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Chapter 2 Classical EncryptionTechniques

- Jen-Chang Liu, 2005
- Adopted from
- lectures by Lawrie Brown

- Many savages at the present day regard their

names as vital parts of themselves, and therefore

take great pains to conceal their real names,

lest these should give to evil-disposed persons a

handle by which to injure their owners. The

Golden Bough, Sir James George Frazer

Sir James George Frazer

- ?????????The Golden Bough?,??Sir James Frazer

(1854-1941),?????????????,????????

????????????????????????????? ?? - ????????6?27????? ??????????????,????????????????

,? ????????????,??????????????

Review Model for Network Security

3

1

2

3 roles to play in security system

Cryptography

???

- Cryptographic systems can be characterized by
- encryption operations used for transforming

plaintext to ciphertext - substitution / transposition (permutation) /

product - number of keys used
- single-key or secret-key / two-key or public-key
- way in which plaintext is processed
- block / stream

Whats the secret information?

Outline

- Symmetric cipher model
- Substitution technique
- Transposition technique
- Rotor machines
- Steganography

Symmetric Cipher Model

???

Symmetric Encryption

- conventional / single-key / single-key

encryption - sender and recipient share a common key
- was the only type prior to invention of

public-key in 1970s

Basic Terminology

??

- plaintext - the original message
- ciphertext - the coded message
- cipher - algorithm for transforming plaintext to

ciphertext - key - info used in cipher known only to

sender/receiver - encipher (encrypt) - converting plaintext to

ciphertext - decipher (decrypt) - recovering ciphertext from

plaintext - cryptography - study of encryption

principles/methods - cryptanalysis (codebreaking) - the study of

principles/ methods of deciphering ciphertext

without knowing key - cryptology - the field of both cryptography and

cryptanalysis

??

Mathematical formulation

- Y EK(X)
- X DK(Y)

Cryptosystem

Ref Cryptography theory and Practice, D. Stinson

- A cryptosystem is a five-tuple (P,C,K,E,D), where

the following conditions are satisfied - 1. P is a finite set of possible plaintexts
- 2. C is a finite set of possible ciphertexts
- 3. K ,the keyspace,is a finite set of possible

keys - 4. For each k?K, there is an encryption rule ek

?E and a corresponding decryption rule dk ?D.

Each ekP?C and dkC?P are functions such that

dk(ek(x))x for each x?P

Example Caesar Cipher

- earliest known substitution cipher by Julius

Caesar - first attested use in military affairs
- example
- meet me after the toga party
- PHHW PH DIWHU WKH WRJD SDUWB

Example Caesar Cipher (cont.)

- Plaintext alphabets

- Ciphertext alphabets

- Encryption algorithm

Y EK(X)(X3) mod 26

Security Requirements

- two requirements for secure use of symmetric

encryption - a strong encryption algorithm
- assume encryption algorithm is known, the

opponent is unable to decipher the ciphertext

(Kerckhoffs principle) - a secret key known only to sender / receiver
- implies a secure channel to distribute key

Cryptanalysis of Caesar Cipher

- Assume that the encryption is known as a Caesar

cipher - Try 25 possible keys brute force

PHHW PH DIWHU WKH WRJD SDUWB

k0

OGGV OG CHUGT VJG VQIC RCTVA

k1

MEET ME AFTER THE TOGA PARTY

k3

k25

Cryptanalysis of Caesar Cipher

- Why brute force attack works?
- Encryption (decryption) algorithm is known
- 25 keys ? too small
- The language of plaintext is recognizable
- Ex. A zipped file

Brute Force Search

- Given encryption algorithm, its always possible

to simply try every key - On average, try half of all keys
- assume either know / recognise plaintext

decryption

DES

AES

3DES

Degree of security for encryption schemes

- unconditional security
- no matter how much computer power is available,

the cipher cannot be broken since the ciphertext

provides insufficient information to uniquely

determine the corresponding plaintext - ????????????
- computational security
- given limited computing resources (eg time needed

for calculations is greater than age of

universe), the cipher cannot be broken

Types of Cryptanalytic Attacks

Mini break

- There will be a programming project this semester
- Implementation of DES or AES

Outline

- Symmetric cipher model
- Caesar cipher
- Substitution technique
- Transposition technique
- Rotor machines
- Steganography

Classical Substitution Ciphers

- where letters of plaintext are replaced by other

letters or by numbers or symbols - if plaintext is viewed as a sequence of bits,

then substitution involves replacing plaintext

bit patterns with ciphertext bit patterns

A B C . . Y Z

A B C . . Y Z

Caesar Cipher

- can define transformation as
- 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 E F G H I J K L M N O P Q R S T U V W X Y Z A B

C - then have Caesar cipher as
- C E(p) (p k) mod (26)
- p D(C) (C k) mod (26)

Caesar cipher can be cryptoanalyzed by

brute-force attack gt Far from secure

Monoalphabetic Cipher

- rather than just shifting the alphabet
- each plaintext letter maps to a different random

ciphertext letter

E(.)

