Ciphers: Making and Breaking Ralph Morelli Trinity College, Hartford ([email protected]) Smithsonian Institute October 31, 2009 © 2009 Ralph Morelli You are free to reuse and remix this presentation under a creative commons license provided you give credit to the author. http://creativecommons.org/licenses/by/3.0/us/ This presentation was created using Open Office 3.0, free and open source software. http://www.openoffice.org/ Part II: Cryptology in Transition Outline Polyalphabetic Substitution Alberti Cipher Vigenère Cipher – Le Chiffre Indéchiffrable Kasiski Decipherment Mechanical Ciphers The Enigma Machine WWII Leon Battista Alberti (1404-1472) Leon Battista Alberti (1404-1472) Renaissance man. Architect, author, artist, poet, philosopher. Father of Modern Cryptography – First western exposition of frequency analysis. – Invention of polyalphabetic cipher. Courtyard of the Uffizi Palace Alberti the Architect Santa Maria Novella – Florence De Cifris First comprehensive account of cryptanalysis in the West. Invention of the polyalphabetic cipher. Alberti Cipher Disk Outer disk stationary with regular alphabet. Inner disk moveable with permuted alphabet. An inner disk letter (k) is picked as index, and aligned with some letter on outer disk (B). The index is changed every 3 or 4 words and inserted into the message. “Ciao amici” might be encrypted as “BlvgyCeztkt”. Compare Letter Frequencies Plain Caesar Simple Polyalphabetic Polyalphabetic Development Alberti (~ 1472): devised genuine polyalphabetic cipher with mixed alphabet plus a practical cipher disk device. Abbot Trithemius (~ 1508): used tables of regular alphabets to be used in fixed order. Giovanni Battista Belaso (~ 1550 ): invented principle of a key or keyword to select alphabets. Giovanni Battista Porta (~ 1563): “invented” using mixed alphabets. Blaise de Vigenère (~ 1586): combined table or Trithemius, keyword of Belaso, and mixed alphabets of Porta into an autokey cipher. Johannes Trithemius (1462-1516) Abbot, occultist. First printed book crypto book. Most famous for Steganagraphia (banned book). Believed to be about occult. Decrypted in 1998. Trithemius Cipher • The Trithemius Cipher cycles through each row of the table. Encryption: Meetusatthebridge ABCDEFGHIJKLMNOPQ MFEWYXGABQOMDVRVG So-called “Chiffre Indéchiffrable” • The Bellaso Cipher uses a keyword to select alphabets. Encryption: ZEBRASZEBRASZEBRAS therearesomethirty SLFIESQITFMWSLJRTQ ** ** Decryption: ZEBRASZEBRASZEBRAS slfiesqitfmwsljrtq THEREARESOMETHIRTY Vigenère's Autokey Cipher A B C D E F G H I J K L M N O P Q R S T U V W X Y Z • Uses mixed A Z E B R A F I S H C D G J K L M N O P Q T U V W X Y B E B R A F I S H C D G J K L M N O P Q T U V W X Y Z alphabets and the text C B R A F I S H C D G J K L M N O P Q T U V W X Y Z E itself as the key. D R A F I S H C D G J K L M N O P Q T U V W X Y Z E B E A F I S H C D G J K L M N O P Q T U V W X Y Z E B R Encryption: F F I S H C D G J K L M N O P Q T U V W X Y Z E B R A G I S H C D G J K L M N O P Q T U V W X Y Z E B R A F H S H C D G J K L M N O P Q T U V W X Y Z E B R A F I Therearesomethirty (MSG=col) I H C D G J K L M N O P Q T U V W X Y Z E B R A F I S J C D G J K L M N O P Q T U V W X Y Z E B R A F I S H Xtherearesomethirt (KEY=row) K D G J K L M N O P Q T U V W X Y Z E B R A F I S H C OZGUUAOUVIZNWZMYDP (Crypto) L G J K L M N O P Q T U V W X Y Z E B R A F I S H C D M J K L M N O P Q T U V W X Y Z E B R A F I S H C D G N K L M N O P