TCN - Lecture 6

8/7/2019 TCN - Lecture 6

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CLASSICAL CIPHERS

By

Mr. Fasee UllahCUSIT

Peshawar


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Agenda

Types of classical ciphers

Asymmetric cryptography

Application of Asymmetric encryption


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Symmetric Cipher Model

A symmetric encryption scheme has five ingredients

Plaintext: This is the original message or data

Encryption algorithm: The encryption algorithm performs

various substitutions and transformations on theplaintext

Secret key: The secret key is also input to the encryptionalgorithm

The algorithm will produce a different output

depending on the specific key being used at the time The exact substitutions and transformations performed

by the algorithm depend on the key


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Contd

Ciphertext: This is the scrambled message produced

as output

It depends on the plaintext and the secret key and,

as it stands, is unintelligible

Decryption algorithm: This is essentially the

encryption algorithm run in reverse

It takes the ciphertext and the secret key andproduces the original plaintext


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Classical Substitution Ciphers

Substitution techniques use classical encryptiontechnique

A study of these techniques enables us to explain the

basic approaches to symmetric encryption used today Two basic block of encryption techniques are

substitution

Transposition

A substitution technique is one in which the letters ofplaintext are replaced by other letters or by numbersor symbols


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Caesar Cipher

earliest known substitution cipher

by Julius Caesar

first attested use in military affairs

replaces each letter by 3rd letter on

meet me after the toga party


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Caesar Cipher

example:Plain text: meet me after the toga

party

Cipher Text: PHHWPH DIWHUWKHWRJDSDUWB

Note: Plaintext always in lowercase;

ciphertext is in uppercase;

key values are in lowercase


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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 JK L M N O P Q R S T U V W X Y Z A B C

mathematically give each letter a numbera 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

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 25

then have Caesar cipher as:

c = E(p) = (p + k) mod (26)p = D(c) = (c k) mod (26)


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Cryptanalysis of Caesar Cipher

only have 26 possible ciphers

A maps to A,B,..Z

could simply try each in turn

a brute force search

given ciphertext, just try all shifts of letters

do need to recognize when have plaintext

eg. break ciphertext "GCUA VQ DTGCM"


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Monoalphabetic Cipher

rather than just shifting the alphabet

could shuffle (jumble) the letters arbitrarily

each plaintext letter maps to a different random

ciphertext letter hence key is 26 letters long

Plain: abcdefghijklmnopqrstuvwxyz

Cipher: DKVQFIBJWPESCXHTMYAUOLRGZN

Plaintext: ifwewishtoreplaceletters

Ciphertext: WIRFRWAJUHYFTSDVFSFUUFYA


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Monoalphabetic Cipher Security

now have a total of 26! = 4 x 1026 keys

with so many keys, might think is secure to eliminate

brute-force techniques

but would be !!!WRONG!!!

problem is language characteristics


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Language Redundancy and

Cryptanalysis

human languages are redundant

eg "th lrd s m shphrd shll nt wnt"

letters are not equally commonly used

in English E is by far the most common letter

followed by T,R,N,I,O,A,S

other letters like Z,J,K,Q,X are fairly rare

have tables of single, double & triple letterfrequencies for various languages


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English Letter Frequencies


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Relative Frequencies of letters in

ciphertext

P 13.33 H 5.83 F 3.33 B 1.67 C 0.00

Z 11.67 D 5.00 W 3.33 G 1.67 K 0.00

S 8.33 E 5.00 Q 2.50 Y 1.67 L 0.00

U 8.33 V 4.17 T 2.50 I 0.83 N 0.00

O 7.50 X 4.17 A 1.67 J 0.83 R 0.00

M 6.67


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Example Cryptanalysis

given ciphertext:UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ

VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX

EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ

count relative letter frequencies

guess P & Z are e and t

guess ZW is th and hence ZWP is the

proceeding with trial and error finally get:it was disclosed yesterday that several informal butdirect contacts have been made with political

representatives of the viet cong in moscow


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Playfair Cipher

not even the large number of keys in a

monoalphabetic cipher provides security

one approach to improving security was to encrypt

multiple letters

the Playfair Cipher is an example

invented by Charles Wheatstone in 1854, but

named after his friend Baron Playfair


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Playfair Key Matrix

a 5X5 matrix of letters based on a keyword

fill in letters of keyword

fill rest of matrix with other letters eg. using the keyword MONARCHY

MM OO NN AA RR

CC HH YY BB DD

EE FF GG I/JI/J KK

LL PP QQ SS TT

UU VV WW XX ZZ


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Encrypting and Decrypting

plaintext is encrypted two letters at a time

wrap from right side back to left, or from bottom backto top.