A B C . . Y Z

A B C . . Y Z

26! Possible transforms

. . .

Monoalphabetic Cipher Security

- now have a total of 26! 4 x 1026 keys
- Very secure !?

- How to break?

Language Redundancy and Cryptanalysis

- human languages are redundant

Cryptanalysis of monoalphabetic cipher

Given ciphertext

Calculate its relative frequencies

Compare it with the previous table

Cryptanalysis (cont.)

- One alphabet frequencies guess P Z are e and t
- Digrams and trigrams frequencies of compound

letters - guess ZW is th and hence ZWP is the
- proceeding with trial and error

UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ VUE

PHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX EPYEPOPDZSZU

FPOMBZWPFUPZHMDJUDTMOHMQ

How to improve monoalphabetic cipher?

- Encrypt multiple letters of plaintext at the same

time - Playfair cipher
- Hill cipher
- Use multiple cipher alphabets
- Polyalphabetic cipher

Playfair Cipher

- Best-known multiple-letter encryption cipher
- invented by Charles Wheatstone in 1854, but named

after his friend Baron Playfair

Example digram mapping

c

x

g

y

26x26 diagrams

Playfair Key Matrix

- a 5X5 matrix of letters based on a keyword
- eg. using the keyword MONARCHY
- M O N A R
- C H Y B D
- E F G I/J K
- L P Q S T
- U V W X Z

- fill in letters of keyword
- fill rest of matrix with other letters in
- alphabetic order

Playfair Encrypting and Decrypting

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

V W X Z

- plaintext encrypted two letters at a time
- if a pair is a repeated letter, insert a filler

like 'X', eg. "balloon" encrypts as "ba lx lo

on"

- if both letters fall in the same row, replace

each with letter to right (wrapping back to start

from end), eg. ar" encrypts as "RM"

- if both letters fall in the same column, replace

each with the letter below it (again wrapping to

top from bottom), eg. mu" encrypts to "CM"

- otherwise each letter is replaced by the one in

its row in the column of the other letter of the

pair, eg. hs" encrypts to "BP", and ea" to "IM"

or "JM" (as desired)

Security of the Playfair Cipher

- security much improved over monoalphabetic
- 26 x 26 676 digrams
- would need a 676 entry frequency table to analyse

(verses 26 for a monoalphabetic) - was widely used for many years (eg. US British

military in WW1) - it can be broken, given a few hundred letters
- since still has much of plaintext structure

Idea Relative frequency of occurrence of letters

in ciphertext

Make the freq. Distribution information

concealed gt flatter

Hill cipher

- Mathematician Lester Hill in 1929
- Multi-letter cipher
- Ex. 3-letter cipher

p1

c1

p2

c2

?

p3

c3

Input 263

Output 263

Hill cipher (cont.)

- Encryption C KP mod 26
- Decryption P K-1C mod 26
- Idea hide single-letter frequencies
- 2x2 key matrix hide single-letter freq.
- 3x3 key matrix hide single-letter and digram

freq.

How to attack Hill cipher?

Cryptanalysis on Hill cipher

- Known ciphertext X

How to improve monoalphabetic cipher?

- Encrypt multiple letters of plaintext at the same

time - Playfair cipher
- Hill cipher
- Use multiple cipher alphabets
- Polyalphabetic cipher

Monoalph. Cipher

a

k

Polyalph. Cipher

Rule 1

a

k

Rule 2

J

Polyalphabetic Ciphers

- Polyalphabetic substitution ciphers
- A set of related monoalphabetic substitution

rules is used - use a key to select which alphabet is used for

each letter of the message

Vigenère Cipher

- simplest polyalphabetic substitution cipher is

the Vigenère Cipher - 26 Caesar ciphers
- Each Caesar cipher is labelled by a key letter
- See Table 2.3

key

plaintext

Example Vigenère Cipher

- Encryption need a key and the plaintext
- Eg. using keyword deceptive
- key deceptivedeceptivedeceptive
- plaintext wearediscoveredsaveyourself
- ciphertextZICVTWQNGRZGVTWAVZHCQYGLMGJ
- Decryption the table and the key are known

- advantage multiple ciphertext letters for each

plaintext letter - gt hide letter frequency
- gt See Fig. 2.6

Cryptanalysis on Substitution Cipher

- Calculate the statistical properties of the

ciphertext - Match language letter freq.
- Monoalphabetic cipher
- Polyalphabetic cipher (Vigenère Cipher)
- Find the length of keyword
- Attack each monoalphabetic cipher