Q T U V W X Y Z E B R A F I S H C D G K Decryption: O L M N O P Q T U V W X Y Z E B R A F I S H C D G K L P M N O P Q T U V W X Y Z E B R A F I S H C D G K L M OZGUUAOUVIZNWZMYDP(MSG=ltr) Q N O P Q T U V W X Y Z E B R A F I S H C D G K L M N R O P Q T U V W X Y Z E B R A F I S H C D G K L M N O XthereareS.. (KEY=row) S P Q T U V W X Y Z E B R A F I S H C D G K L M N O P T Q T U V W X Y Z E B R A F I S H C D G K L M N O P Q O in row X gives column T U T U V W X Y Z E B R A F I S H C D G K L M N O P Q T V U V W X Y Z E B R A F I S H C D G K L M N O P Q T U ... W V W X Y Z E B R A F I S H C D G K L M N O P Q T U V V in row E gives column S X W X Y Z E B R A F I S H C D G K L M N O P Q T U V W Y X Y Z E B R A F I S H C D G K L M N O P Q T U V W X Z Y Z E B R A F I S H C D G K L M N O P Q T U V W X Y Jefferson's Wheel Cipher Invented in 1795. 26 wheels with random 26- letter alphabets. Reinvented by Etienne Bazeries in 1890s with 20-30 wheels. Rearrange the wheels (key) and write message in one row and transmit any other row. U.S. Army M-94, 1923-1942. Our Polyalphabetic Cipher Disk Outer disk stationary Z Y A with regular alphabet. X z x y e B W b Inner disk moveable w C U/ r with permuted alphabet. Vu/v D T a Keyword = zebrafish t E f S q F i/j p R s G o Q h n H J P c m d I/ l O k g K N L M Cipher Disk Exercise 1. Pick a keyword and write it in lower case letters, L to R, on the inner disk. 2. Fill in the rest of the alphabet on the inner disk (i/j and u/v go in one cell each). 3. Pick a key (e.g., A = k) and align the disks. 4. Encrypt: For each plaintext letter, find it on the outer disk and substitute the lower case letter on the inner disk. 5. Decrypt: For each ciphertext letter, find it on the inner disk and substitute the upper case letter on the outer disk. Breaking the Unbreakable Cipher Breaking the Vigenère Cipher Vigenère cipher – a keyword of length n is used to select from among 26 Caesar-shifted alphabets. Thought to be unbreakable for ~ 300 years. 1863: Friederich Kasiski, a Prussian major, developed a method to break it. 1846: Charles Babbage, a British mathematician, philosopher, and inventor, discovered the same method. Basic approach: Find the length of the keyword, n, and use frequency analysis on the n columns, each of which is a Caesar shifted alphabet. Kasiski Method Location: 01234 56789 01234 56789 01234 56789 ... Keyword: RELAT IONSR ELATI ONSRE LATIO NSREL ... Plaintext: TOBEO RNOTT OBETH ATIST HEQUE STION ... Ciphertext: KSMEH ZBBLK SMEMP OGAJX SEJCS FLZSY ... Repeated Location Distance Factors Bigram KS 9 9 9, 3 SM 10 9 9, 3 ME 11 9 9, 3 ... ... ... ... Find the distances between repeated bigrams, some of which are due to repeated bigrams in the plaintext. Factor the distances—the keyword should have length equal to one factor. Break the text into columns and use frequency analysis on each column to identify the shifted alphabet used to encrypt that column. Automating Kasiski's Method Index of Coincidence Index of coincidence – the number of times two identical letters occur in the same position in two adjacent texts. William F. Friedman (Father of American cryptography). Language Normalized IC (1/26) Plain English 0.067 German 0.079 Caesar English 0.065 Simple English 0.065 Substitution Uniform distribution 0.0385 IC – Example Plain Caesar Simple Polyalphabetic 0.064 0.064 0.064 0.040 The Chi-square Test Used for comparing and observed frequency distribution with an expected distribution.