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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,
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