. It had two alphabets, one on a fixed outer ring, and the other on the rotating disk. A letter is enciphered by looking for that letter on the outer ring, and encoding it as the letter underneath it on the disk. The disk started with A underneath B, and the user rotated the disk by one letter after encrypting each letter.

</p><p>The cipher was trivial to break, and Alberti's machine implementation not much more difficult. <i>Key progression</i> in both cases was poorly concealed from attackers. Even Alberti's implementation of his polyalphabetic cipher was rather easy to break (the capitalized letter is a major clue to the cryptanalyst). For most of the next several hundred years, the significance of using multiple substitution alphabets was missed by almost everyone. Polyalphabetic substitution cipher designers seem to have concentrated on obscuring the choice of a few such alphabets (repeating as needed), not on the increased security possible by using many and never repeating any.

</p><p>The principle (particularly Alberti's unlimited additional substitution alphabets) was a major advance—the most significant in the several hundred years since <a href="Frequency_analysis" title="Frequency analysis">frequency analysis</a> had been developed. A reasonable implementation would have been (and, when finally achieved, was) vastly harder to break. It was not until the mid-19th century (in <a href="Charles_Babbage" title="Charles Babbage">Babbage</a>'s secret work during the <a href="Crimean_War" title="Crimean War">Crimean War</a> and <a href="Friedrich_Kasiski" title="Friedrich Kasiski">Friedrich Kasiski</a>'s generally equivalent public disclosure some years later) that <a href="Cryptanalysis" title="Cryptanalysis">cryptanalysis</a> of well-implemented polyalphabetic ciphers got anywhere at all. <i>See</i> <a href="Kasiski_examination" title="Kasiski examination">Kasiski examination</a>.

</p><p><a href="Abramo_Colorni" title="Abramo Colorni">Abramo Colorni</a> described polyalphabetic ciphers in his 1593 work, <i>Scotographia</i>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2></div>

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</style><cite id="CITEREFLennon2018" class="citation book cs1">Lennon, Brian (2018). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=jbpTDwAAQBAJ&pg=PT26"><i>Passwords: Philology, Security, Authentication</i></a>. <a href="Harvard_University_Press" title="Harvard University Press">Harvard University Press</a>. p. 26. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9780674985377</bdi>.</cite></span>

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<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFMaclean2012" class="citation cs2">Maclean, Donald (20 February 2012), <a rel="nofollow" class="external text" href="http://donaldmaclean.wordpress.com/2012/02/20/al-kindi/"><i>Al-Kindi</i></a><span class="reference-accessdate">, retrieved <span class="nowrap">13 April</span> 2012</span></cite></span>

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<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">Johann Tritheim, <i>Polygraphiae libri sex</i> … (Basel, Switzerland: Michael Furter and Adam Petri, 1518), <i>Liber quintus</i> (fifth book), pages 461-462; the <i>Recta transpositionis tabula</i> (square table of transpositions, or "Vigenère table") appears on <a rel="nofollow" class="external text" href="http://lcweb2.loc.gov/cgi-bin/ampage?collId=rbc3&fileName=rbc0001_2009fabyan12345page.db&recNum=470">page 463.</a></span>

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<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite id="CITEREFStrasser2007" class="citation cs2">Strasser, Gerhard F. (2007), <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://linkinghub.elsevier.com/retrieve/pii/B9780444516084500122">"The rise of cryptology in the European Renaissance"</a></span>, <i>The History of Information Security</i>, Elsevier, pp. <span class="nowrap">277–</span>325, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fb978-044451608-4%2F50012-2">10.1016/b978-044451608-4/50012-2</a>, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-444-51608-4</bdi><span class="reference-accessdate">, retrieved <span class="nowrap">2024-10-20</span></span></cite></span>

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<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

<ul><li><cite id="CITEREFAlberti1997" class="citation cs2"><a href="Leon_Battista_Alberti" title="Leon Battista Alberti">Alberti, Leon Battista</a> (1997), <i>A Treatise on Ciphers, trans. A. Zaccagnini. Foreword by <a href="David_Kahn_(writer)" title="David Kahn (writer)">David Kahn</a></i>, Torino: Galimberti</cite></li>

<li><cite id="CITEREFChurchhouse2002" class="citation cs2">Churchhouse, Robert (2002), <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/codesciphersjuli0000chur"><i>Codes and Ciphers: Julius Caesar, the Enigma and the Internet</i></a></span>, Cambridge: Cambridge University Press, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-521-00890-7</bdi></cite></li>

<li><cite id="CITEREFGaines1939" class="citation cs2"><a href="Helen_Fouch%C3%A9_Gaines" title="Helen Fouché Gaines">Gaines, Helen Fouché</a> (1939), <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/cryptanalysis00hele"><i>Cryptanalysis</i></a></span>, Dover, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-486-20097-3</bdi></cite> <span class="cs1-hidden-error citation-comment"><code class="cs1-code">{{citation}}</code>: </span><span class="cs1-hidden-error citation-comment">ISBN / Date incompatibility (help)</span></li></ul>

<ul><li><a href="Topics_in_cryptography" class="mw-redirect" title="Topics in cryptography">Topics in cryptography</a></li></ul>

