# CH Conventional Encryption Classical Techs by MikeJenny

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```									                                         Classical Encryption Techniques

Classical Encryption Techniques
• Substitution Techniques
– Caesar Cipher
– Monoalphabetic Ciphers
– Playfair Cipher
– Hill Cipher
– Polyalphabetic Ciphers
•   Transposition (Permutation) Techniques
– Rail Fence Technique
– Block (Columnar) Transposition Technique
Substitution Techniques

Caesar Cipher
• 2000 years ago, by Julius Caesar
• A simple substitution cipher, known as Caesar cipher
• Replace each letter with the letter standing 3 places
further down the alphabet
– Plain:      meet me after the toga party
– Cipher: PHHW PH DIWHU WKH WRJD SDUWB
• No key, just one mapping (translation)
0123456...
Plain: abcdefghijklmnopqrstuvwxyz
Cipher: DEFGHIJKLMNOPQRSTUVWXYZABC
3456789...
• ci=E(3,pi)=(pi+3) mod 26;
pi=D(3,ci)=(ci-3) mod 26
Substitution Techniques

Generalized Caesar Cipher

• Can use any shift from 1 to 25, i.e., replace each letter
by a letter a fixed distance away
ci=E(k,pi)=(pi+k) mod 26;
pi=D(k,ci)=(ci-k) mod 26
• Shift cipher
• Key = k
• Key letter: the letter a plaintext A maps to
– e.g. a key letter of F means A maps to F, B to G, …, Y
to D, Z to E
• Hence have 26 (25 useful) ciphers
– Key space = 26
Substitution Techniques

Monoalphabetic Substitution Ciphers
• Further generalization of the Caesar cipher
• Plain: abcdefghijklmnopqrstuvwxyz
Cipher: DEFGHIJKLMNOPQRSTUVWXYZABC
is obtained by allowing any permutation of 26
characters for the cipher
•   Key size = 26
•   Key space = 26!  4x1026
•   Unique mapping of plaintext alphabet to ciphertext
alphabet  Monoalphabetic

• For a long time thought secure, but easily breakable by
frequency analysis attack
Substitution Techniques

Relative Frequency of Letters in English Text
Substitution Techniques

Homophones
• Monoalphabetic substitution ciphers are easy to break
through letter frequency analysis
•   Multiple substitutes (homophones) for a single letter can
be used to hide the single-letter frequency information
•   But even with homophones, multiple-letter patterns (e.g.
digram frequencies) still survive in the ciphertext

• Two approaches for this problem
– Encrypt multiple letters of plaintext
• Playfair cipher
• Hill cipher
– Use multiple cipher alphabets
• Polyalphabetic cipher
Substitution Techniques

Playfair Cipher
• Best-known multiple-letter substitution cipher
• Digram cipher (digram to digram, i.e., E(pipi+1) = cici+1
through keyword-based 5x5 transformation table)
•
M   O   N   A   R
Keyword = monarchy
C   H   Y   B   D
Plaintext: H S E A A R M U
E   F   G   I/J K
Ciphertext: B P I M R M C M
L   P   Q   S   T
U   V   W X     Z

• Great advance over simple monoalphabetic cipher (26
letters  26x26=676 digrams)
•   Still leaves much of the structure of the plaintext language
 relatively easy to break
•   Can be generalized to polygram cipher
Substitution Techniques

Relative Frequency of Occurrence of Letters
Substitution Techniques

Polyalphabetic Cipher

• Typically a set of monoalphabetic substitution rules is used
• Key determines which rule to use
Substitution Techniques

Vigenère cipher

•   Best-known polyalphabetic ciphers
•   Each key letter determines one of 26 Caesar (shift) ciphers
•   ci = E(pi) = pi + ki mod(key length) mod 26
•   Example:
Key:          deceptivedeceptivedeceptive
Plaintext:    wearediscoveredsaveyourself
Cipheretxt:   ZICVTWQNGRZGVTWAVZHCQYGLMGJ

• Keyword is repeated to make a key as long as the
plaintext
Substitution Techniques

Vigenère cipher - 2
Substitution Techniques

Vigenère cipher - 3
• If the keyword length is N, then Vigenère cipher, in effect,
consists of N monoalphabetic substitution ciphers
 Consider each of the ciphers separately
•   Improvement over the Playfair cipher, but language
structure and frequency information still remain
•   Vigenère autokey system: after key is exhausted, use
plaintext for running key (to eliminate the periodic
nature) Key:         deceptivewearediscoveredsav
Plaintext:    wearediscoveredsaveyourself
Cipheretxt:   ZICVTWQNGKZEIIGASXSTSLVVWLA
Transposition Techniques

Transposition (Permutation) Techniques
• Hide the message by rearranging the letter order without
altering the actual letters used
•   Rail Fence Cipher
– Write message on alternate rows, and read off cipher row
by row
– Eg M e m a t r h t g p r y    MEMATRHTGPRYETEFETEOAAT
e t e f e t e o a a t

• Block (Columnar) Transposition Ciphers
– Message is written in rectangle, row by row, but read off
column by column; The order of columns read off is the
key        Key:        4 3 1 2 5 6 7
Plaintext: a t t a c k p
o s t p o n e
– Example:               d u n t i l t
w o a m x y z
Ciphertext:TTNAAPTMTSUOAODWCOIXKNLYPETZ

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