Hill Cipher

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Hill Cipher
(Network Security)
Umer Farooq Roll No 3049 Bs (Hons)-IT-Evening Se
ssion 2013-2017 University Of Okara
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Outline

• Hill Cipher
• Definition
• History
• Key Point
• Key Table
• Examples
• Encryption
• Decryption
• Online Hill Cipher

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Hill Cipher

• Hill cipher is a polygraphic substitution
  cipher based on linear algebra.
• Invented by Lester S. Hill in 1929, it was the
  first polygraphic cipher in which it was
  practical (though barely) to operate on more than
  three symbols at once. 
• In Hill Cipher Index of Ceaser Cipher is used.
• Plain Text is used Column Matrix.
• Key is given in Matrix Form.

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Key Points

• Each letter is represented by a number modulo 26.
• Simple scheme A 0, B 1, ..., Z 25 is used,
  but this is not an essential feature of the
  cipher.
• To encrypt a message, each block of n letters
  (considered as an n-component vector) is
  multiplied by an invertible n  n matrix,
  against modulus 26.
• To decrypt the message, each block is multiplied
  by the inverse of the matrix used for encryption.
• The matrix used for encryption is the cipher key,
  and it should be chosen randomly from the set of
  invertible n  n matrices (modulo 26).

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Key
0 1 2 3 4 5
A B C D E F
6 7 8 9 10 11
G H I J K L
12 13 14 15 16 17
M N O P Q R
18 19 20 21 22 23
S T U V W X
24 25
Y Z
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Example

• Encryption
• Plain Text NETWORK
• Where N 13, E 4,
• T 19, W 22, O 14,
• R 17, K 10 
• Key is 2 x 2 so we use
• Pairs of Plain Text
• i.e. NE, TW, OR, KX
• Key 2 3 1 3

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Encryption Start

• NE 
• N 13 E 4 MOD 26
• 2 3 1 3 13 4 38 25
• 38 MOD 26 12
• 25 MOD 26 25
•  12 M 25 Z
• CIPHER of Plain Text
• NE MZ
• TW 
• T 19, W 22 MOD 26 
• 2 3 1 3 19 22 104 85
• 104 MOD 26 0
• 85 MOD 26 7
• 0 A 7 H
• CIPHER of Plain Text
• TW AH

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Encryption Cont. . .

• OR
• O 14, R 17 MOD 26
• 2 3 1 3 14 17 79 65
• 79 MOD 26 1
• 65 MOD 26 13
• 1 B 13 N
• CIPHER of Plain Text
• OR BN
• KX
• K 10, X 23 MOD 26
• 2 3 1 3 10 23 89 79
• 89 MOD 26 11
• 79 MOD 26 1
• 11 L 1 B 
• CIPHER of Plain Text
• KX LB

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Encryption Complete

• Plain Text NE TW OR
• Cipher MZ AH BN

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Decryption Start

• Decryption
• CIPHER MZ AH BN LB
• Formula
• C K x P MOD 26
• P K-1 C (Order of K C is important)
• First Find the K-1
• K-1 (Adj of K) x K-1
• K 2 3 1 3
• In Adj of K interchange a11 with a22 and change
  the sign of a12 a21  
• Adj of K K (a11 x a22) (a12 x a21)
• K (3 x 2) (3 x 1)
• K 6 (3) 6 3 3
• K-1 3s Inverse is 9  

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Table of Find Inverse of Determinant
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Decryption Cont . . .

• Now Formula
• K-1 (Adj of K) x K-1 MOD 26 
• K-1 3 -3 -1 2 (9) MOD 26
• K-1 27 -27 -9 18 MOD 26
• 27 MOD 26 1
• -27 MOD 26 -27 26 -1 26 25
• -9 MOD 26 -9 26 17
• 18 MOD 26 18
• K-1 1 25 17 18

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Decryption Cont . . .

• CIPHER MZ AH BN LB 
• MZ
• M 12, Z 25
• P K-1 C MOD 26
• P 1 25 17 18 12 25 MOD 26
• P 637 654 MOD 26
• P 13 4
• N 13 E 4
• Thus MZ NE 

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Decryption Cont . . .

• CIPHER AH BN LB
• AH
• A 0, H 7
• P K-1 C Mod 26
• P 1 25 17 18 0 7 MOD 26
• P 175 126 MOD 26
• P 19 22
• T 19 W 22
• Thus AH TW

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Decryption Cont . . .

• CIPHER BN LB
• BN
• B 1, N 13
• P K-1 C Mod 26
• P 1 25 17 18 1 13 MOD 26
• P 326 251 MOD 26
• P 14 17
• O 14 R 17
• Thus BN OR 

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Decryption Cont . . .

• CIPHER LB
• LB
• L 11, B 1
• P K-1 C Mod 26
• P 1 25 17 18 11 1 MOD 26
• P 36 205 MOD 26
• P 10 23
• K 10 X 23
• Thus LB KX 

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Decryption COMPLETE

• Cipher Text MZ AH BN LB
• Plain Text NE TW OR KX

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ONLINE Hill Cipher

• http//www.dcode.fr/hill-cipher

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Thank You