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<ul><li><a href="Alberti_cipher" title="Alberti cipher">Alberti</a></li>

<li><a href="Enigma_machine" title="Enigma machine">Enigma</a></li>

<li><a href="Trithemius_cipher" class="mw-redirect" title="Trithemius cipher">Trithemius</a></li>

<li><a href="Vigen%C3%A8re_cipher" title="Vigenère cipher">Vigenère</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="Polybius_square" title="Polybius square">Polybius square</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="ADFGVX_cipher" title="ADFGVX cipher">ADFGVX</a></li>

<li><a href="Bifid_cipher" title="Bifid cipher">Bifid</a></li>

<li><a href="Nihilist_cipher" title="Nihilist cipher">Nihilist</a></li>

<li><a href="Trifid_cipher" title="Trifid cipher">Trifid</a></li>

<li><a href="VIC_cipher" title="VIC cipher">VIC cipher</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Square</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Playfair_cipher" title="Playfair cipher">Playfair</a></li>

<li><a href="Two-square_cipher" title="Two-square cipher">Two-square</a></li>

<li><a href="Four-square_cipher" title="Four-square cipher">Four-square</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="Substitution_cipher" title="Substitution cipher">Substitution</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Affine_cipher" title="Affine cipher">Affine</a></li>

<li><a href="Atbash" title="Atbash">Atbash</a></li>

<li><a href="Autokey_cipher" title="Autokey cipher">Autokey</a></li>

<li><a href="Beaufort_cipher" title="Beaufort cipher">Beaufort</a></li>

<li><a href="Caesar_cipher" title="Caesar cipher">Caesar</a></li>

<li><a href="Chaocipher" title="Chaocipher">Chaocipher</a></li>

<li><a href="Great_Cipher" title="Great Cipher">Great</a></li>

<li><a href="Pigpen_cipher" title="Pigpen cipher">Pigpen</a></li>

<li><a href="Running_key_cipher" title="Running key cipher">Running key</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="Transposition_cipher" title="Transposition cipher">Transposition</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Transposition_cipher#Columnar_transposition" title="Transposition cipher">Columnar</a></li>

<li><a href="Transposition_cipher#Double_transposition" title="Transposition cipher">Double</a></li>

<li><a href="Transposition_cipher#Myszkowski_transposition" title="Transposition cipher">Myszkowski</a></li>

<li><a href="Rail_fence_cipher" title="Rail fence cipher">Rail fence</a></li>

<li><a href="Transposition_cipher#Route_cipher" title="Transposition cipher">Route</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

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<li><a href="Rasterschl%C3%BCssel_44" title="Rasterschlüssel 44">Rasterschlüssel 44</a></li>

<li><a href="Reihenschieber" title="Reihenschieber">Reihenschieber</a></li>

<li><a href="Reservehandverfahren" title="Reservehandverfahren">Reservehandverfahren</a></li>

<li><a href="Slidex" title="Slidex">Slidex</a></li>

<li><a href="Solitaire_(cipher)" title="Solitaire (cipher)">Solitaire</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Code_(cryptography)" title="Code (cryptography)">Codes</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Code_talker" title="Code talker">Code talker</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Steganography" title="Steganography">Steganography</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Bacon's_cipher" title="Bacon's cipher">Bacon</a></li>

<li><a href="Grille_(cryptography)" title="Grille (cryptography)">Grille</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Cryptanalysis</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Cryptogram" title="Cryptogram">Cryptogram</a></li>

<li><a href="Frequency_analysis" title="Frequency analysis">Frequency analysis</a></li>

<li><a href="Index_of_coincidence" title="Index of coincidence">Index of coincidence</a> (Units: <a href="Hartley_(unit)" title="Hartley (unit)">Ban</a> and <a href="Nat_(unit)" title="Nat (unit)">Nat</a>)</li>

<li><a href="Information_leakage" title="Information leakage">Information leakage</a></li>

<li><a href="Kasiski_examination" title="Kasiski examination">Kasiski examination</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Cryptography149" style="font-size:114%;margin:0 4em"><a href="Cryptography" title="Cryptography">Cryptography</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">General</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="History_of_cryptography" title="History of cryptography">History of cryptography</a></li>

<li><a href="Outline_of_cryptography" title="Outline of cryptography">Outline of cryptography</a></li>

<li><a href="Classical_cipher" title="Classical cipher">Classical cipher</a></li>

<li><a href="Cryptographic_protocol" title="Cryptographic protocol">Cryptographic protocol</a>

<ul><li><a href="Authentication_protocol" title="Authentication protocol">Authentication protocol</a></li></ul></li>

<li><a href="Cryptographic_primitive" title="Cryptographic primitive">Cryptographic primitive</a></li>

<li><a href="Cryptanalysis" title="Cryptanalysis">Cryptanalysis</a></li>

<li><a href="Cryptocurrency" title="Cryptocurrency">Cryptocurrency</a></li>

<li><a href="Cryptosystem" title="Cryptosystem">Cryptosystem</a></li>

<li><a href="Cryptographic_nonce" title="Cryptographic nonce">Cryptographic nonce</a></li>

