1. Substitution Ciphers

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

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

7. Pigpen Cipher diagram (cont’d)S U V X W Y Z A C W G

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

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

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

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

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

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

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. 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. 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 =

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

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