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Chapter 2Classical Encryption Techniques

Basic Concepts

Models of Encryption and Decryption

Information Security Chapter 2 Classical Encryption Methods

Classical Encryption Methods

Substitution Techniques

Transposition Techniques

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Basic Concepts

plaintext: the original clear message

ciphertext: the transformed message cipher: an algorithm for transforming or

encrypting or ciphering a clear message into


c p ertext w t w c any unaut or ze partycannot find the plaintext.

key: a data unit used for encryption or decryption.

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Basic Concepts

encipher/encrypt: the process of converting

plaintext to ciphertext using a cipher and akey.

decipher/decrypt: the process of converting


ciphertext back into plaintext using a cipherand a key.

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Basic Concepts

cryptography: the science/maths of transforming a

plaintext into a ciphertext and then transforming

the ciphertext back into the plaintext.

cryptographic systems are characterized as:


plain text to ciphertext.

The number of keys used.

The way in which the plaintext is processed.

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Basic Concepts

cryptanalysis: the study of transforming a

ciphertext back into the original plaintext without

knowledge of the key. There are two generalapproaches to attack a conventional scheme:


Brute-force attack

cryptology: both cryptography and cryptanalysis.

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Encryption: a process of encoding a message so

that its meaning is not obvious.

Decryption: the reverse process: transforming an

encrypted message back into its normal form.


decryption key are the same.

Asymmetric key encryption: Encryption key

and decryption key are different.

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Symmetric


public/encryption key of Recipient secret key/decryption key of Recipient

e.g. RSA

Asymmetric

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Security of An Encryption Scheme

Unconditionally Secure: the ciphertext generatedby the scheme does not contain enough

information to determine the plaintext no matterhow much ciphertext is available.

Computationally Secure: if the two criteria are


met: the cost of breaking the cipher exceeds the

value of the encrypted information.

the time required to break the cipher exceedsthe useful lifetime of the information.

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Notation

Encryption: C = E(P) or C = Ekey(P)

Decryption: P = D(C) = D(E(P)) or P = Dkey(C)


C=Ekey(P), P=Dkey(C)

Asymmetric cryptosystem:

C=EEncryptionKey(P), P=DDecryptionKey(C)

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Mechanism to Make a Cipher

Two basic building blocks of all

conventional encryption techniques:Substitution and Transposition (permutation)


Substitution: the letters of plaintext arereplaced by other letters or numbers of

symbols

Transposition: the letters of plaintext are

reordered

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Caesar Cipher

Substitution: a letter is replaced by another letter or symbol

Example: Move each letter of the alphabet to the letter

three to the right in the predetermined order of the lettersof the alphabet. AD, BE, CF,

Caesar cipher moves the ith letter of an alphabet to the


+ t etter. a= , = , c= ,..., i= ,... Encryption C= E(Pi) = i+ k(mod 26)

Decryption Pi = D(C)= C-k (mod 26)

Example: IFMMP = E(HELLO) with k=1

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Cryptanalysis of Caesar Cipher

The encryption/decryption algorithms are known

There are only 25 possible keys (1,...,25), so it is

easy to break by Brute force cryptoanalysis.

The language of the plaintext is known and easily


Can we make it harder?

include all ASCII codes - 255 keys

Zip the file and then encrypt it - ciphertext becomesunreadable.

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Cryptanalysis of Caesar Cipher

Cryptanalysis by letter frequency

distributions.

If encipherment is achieved by a simple letter

shift then a frequency count of the letter


s r u ons n e c p er ex w y e esame pattern as the original host language of

the plaintext but shifted.

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English Letter Frequency Distribution

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General Monoalphabetic Cipher

Better substitution

Method:

Select a secret word/key (avoid repeating words)

Example: Choose secret words `star wars'. `starwars' has the letters a r and s re eated so we use


only the letters s, t, a, r, w. Write alphabets into a rectangle, e.g.

