Ciphers: Making and Breaking Ralph Morelli Trinity College, Hartford (Ralph.Morelli@Trincoll.Edu)

Ciphers: Making and Breaking Ralph Morelli Trinity College, Hartford ([email protected])

Smithsonian Institute October 31, 2009

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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)

 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

S q

F i/j

G o

h n

P c

d I/ l

O k g

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.

 Goodness-of-fit statistic – the smaller the better.

Automated Algorithm

 Assumes: long enough polyalphabetic cipher text  For each possible keyword length, 2, 3, 4, ..., k – Divide the text into k columns. – Compute the average the IC for the columns. – Select the IC that is closest to 0.067  For each of the k columns – For each possible shift, 1..26. – Compute the Chi-square value. – Select the minimum as the correct Caesar alphabet.

Demo: http://starbase.cs.trincoll.edu/~crypto Rotor Machines

The Enigma Machine

The Enigma Rotor

Rotor Details

Wiring Diagram

Cool Simulation: http://enigmaco.de/enigma/enigma.html

Enigma Cryptanalysis: Poles

 1931: Poles deduced the wirings of rotors from betrayed documents and made a replica.  Code book with daily keys  Plugboard settings: A/K, B/G, M/S, …  Rotor order: 2-3-1  Rotor setting: Q-C-W  Message key transmitted twice: RAMRAM – LVGHIB  Polish cryptanalysis – cracked the day keys:  L and H encrypt R, V and I encrypt A, G and B encrypt M.  Letter chains (A—F—W—A) led to deduction of daily key.  Marian Rejewski: Number of links independent of plugboard so 1017 daily keys reduced to 6 x 263 = 105,456.

Breaking Enigma

Alan Turing Marian Rejewski Government Code Polish Biuro Syzfrow and Cypher School

Hut 6, Bletchley Park

Enigma Cryptanalysis: Brits

 Alan Turing, GC&CS, Bletchley Park  159,000,000,000,000,000,000 daily keys.  Exploited cycles within cribs of probable words. f u h r e r f--R--r--E--e--F R J T E F H  Turing bombes—16 in all, each with 12 sets of Enigma rotors for loops of up to 12 links.  Given a crib, the bombes would work out the rotor settings (independent of plugboard). Bletchley Park Bombe

Replica used in Enigma movie.

Bletchley Park Model Principles and Observations

 Kerckhoff's principle – the cipher requires a key and should work even if the cipher is known.

 Simplicity – More secure ciphers went unused because they were thought to be too difficult.

 Cryptanalysts were ahead of cryptographers.

 Mary Queen of Scots' problem: Implementation, implementation, implementation.