Cryptography and Network SecurityChapter 2 Fifth Edition
by William Stallings
Prepared By: Asghar Ali Shah
PhD-CS Scholar
Email: alishahsadiq@gmail.com

Slide 2:

Chapter 2 – Classical EncryptionTechniques "I am fairly familiar with all the forms of secret writings, and am myself the author of a trifling monograph upon the subject, in which I analyze one hundred and sixty separate ciphers," said Holmes..
—The Adventure of the Dancing Men, Sir Arthur Conan Doyle

Slide 3:

Symmetric Encryption or conventional / private-key / single-key
sender and recipient share a common key
all classical encryption algorithms are private-key
was only type prior to invention of public-key in 1970’s
and by far most widely used (still)
is significantly faster than public-key crypto

Slide 4:

Some Basic Terminology plaintext - original message, normal text
ciphertext - coded message, text after encryption
cipher - algorithm for transforming plaintext to ciphertext
Secret key - info used in cipher known only to sender/receiver. Input to the encryption algorithem
encipher (encrypt) - converting plaintext to ciphertext
decipher (decrypt) - recovering plaintext from ciphertext
cryptography - study of encryption principles/methods
cryptanalysis (codebreaking) - study of principles/ methods of deciphering ciphertext without knowing key
cryptology - field of both cryptography and cryptanalysis

Slide 5:

Symmetric Cipher Model

Slide 6:

Requirements two requirements for secure use of symmetric encryption:
a strong encryption algorithm
a secret key known only to sender / receiver
mathematically have:
Y = E(K, X) = EK(X) = {X}K
X = D(K, Y) = DK(Y)
assume encryption algorithm is known
Kerckhoff’s Principle: security in secrecy of key alone, not in obscurity of the encryption algorithm
implies a secure channel to distribute key
Central problem in symmetric cryptography

Slide 7:

Cryptography can characterize cryptographic system by:
type of encryption operations used
Substitution (putting one element into another)
Transposition (elements in the plaintext is rearranged)
Product (multiple stages of substitution and transposition)
number of keys used
single-key or private (Symmetric )
two-key or public (Asymmetric)
way in which plaintext is processed
block
stream

Slide 8:

Cryptanalysis objective to recover key not just message
general approaches:
cryptanalytic attack
brute-force attack
if either succeed all key use compromised

Slide 9:

Cryptanalytic Attacks ciphertext only
only know algorithm & ciphertext, is statistical, can identify plaintext
known plaintext
know/suspect plaintext & ciphertext
chosen plaintext
select plaintext and obtain ciphertext
chosen ciphertext
select ciphertext and obtain plaintext
chosen text
select plaintext or ciphertext to en/decrypt

Slide 10:

Cipher Strength unconditional security
no matter how much computer power or time 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 (e.g. time needed for calculations is greater than age of universe), the cipher cannot be broken

Slide 11:

Encryption Mappings A given key (k)
Maps any message Mi to some ciphertext E(k,Mi)
Ciphertext image of Mi is unique to Mi under k
Plaintext pre-image of Ci is unique to Ci under k
Notation
key k and Mi in M, Ǝ! Cj in C such that E(k,Mi) = Cj
key k and ciphertext Ci in C, Ǝ! Mj in M such that E(k,Mj) = Ci
Ek(.) is “one-to-one” (injective)
If |M|=|C| it is also “onto” (surjective), and hence bijective. M=set of all plaintexts C=set of all ciphertexts

Slide 12:

Encryption Mappings (2) A given plaintext (Mi)
Mi is mapped to some ciphertext E(K,Mi) by every key k
Different keys may map Mi to the same ciphertext
There may be some ciphertexts to which Mi is never mapped by any key
Notation
key k and Mi in M, Ǝ! ciphertext Cj in C such that E(k,Mi) = Cj
It is possible that there are keys k and k’ such that E(k,Mi) = E(k’,Mi)
There may be some ciphertext Cj for which Ǝ key k such that E(k,Mi) = Cj

Slide 13:

Encryption Mappings (3) A ciphertext (Ci)
Has a unique plaintext pre-image under each k
May have two keys that map the same plaintext to it
There may be some plaintext Mj such that no key maps Mj to Ci
Notation
key k and ciphertext Ci in C, Ǝ! Mj in M such that E(k,Mj) = Ci
There may exist keys k, k’ and plaintext Mj such that E(k,Mj) = E(k’,Mj) = Ci
There may exist plaintext Mj such that Ǝ key k such that E(k,Mj) = Ci

Slide 14:

Encryption Mappings (4) Under what conditions will there always be some key that maps some plaintext to a given ciphertext?
If for an intercepted ciphertext cj, there is some plaintext mi for which there does not exist any key k that maps mi to cj, then the attacker has learned something
If the attacker has ciphertext cj and known plaintext mi, then many keys may be eliminated