1. if a pair is a repeated letter, insert a filler like 'X', eg."balloon" encrypts as "ba lx lo on"

2. if both letters fall in the same row, replace each with letterto right eg. ar" encrypts as "RM"

3. if both letters fall in the same column, replace each withthe letter below it (again wrapping to top from bottom), eg.mu" encrypts to "CM"

4. otherwise each letter is replaced by the one in its row inthe column of the other letter of the pair, eg. hs" encryptsto "BP", and ea" to "IM" or "JM" (as desired)


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Security of Playfair Cipher

security much improved over monoalphabetic

since have 26 x 26 = 676 digrams

was widely used for many years eg. by US & British military in WW1


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Polyalphabetic Ciphers

polyalphabetic substitution ciphers

improve security using multiple cipher

alphabets make cryptanalysis harder with more

alphabets to guess

use a key to select which alphabet is used foreach letter of the message

repeat from start after end of key is reached


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Vigenre Cipher

simplest polyalphabetic substitution cipher

key is multiple letters long K = k1 k2 ...

i

th

letter specifies i

th

alphabet to use use each alphabet in turn


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Example of Vigenre Cipher

write the plaintext out

write the keyword repeated above it

eg using keyword deceptive

key: deceptivedeceptivedeceptive

plaintext: wearediscoveredsaveyourself

ciphertext:ZICVTWQNGRZGVTWAVZHCQYGLMGJ


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Security of Vigenre Ciphers

have multiple ciphertext letters for each plaintext

letter

hence letter frequencies are obscured

but not totally lost


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One-Time Pad

Each new message requires a new key of the same length as thenew message

Such a technique called One Time Pad

is unbreakable since ciphertext bears no statistical relationship to

the plaintext can only use the key once though

The one-time pad offers complete security but, in practice, has twofundamental difficulties:

1. There is the practical problem of making large quantities of randomkeys

2. And the problem of key distribution and protection, where forevery message to be sent, a key of equal length is needed byboth sender and receiver


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Transposition Ciphers

now consider classical transposition or permutation

ciphers

these hide the message by rearranging the letter

order

without altering the actual letters used


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Rail Fence cipher

write message letters out diagonally over a numberof rows

then read off cipher row by row

eg. write message out as:m e m a t r h t g p r y

e t e f e t e o a a t

giving ciphertext

MEMATRHTGPRYETEFETEOAAT


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Row Transposition Ciphers

a more complex transposition

write letters of message out in rows over a specifiednumber of columns

then reorder the columns according to some keybefore reading off the rowsKey: 3 4 2 1 5 6 7

Plaintext: a t t a c k p

o s t p o n e

d u n t ilt

w o a m x y z

Ciphertext: TTNAAPTMTSUOAODWCOIXKNLYPETZ


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Product Ciphers

ciphers using substitutions or transpositions are notsecure 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 newmuch harder cipher

this is bridge from classical to modern ciphers


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Rotor Machines

before modern ciphers, rotor machines were mostcommon complex ciphers in use

widely used in WW2 German Enigma, Allied Hagelin, Japanese Purple

implemented a very complex, varyingsubstitution cipher

used a series of cylinders, each giving one

substitution, which rotated and changed aftereach letter was encrypted with 3 cylinders have 263=17576 alphabets


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An Example of Rotor Machine


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Hagelin Rotor Machine


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Summary

have considered:

classical cipher techniques and terminology

monoalphabetic substitution ciphers

cryptanalysis using letter frequencies

Playfair cipher

polyalphabetic ciphers

transposition ciphers product ciphers and rotor machines

stenography


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Assignment 20/09/2010

Explain each cipher with examples:

Hill Cipher

Kasiski cipher

Autokey Cipher

Application of Symmetric encryption

Documents

TCN - Lecture 6