<li><a href="Cryptovirology" title="Cryptovirology">Cryptovirology</a></li>

<li><a href="Hash_function" title="Hash function">Hash function</a>

<ul><li><a href="Cryptographic_hash_function" title="Cryptographic hash function">Cryptographic hash function</a></li>

<li><a href="Key_derivation_function" title="Key derivation function">Key derivation function</a></li>

<li><a href="Secure_Hash_Algorithms" title="Secure Hash Algorithms">Secure Hash Algorithms</a></li></ul></li>

<li><a href="Digital_signature" title="Digital signature">Digital signature</a></li>

<li><a href="Kleptography" title="Kleptography">Kleptography</a></li>

<li><a href="Key_(cryptography)" title="Key (cryptography)">Key (cryptography)</a></li>

<li><a href="Key_exchange" title="Key exchange">Key exchange</a></li>

<li><a href="Key_generator" title="Key generator">Key generator</a></li>

<li><a href="Key_schedule" title="Key schedule">Key schedule</a></li>

<li><a href="Key_stretching" title="Key stretching">Key stretching</a></li>

<li><a href="Keygen" title="Keygen">Keygen</a></li>

<li>Machines</li>

<li><a href="Cryptojacking_malware" class="mw-redirect" title="Cryptojacking malware">Cryptojacking malware</a></li>

<li><a href="Ransomware" title="Ransomware">Ransomware</a></li>

<li><a href="Random_number_generation" title="Random number generation">Random number generation</a>

<ul><li><a href="Cryptographically_secure_pseudorandom_number_generator" title="Cryptographically secure pseudorandom number generator">Cryptographically secure pseudorandom number generator</a> (CSPRNG)</li></ul></li>

<li><a href="Pseudorandom_noise" title="Pseudorandom noise">Pseudorandom noise</a> (PRN)</li>

<li><a href="Secure_channel" title="Secure channel">Secure channel</a></li>

<li><a href="Insecure_channel" class="mw-redirect" title="Insecure channel">Insecure channel</a></li>

<li><a href="Subliminal_channel" title="Subliminal channel">Subliminal channel</a></li>

<li><a href="Encryption" title="Encryption">Encryption</a></li>

<li><a href="Decryption" class="mw-redirect" title="Decryption">Decryption</a></li>

<li><a href="End-to-end_encryption" title="End-to-end encryption">End-to-end encryption</a></li>

<li><a href="Harvest_now%2C_decrypt_later" title="Harvest now, decrypt later">Harvest now, decrypt later</a></li>

<li><a href="Information-theoretic_security" title="Information-theoretic security">Information-theoretic security</a></li>

<li><a href="Plaintext" title="Plaintext">Plaintext</a></li>

<li><a href="Codetext" class="mw-redirect" title="Codetext">Codetext</a></li>

<li><a href="Ciphertext" title="Ciphertext">Ciphertext</a></li>

<li><a href="Shared_secret" title="Shared secret">Shared secret</a></li>

<li><a href="Trapdoor_function" title="Trapdoor function">Trapdoor function</a></li>

<li><a href="Trusted_timestamping" title="Trusted timestamping">Trusted timestamping</a></li>

<li><a href="Key-based_routing" title="Key-based routing">Key-based routing</a></li>

<li><a href="Onion_routing" title="Onion routing">Onion routing</a></li>

<li><a href="Garlic_routing" title="Garlic routing">Garlic routing</a></li>

<li><a href="Kademlia" title="Kademlia">Kademlia</a></li>

<li><a href="Mix_network" title="Mix network">Mix network</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Mathematics</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Cryptographic_hash_function" title="Cryptographic hash function">Cryptographic hash function</a></li>

<li><a href="Block_cipher" title="Block cipher">Block cipher</a></li>

<li><a href="Stream_cipher" title="Stream cipher">Stream cipher</a></li>

<li><a href="Symmetric-key_algorithm" title="Symmetric-key algorithm">Symmetric-key algorithm</a></li>

<li><a href="Authenticated_encryption" title="Authenticated encryption">Authenticated encryption</a></li>

<li><a href="Public-key_cryptography" title="Public-key cryptography">Public-key cryptography</a></li>

<li><a href="Quantum_key_distribution" title="Quantum key distribution">Quantum key distribution</a></li>

<li><a href="Quantum_cryptography" title="Quantum cryptography">Quantum cryptography</a></li>

<li><a href="Post-quantum_cryptography" title="Post-quantum cryptography">Post-quantum cryptography</a></li>

<li><a href="Message_authentication_code" title="Message authentication code">Message authentication code</a></li>

<li><a href="Cryptographically_secure_pseudorandom_number_generator" title="Cryptographically secure pseudorandom number generator">Random numbers</a></li>

<li><a href="Steganography" title="Steganography">Steganography</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<ul><li><span class="noviewer" typeof="mw:File"><span title="Category"></span></span> Category</li></ul>

</div></td></tr></tbody></table><div></div></td></tr></tbody></table></div></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2025-05-26" href="https://en.wikipedia.org/wiki/?title=Polyalphabetic_cipher&oldid=1292263399">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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