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STARW

BCDEF

GHIJK

LMNOP

QUVXY

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The substitution table

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25A 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

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


I KNOW ONLY THAT I KNOW NOTHING

H UINF NIAP OCSO H UINF INOCHIT

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Monoalphabetic ciphers are easy to breakbecause they reflect the frequency data ofthe original alphabet

A countermeasure is to provide multiple


substitutes, known as homophones, for asingle letter. e.g: letter e be assigned

different cipher symbols such as: 16,74,35

and 21, with each homophone used in

rotation

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Playfair: A Multiple Letter Encryption Cipher

The best-known multiple-letter cipher.

The algorithm is based on the use of a 55 matrix

of letters constructed using a key word.


C H Y B DE F G I/J K

L P Q S T

U V W X Z

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Playfair Cipher

The plaintext is encrypted a pair at a time, left over oneneeds to be paired by a filler letter.

Repeating letters of the same pair are separated with afiller letter.

Letters of a pair that fall in the same row are each replacedb the letter to the ri ht. The row is circular with the 1st


letter following the last one. Letters of a pair that fall in the same column are each

replaced by the letter beneath. The column is circular withthe 1st letter following the last one.

Otherwise, each plaintext letter is replaced by the letterthat lies in its own row and the column occupied by theother plaintext letter.

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Playfair Cipher

An example: Whats the cipher text for

encrypting Playfair Cipher by Playfair Cipher?

Pair combination:

pl ay fa ir ci ph er


no er etter nee e .

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Hill Cipher: Another Multiletter Cipher

The plaintext is encrypted every m successiveletters at a time for m ciphertext letters.

The substitution is determined by m linearequations with each letter is assigned a numericalvalue (a=0, b=1, z=25).


For m=3, the system is as follows:c1 = (k11p1 + k12p2 + k13p3) mod 26

c2 = (k21p1 + k22p2 + k23p3) mod 26

c3 = (k31p1 + k32p2 + k33p3) mod 26

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Hill Cipher

this can be expressed in terms of column vector

and matrices:

c1 k11 k12 k13 p1

c2 = k21 k22 k23 p2 mod 26


c3 31 32 33 p3

or C=KP mod 26

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Polyalphabetic Substitution Cipher

Monoalphabetic substitution ciphers hide the

distribution via the use of homomorphisms.

Cryptanalysis: frequency distribution.

Polyalphabetic substitution ciphers hide it by


,

alphabets. It has a flatter frequency distribution.

A set of substitution rules

A key determines which rule to choose

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Polyalphabetic Cipher - Vigenre Cipher

Select a key from 26 letters

Create a substitution table

Example

Encryption:


deceptivedeceptivedeceptive

wearediscoveredsaveyourself

zicvtwqngrzgvtwavzhcqyglmgj

Key:Plaintext:

Ciphertext:

d+w=z mod26, e+e=i mod26, ...

Decryption:

w=z-d mod26, e=i-e mod26, ...

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Transposition

plaintext permutation cipertextThe simplest one: plaintext is written as a sequence of

diagonals and then read off as a sequence of rows

Information Security Chapter 2 Classical Encryption Methods 26

e.g: meet me after the toga party is written as:

m e m a t r h t g p r y

e t e f e t e o a a t

the encrypted message is:mematrhtgpryetefeteoaat

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More complex one: write the message in a rectangle, row by

row, read off column by column but permute the order of

the columns

2 4 1 3

Example:2 4 1 3

keyencryption

Information Security Chapter 2 Classical Encryption Methods 27

U T E RS E C U

R I T Y

plaintext:

decryption

E U R TC S U E

T R Y I

ciphertext

COMPUTERSECURITY MECTCUSRPRUYOTEI

Note: If the message length is not a multiple of a row, the last

column is not full. Some infrequent letter(s) should be filled.

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One-Time Pad

An encryption scheme (by Joseph Mauborgne,AT&T).

What is one-time pad?

A large non-repeating set of truly random key letters as

long as the message, written on sheets of paper, and

glued together in a pad.


Encryption:

Decryption:

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Ciphertext_letter = (Plaintext_letter + Key_letter) mod 26

Ciphertext_bit = Plaintext_bit Key_bit

Plaintext_letter = ( Ciphertext_letter - Key_letter) mod 26

Plaintext_bit = Ciphertext_bit Key_bit

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