39601372 Substitution Techniques

7/31/2019 39601372 Substitution Techniques

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Substitution Techniques


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Classical Ciphers

Plaintext is viewed as a sequence of elements (e.g., bits orcharacters)

Substitution cipher: replacing each element of theplaintext with another element.

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

Product cipher: using multiple stages of substitutions andtranspositions


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Classical Substitution Ciphers

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

or if plaintext is viewed as a sequence of bits, thensubstitution involves replacing plaintext bit patterns withciphertext 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 furtherdown 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 RS 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 party

Ciphertext: PHHW PH DIWHU WKH SDUWB


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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 adifferent 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 zD KVQ F I B J W P E S C X H T M Y A U O L R G Z N

Plaintext: ifwewish 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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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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Vigenre 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, C

e, C

c, C

u,C

r, C

i, C

t, C

yin

turn.

Repeat from start after Cy.

Decryption simply works in reverse.


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Examplewrite the plaintext outwrite 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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Hill Cipher Multiletter cipher Invented by the mathematician Lester Hill in 1929

m successive Plaintext letters encrypted at a time Substitution is determined bym linear equations For each character ,numerical value is assigned

a=0,b=1,c=2,..z=25Form=3,system can be described as follows


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Hill Cipher .

3 representing


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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,

39601372 Substitution Techniques

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