Substitution Ciphers

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Substitution Ciphers
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Substitution Ciphers

• Monoalphabetic cipher
• Caesar cipher
• Polyalphabetic cipher
• Vigenère cipher
• Multiple letter cipher
• Playfair cipher

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Monoalphabetic cipher

• Plaintext characters are substituted by a
  different alphabet stream of characters shifted
  to the right or left by n positions
• E.g., ABCDEFGHIJKLMNOPQRSTUVWXYZ
• DEFGHIJKLMNOPQRSTUVWXYZABC
• Caesar cipher corresponds to n 3
• Julius Caesar used the Caesar cipher method

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Monoalphabetic cipher

• The substitution cipher by shifting alphabets
  gives 26! gt 4 x 1026 possibilities
• This might appear to be too many choices to try
  for an exhaustive attack
• This is a weak cipher because it would be easy to
  guess the pattern
• Mono-alphabetic ciphers are vulnerable to
  cryptanalysis attack

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Monoalphabetic cipher

• The shift pattern above could be replaced by
  random assignment of characters for each alphabet
• E.g., ABCDEFGHIJKLMNOPQRSTUVWXYZ
• PMJSQOLEYTVUAXIKCGBWDRNHZF
• This would also give 26! possibilities

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Pigpen Cipher

• Pigpen cipher is a variation on letter
  substitution
• Alphabets are arranged as follows

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Pigpen Cipher diagram (contd)
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Pigpen Cipher

• Alphabets will be represented by the
  corresponding diagram
• E.g., WAG would be
• This is a weak cipher

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ADFGVX Cipher

• This is a variation on substitution cipher and is
  a strong cipher

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ADFGVX Cipher

• Rules
• Remove spaces and punctuation marks from message
• For each letter or number substitute the letter
  pair from the column and row heading
• Next, use a transposition operation on the pair
  of letters using a key word (which the receiver
  knows)
• Rearrange the columns of the new arrangement in
  alphabetical order
• Finally, arrange the letters from consecutive
  columns

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ADFGVX Cipher

• E.g., Message SEE ME IN MALL
• SEEMEINMALL
• VDXDXDGXXDVGAXGXDVDADA
• Use keyword of INFOSEC
• Arrange the stage 1 ciphertext characters in a
  fresh grid with keyword as the column heading
• Ciphertext is written in column order from left
  to right

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ADFGVX Cipher
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ADFGVX Cipher
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ADFGVX Cipher

• Ciphertext is
• GXVDAAXDDVXGDXXDVVXGD
• Recipient reverses the process using the same
  keyword and gets the plaintext
• Reason for this cipher using the name ADFGVX is
  that in Morse code these characters all have
  dissimilar patterns of dots and dashes

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Polyalphabetic Cipher

• In monoalphabetic cipher the problem was that
  each character was substituted by a single
  character
• Cryptanalysts are helped by the fact that they
  have to see what character would correspond in
  plaintext for a given ciphertext character
• Polyalphabetic ciphers goal is to make this
  process difficult

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Polyalphabetic Cipher

• In polyalphabetic cipher, each plaintext
  character may be replaced by more than one
  character
• Since there are only 26 alphabets this process
  will require using a different representation
  than the alphabets
• Alphabets A through Z are replaced by 00, 01,
  02, , 25
• We need two digits in this representation since
  we need to know how to reverse the process at the
  decryption side

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Polyalphabetic Cipher

• The most common method used is Vigenère cipher
• Vigenère cipher starts with a 26 x 26 matrix of
  alphabets in sequence. First row starts with
  A, second row starts with B, etc.
• Like the ADFGVX cipher, this cipher also requires
  a keyword that the sender and receiver know ahead
  of time
• Each character of the message is combined with
  the characters of the keyword to find the
  ciphertext character

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Vigenère Cipher Table

• 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
• A 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
• B B 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
• C C D E F G H I J K L M N O P Q R S T U V W X Y
  Z A B
• D D E F G H I J K L M N O P Q R S T U V W X Y Z
  A B C
• E E F G H I J K L M N O P Q R S T U V W X Y Z A
  B C D
• F F G H I J K L M N O P Q R S T U V W X Y Z A B
  C D E
• G G H I J K L M N O P Q R S T U V W X Y Z A B C
  D E F
• H H I J K L M N O P Q R S T U V W X Y Z A B C D
  E F G
• I I J K L M N O P Q R S T U V W X Y Z A B C D
  E F G H
• J J K L M N O P Q R S T U V W X Y Z A B C D E F
  G H I
• K K L M N O P Q R S T U V W X Y Z A B C D E F G
  H I J
• L L M N O P Q R S T U V W X Y Z A B C D E F G H
  I J K
• M M N O P Q R S T U V W X Y Z A B C D E F G H I J
  K L

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Vigenère Cipher Table (contd)

• 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
• N N O P Q R S T U V W X Y Z A B C D E F G H I J
  K L M
• O O P Q R S T U V W X Y Z A B C D E F G H I J K
  L M N
• P P Q R S T U V W X Y Z A B C D E F G H I J K L
  M N O
• Q Q R S T U V W X Y Z A B C D E F G H I J K L M
  N O P
• R R S T U V W X Y Z A B C D E F G H I J K L M N
  O P Q
• S S T U V W X Y Z A B C D E F G H I J K L M N O
  P Q R
• T T U V W X Y Z A B C D E F G H I J K L M N O P
  Q R S
• U U V W X Y Z A B C D E F G H I J K L M N O P Q
  R S T
• V V W X Y Z A B C D E F G H I J K L M N O P Q R
  S T U
• W W X Y Z A B C D E F G H I J K L M N O P Q R S
  T U V
• X X Y Z A B C D E F G H I J K L M N O P Q R S T
  U V W
• Y Y Z A B C D E F G H I J K L M N O P Q R S T U
  V W X
• Z Z 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