Yes

No

key deceptivedeceptivedeceptive plaintext

wearediscoveredsaveyourself ciphertextZICVTWQNGRZ

GVTWAVZHCQYGLMGJ

Guess key length

Improve over Vigenère Cipher (1)

- Avoid repetition of key
- Autokey system

key deceptivewearediscoveredsav plaintext

wearediscoveredsaveyourself ciphertextZICVTWQNGKZ

EIIGASXSTSLVVWLA

Improve over Vigenère Cipher (2)

- Avoid repetition of key
- Gilbert Vernam, 1918
- Use of a running loop of tape that eventually

repeat the key - A very long but repeating keyword

One-Time Pad

- Unconditional security !!!
- Improve on Vigenère Cipher, by Jeseph Mauborgne
- Use a random key that was truly as long as the

message, no repetitions

Example one-time pad

- Known Vigenère Cipher with one-time key
- Given ciphertext ANKYODKYUREPFJBYOJDSPLREYIUNOFDO

IUERFPLUYTS

Decrypt by hacker 1

Ciphertext ANKYODKYUREPFJBYOJDSPLREYIUNOFDOIUERFP

LUYTS Key pxlmvmsydofuyrvzwc

tnlebnecvgdupahfzzlmnyih Plaintext mr mustard

with the candlestick in the hall

Decrypt by hacker 2

Ciphertext ANKYODKYUREPFJBYOJDSPLREYIUNOFDOIUERFP

LUYTS Key pftgpmiydgaxgoufhklllmhsqdqogtew

bqfgyovuhwt Plaintext miss scarlet with the

knife in the library

Which one?

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 ? 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 ? 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 ? A C D E F G H I J K L M N O P Q R S T U

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

V W X Z ? 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 ? 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

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 ?

Problem with one-time pad

- Truly random key with arbitrary length?
- Distribution and protection of long keys
- The key has the same length as the plaintext!

Summary

- Caesar cipher
- Monoalphabetic cipher
- Encrypt multiple letters of plaintext at the same

time - Playfair cipher
- Hill cipher
- Use multiple cipher alphabets
- Polyalphabetic cipher
- Vernam cipher
- One-time Pad

Outline

- Symmetric cipher model
- Substitution technique
- Transposition technique
- Rotor machines
- Steganography

Transposition Ciphers

- Transposition cipher permutation on the

plaintext letters - these hide the message by rearranging the letter

order - without altering the actual letters used
- Feature have the same frequency distribution as

the original text

??

Rail Fence cipher

- write message letters out diagonally over a

number of rows - eg. Plaintext meet me after the toga party
- m e m a t r h t g p r y
- e t e f e t e o a a t
- then read off cipher row by row
- MEMATRHTGPRYETEFETEOAAT

Row Transposition Ciphers

- Improve on Rain Fence cipher
- write letters of message out in rows over a

specified number of columns - Key 4 3 1 2 5 6 7
- Plaintext a t t a c k p
- o s t p o n e
- d u n t i l t
- w o a m x y z
- Ciphertext TTNAAPTMTSUOAODWCOIXKNLYPETZ

- reorder the columns according to some key before

reading off the rows

Row Transposition Ciphers (cont.)

- Improve on Row Transposition Ciphers
- Re-encrypt again!
- Why more secure? Observe the change of plaintext

position

Initial plaintext 01 02 03 04 05 06 07 08 09 10

11 12 13 14 15 16 17 18

19 20 21 22 23 24 25 26 27 28

1st permutation 03 10 17 24 04 11 18 25 02 09 16

23 01 08 15 22 05 12 19

26 06 13 20 27 07 14 21 28

2nd permutation 17 09 05 27 24 16 12 07 10 02 22

20 03 25 15 13 04 23 19

14 11 01 26 21 18 08 06 28

Product Ciphers

- ciphers using substitutions or transpositions are

not secure because of language characteristics - hence consider using several ciphers in

succession to make harder, but - two substitutions make a more complex

substitution - two transpositions make more complex

transposition - but a substitution followed by a transposition

makes a new much harder cipher - this is bridge from classical to modern ciphers

Outline

- Symmetric cipher model
- Substitution technique
- Transposition technique
- Rotor machines
- Steganography

Rotor Machines

- apply multiple stages of encryption
- were widely used in WW2
- German Enigma, Allied Hagelin, Japanese Purple
- with 3 cylinders have 26317576 alphabets
- Each cylinder is a monoalphabetic substitution

Three-rotor machine

Steganography

??

- Encryption
- Steganography hides existence of message

encryption

plaintext

ciphertext

(un-recognizable)

steganography

plaintext

another plaintext

(No Transcript)

Summary

- have considered
- classical cipher techniques and terminology
- monoalphabetic substitution ciphers
- cryptanalysis using letter frequencies
- Playfair ciphers
- polyalphabetic ciphers
- transposition ciphers
- product ciphers and rotor machines
- stenography

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