cypher text

1. 1
Substitution Ciphers

2. 2
Substitution Ciphers
• Monoalphabetic cipher
– Caesar cipher
• Polyalphabetic cipher
– Vigenère cipher
• Multiple letter cipher
– Playfair cipher

3. 3
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

4. 4
Monoalphabetic cipher
• The substitution cipher by shifting
alphabets gives 26! > 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

5. 5
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

6. 6
Pigpen Cipher
• Pigpen cipher is a variation on letter
substitution
• Alphabets are arranged as follows:
A B C
D E F
G H I
J K L
M N O
P Q R

7. 7
Pigpen Cipher diagram (cont’d)
T
S
U
V
X
W
Y
Z
C G
A W

8. 8
Pigpen Cipher
• Alphabets will be represented by the
corresponding diagram
• E.g., WAG would be
• This is a weak cipher

9. 9
ADFGVX Cipher
• This is a variation on
substitution cipher
and is a strong cipher
A D F G V X
A 8 p 3 d 1 n
D l t 4 o a h
F 7 k b c 5 z
G j u 6 w g m
V x s v i r 2
X 9 e y 0 f q

10. 10
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

11. 11
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

12. 12
ADFGVX Cipher
I N F O S E C
V D X D X D G
X X D V G A X
G X D V D A V

13. 13
ADFGVX Cipher
C E F I N O S
G D X V D D X
X A D X X V G
V A D G X V D

14. 14
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

15. 15
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 cipher’s goal is to make
this process difficult

16. 16
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

17. 17
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

18. 18
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

19. 19
Vigenère Cipher Table (cont’d)
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

20. 20
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

21. 21
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

22. 22
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)

23. 23
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

24. 24
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

25. 25
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

26. 26
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

27. 27
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

28. 28
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

29. 29
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

30. 30
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

31. 31
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

32. 32
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

33. 33
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

34. 34
Playfair Cipher
• Keyword “Infosec”
I / J N F O S
E C A B D
G H K L M
P Q R T U
V W X Y Z

35. 35
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

36. 36
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

37. 37
Vernam Cipher
• U.S. Army Major Joseph Mauborgne and
AT&T’s 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

38. 38
Vernam Cipher
• E.g., Plaintext: HELLO
Key: KTBXZ
--------------
Ciphertext : RXMIN (using addition mod 26)
Key: KTBXZ
--------------
Plaintext: HELLO (using subtraction mod 26)