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Polyalphabetic Cipher

• E.g., Message SEE ME IN MALL
• Take keyword as INFOSEC
• Vigenère cipher works as follows
• S E E M E I N M A L L
• I N F O S E C I N F O
• -------------------------------------
• A R J A W M P U N Q Z

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Polyalphabetic Cipher

• To decrypt, the receiver places the keyword
  characters below each ciphertext character
• Using the table, choose the row corresponding to
  the keyword character and look for the ciphertext
  character in that row
• Plaintext character is then at the top of that
  column

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Polyalphabetic Cipher

• Decryption of ciphertext
• A R J A W M P U N Q Z
• I N F O S E C I N F O
• -------------------------------------
• S E E M E I N M A L L
• Best feature is that same plaintext character is
  substituted by different ciphertext characters
  (i.e., polyalphabetic)

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Vigenère Cipher

• Easiest way to handle Vigenère cipher is to use
  arithmetic modulo 26
• This approach dispenses with the need for the
  table
• Keyword is converted to numbers and corresponding
  numbers in message and keyword are added modulo 26

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Beale Cipher

• Also known as book cipher
• Keyword is taken as the first few words of a book
  that is agreed upon by sender and receiver
• Everything else works like the Vigenère cipher

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Hill Cipher

• This involves the mathematical concept of
  matrices which we did not discuss
• If you are interested then you can see pages
  37-40 of Stallings, 2nd edition book on
  Cryptography

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Polyalphabetic cipher

• Vigenère cipher uses the fact that the keyword
  character helps to get different ciphertext
  characters from the table
• Instead of the Vigenère table, one could develop
  a new table in which each character is
  represented as an integer and the ciphertext
  could use multiple digits for substitution
  depending on the frequency analysis of the letter
• E.g., Q gets only one substitution value where as
  E gets 12 different substitution values, and so on

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Transposition Cipher

• Also known as a permutation cipher
• Permutation is an arrangement of the original
  order of letters or numbers
• E.g., a 1 2 3
• 3 1 2
• a is a permutation of 1, 2, 3 such that
• 1 3 2 1 3 2

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Transposition Cipher

• a2 1 2 3 a3 1 2 3
• 2 3 1 1 2 3
• a3 is really identity as it does not change the
  order of the elements
• a is said to have order 3, written a 3
• a is an odd permutation as its order is an odd
  number

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Transposition Cipher

• In Transposition cipher position of character
  changes but not its value
• This is different from substitution cipher
• Assign values 0, 1, 2, , 25 to the alphabets
• Choose an integer n as the size of a block
• Split the message into blocks of size n

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Transposition Cipher

• p (p(1), p(2), , p(n)) be a permutation of (1,
  2, , n)
• Message is encrypted using the values of p(1),
  p(2), , p(n)
• E.g. Let n 4
• Let p 1 2 3 4
• 2 4 1 3

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Transposition Cipher

• message proceed meeting as agreed
• Since n 4, we split the message as follows
  proc eedm eeti ngas agre ed
• We pad the last block with two spaces
• Encrypt using the permutation order
• Last block becomes d _ e _ where _ denotes a
  blank space
• Delete the blank spaces in encrypted text

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Transposition Cipher

• Ciphertext using the permutation is
• rcpoemedeietgsnagearde
• To decrypt, the receiver simply takes the inverse
  of the permutation
• In the last block of ciphertext we have de
• The two missing characters corresponding to 3-1
  and 4-1 are thus blanks in plaintext

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Multiple Letter Cipher

• Playfair cipher is a multiple letter cipher
• Each plaintext letter is replaced by a digram in
  this cipher
• Number of digrams is 26 x 26 676
• User chooses a keyword and puts it in the cells
  of a 5 x 5 matrix. I and J stay in one cell.
  Duplicate letters appear only once.
• Alphabets that are not in the keyword are
  arranged in the remaining cells from left to
  right in successive rows in ascending order

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Playfair Cipher

• Keyword Infosec

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Playfair Cipher

• Rules
• Group plaintext letters two at a time
• Separate repeating letters with an x
• Take a pair of letters from plaintext
• Plaintext letters in the same row are replaced by
  letters to the right (cyclic manner)
• Plaintext letters in the same column are replaced
  by letters below (cyclic manner)
• Plaintext letters in different row and column are
  replaced by the letter in the row corresponding
  to the column of the other letter and vice versa

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Playfair Cipher

• E.g., Plaintext CRYPTO IS TOO EASY
• Keyword is INFOSEC
• Grouped text CR YP TO IS TO XO EA SY
• Ciphertext AQ VT YB NI YB YF CB OZ
• To decrypt, the receiver reconstructs the 5 x 5
  matrix using the keyword and then uses the same
  rules as for encryption

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Vernam Cipher

• U.S. Army Major Joseph Mauborgne and ATTs
  Gilbert Vernam developed a cipher in 1917
• Uses a one time arrangement of a key string that
  is as long as the plaintext
• Plaintexts are assumed to be short
• Also known as One-Time Pad cipher
• Key is used only once but characters in key may
  not be distinct

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Vernam Cipher

• E.g., Plaintext HELLO
• Key KTBXZ
• --------------
• Ciphertext RXMIN (using addition mod 26)
• Key KTBXZ
• --------------
• Plaintext HELLO (using subtraction mod 26)