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06/06/22 K.Marimuthu,SCSE Network Securi ty 1 Substitution Techniques
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Page 1: Substitution Techniques

04/08/23 K.Marimuthu,SCSE Network Security 1

Substitution Techniques

Page 2: Substitution Techniques

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Classical Ciphers

• Plaintext is viewed as a sequence of elements (e.g., bits or characters)

• Substitution cipher: replacing each element of the plaintext with another element.

• Transposition (or permutation) cipher: rearranging the order of the elements of the plaintext.

• Product cipher: using multiple stages of substitutions and transpositions

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Classical Substitution Ciphers

• where letters of plaintext are replaced by other letters or by numbers or symbols

• or if plaintext is viewed as a sequence of bits, then substitution involves replacing plaintext bit patterns with ciphertext bit patterns

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Caesar Cipher

• Earliest known substitution cipher• Invented by Julius Caesar

• Each letter is replaced by the letter three positions further down the alphabet.

• Plain: a b c d e f g h i j k l m n o p q r s t

• Cipher: D E F G H I J K L M N O P Q R S T U V W

u v w x y z

X Y Z A B C

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Example

• Plain text : meet me after the toga party

• Ciphertext: PHHW PH DIWHU WKH WRJD SDUWB

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Caesar Cipher

• Mathematically, map letters to numbers:

a, b, c, ..., x, y, z

0, 1, 2, ..., 23, 24, 25• Then the general Caesar cipher is: (Modified Caesar Cipher)

c = EK(p) =E (k ,p)= (p + k) mod 26

p = DK(c) =D (k ,c)= (c – k) mod 26

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Cryptanalysis of Caesar Cipher

• Key space: {0, 1, ..., 25} • Vulnerable to brute-force attacks. • Major weakness of Caesar cipher is its Predictability

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Monoalphabetic Substitution Cipher

• Shuffle the letters and map each plaintext letter to a different random ciphertext letter:

• Plain letters: • 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

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

Plaintext: if we wish to replace letters

Ciphertext: WI RF RWAJ UH YFTSDVF SFUUFYA

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Homophonic Cipher

• One Plaintext alphabet is replaced with fixed alphabet set.

• Ex: A is replaced by the set { D,H,P,R}

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PolyGram Cipher

• Replacement of plaintext happens block-by-block

• Ex:

plaintext: Hello Hell

Ciphertext: YUQQW TEUI

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Playfair Cipher

• One approach to improving security is to encrypt multiple letters at a time.

• The Playfair Cipher is the best known such cipher.

• Invented by Charles Wheatstone in 1854, but named after his friend Baron Playfair.

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Playfair Key Matrix

• Use a 5 x 5 matrix.• Fill in letters of the key (w/o duplicates). • Fill the rest of matrix with other letters.• E.g., key =PLAYFAIR EXAMPLE

PP LL AA YY FF

I/JI/J RR EE XX MM

BB CC DD GG HH

KK NN OO QQ SS

TT UU VV WW ZZ

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Encrypting and Decrypting

Plaintext is encrypted two letters at a time.

1. If a pair is a repeated letter, insert filler like 'X’.

2. If both letters fall in the same row, replace each with the letter to its right (circularly).

3. If both letters fall in the same column, replace each with the the letter below it (circularly).

4. Otherwise, each letter is replaced by the letter in the same row but in the column of the other letter of the pair.

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Example

• Plaintext: My name is Atul

My na me is at ul

• Ciphertext: XF OL IX MK PV LR

• Example : Plaintext: Balloon

Ba ll oo n ba lx lo on

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Polyalphabetic Substitution Ciphers

• A sequence of monoalphabetic ciphers (M1, M2, M3, ..., Mk) is used in turn to encrypt letters.

• A key determines which sequence of ciphers to use.• Each plaintext letter has multiple corresponding ciphertext

letters.• This makes cryptanalysis harder since the letter frequency

distribution will be flatter.

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Vigenère Cipher

• Simplest polyalphabetic substitution cipher• Consider the set of all Caesar ciphers:

{ Ca, Cb, Cc, ..., Cz }• Key: e.g. security• Encrypt each letter using Cs, Ce, Cc, Cu, Cr, Ci, Ct, Cy in turn. • Repeat from start after Cy. • Decryption simply works in reverse.

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Example

• write the plaintext out • write the keyword repeated above it• use each key letter as a caesar cipher key • encrypt the corresponding plaintext letter• eg using keyword deceptive

key: deceptivedeceptivedeceptive

plaintext: we are discovered save yourself

wearediscoveredsaveyourself

ciphertext: ZICVTWQNGRZGVTWAVZHCQYGLMGJ

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Autokey cipher• ideally want a key as long as the message• Vigenère proposed the autokey cipher • with keyword is prefixed to message as key• knowing keyword can recover the first few letters • use these in turn on the rest of the message• but still have frequency characteristics to attack • eg. given key deceptive

key: deceptivewearediscoveredsav

plaintext: wearediscoveredsaveyourself

ciphertext:ZICVTWQNGKZEIIGASXSTSLVVWLA

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Hill Cipher• Multiletter cipher

• Invented by the mathematician Lester Hill in 1929

• m successive Plaintext letters encrypted at a time• Substitution is determined by m linear equations• For each character ,numerical value is assigned a=0,b=1,c=2,………..z=25

For m=3,system can be described as follows

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Hill Cipher ….

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C=KP mod 26C ,P are column Vectors of length 3,representing

ciphertext and plain text. K is 3x3 matrix, key

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Hill Cipher …..

• Ex: Plain text: paymoremoney

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Hill cipher…

• Ciphertext: LNSHDLEWMTRW

• For decryption,