Slide 15:

Brute Force Search always possible to simply try every key
most basic attack, exponential in key length
assume either know / recognise plaintext

Slide 16:

Classical Substitution Ciphers where letters of plaintext are replaced by other letters or by numbers or symbols
or if plaintext is viewed as a sequence of bits, then substitution involves replacing plaintext bit patterns with ciphertext bit patterns

Slide 17:

Caesar Cipher earliest known substitution cipher
by Julius Caesar
first attested use in military affairs
replaces each letter by 3rd letter on
example:
meet me after the toga party
PHHW PH DIWHU WKH WRJD SDUWB

Slide 18:

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 = IN
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 = OUT
mathematically give each letter a number
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
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 (rotation) cipher as:
c = E(k, p) = (p + k) mod (26)
p = D(k, c) = (c – k) mod (26)

Slide 19:

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"

Slide 20:

Affine Cipher broaden to include multiplication
can define affine transformation as:
c = E(k, p) = (ap + b) mod (26)
p = D(k, c) = (a-1(c – b)) mod (26)
key k=(a,b)
a must be relatively prime to 26
so there exists unique inverse a-1

Slide 21:

Affine Cipher - Example example k=(17,3):
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 = IN
D U L C T K B S J A R I Z Q H Y P G X O F W N E V M = OUT
example:
meet me after the toga party
ZTTO ZT DKOTG OST OHBD YDGOV
Now how many keys are there?
12 x 26 = 312
Still can be brute force attacked!

Slide 22:

Monoalphabetic Cipher rather than just shifting the alphabet
could shuffle (permute) 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

Slide 23:

Monoalphabetic Cipher Security key size is now 25 characters…
now have a total of 26! = 4 x 1026 keys
with so many keys, might think is secure
but would be !!!WRONG!!!
problem is language characteristics

Slide 24:

Language Redundancy and Cryptanalysis human languages are redundant
e.g., "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 letter frequencies for various languages

Slide 25:

English Letter Frequencies

Slide 26:

English Letter Frequencies

Slide 27:

What kind of cipher is this?

Slide 28:

What kind of cipher is this?

Slide 30:

Use in Cryptanalysis key concept - monoalphabetic substitution ciphers do not change relative letter frequencies
discovered by Arabian scientists in 9th century
calculate letter frequencies for ciphertext
compare counts/plots against known values
if caesar cipher look for common peaks/troughs
peaks at: A-E-I triple, N-O pair, R-S-T triple
troughs at: J-K, U-V-W-X-Y-Z
for monoalphabetic must identify each letter
tables of common double/triple letters help
(digrams and trigrams)
amount of ciphertext is important – statistics!

Slide 31:

Example Cryptanalysis given ciphertext:
UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ
VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX
EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ
count relative letter frequencies (see text)

Slide 32:

Example Cryptanalysis given ciphertext:
UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ
VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX
EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ
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 but
direct contacts have been made with political
representatives of the viet cong in moscow

Slide 33:

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

Slide 34:

Playfair Key Matrix a 5X5 matrix of letters based on a keyword
fill in letters of keyword (sans duplicates)
fill rest of matrix with other letters
eg. using the keyword MONARCHY

Slide 35:

Encrypting and Decrypting plaintext is encrypted two letters at a time
if a pair is a repeated letter, insert filler like 'X’
if both letters fall in the same row, replace each with letter to right (wrapping back to start from end)
if both letters fall in the same column, replace each with the letter below it (wrapping to top from bottom)
otherwise each letter is replaced by the letter in the same row and in the column of the other letter of the pair

Slide 36:

Playfair Example Message = Move forward
Plaintext = mo ve fo rw ar dx
Here x is just a filler, message is padded and segmented
Ciphertext = ON UF PH NZ RM BZ mo -> ON; ve -> UF; fo -> PH, etc.

Slide 37:

Security of Playfair Cipher security much improved over monoalphabetic
since have 26 x 26 = 676 digrams
would need a 676 entry frequency table to analyse (versus 26 for a monoalphabetic)
and correspondingly more ciphertext
was widely used for many years
eg. by US & British military in WW1
it can be broken, given a few hundred letters
since still has much of plaintext structure

Slide 38:

Polyalphabetic Ciphers polyalphabetic substitution ciphers
improve security using multiple cipher alphabets
make cryptanalysis harder with more alphabets to guess and flatter frequency distribution
use a key to select which alphabet is used for each letter of the message
use each alphabet in turn
repeat from start after end of key is reached

Slide 39:

Vigenère Cipher simplest polyalphabetic substitution cipher
effectively multiple caesar ciphers
key is multiple letters long K = k1 k2 ... kd
ith letter specifies ith alphabet to use
use each alphabet in turn
repeat from start after d letters in message
decryption simply works in reverse

Slide 40:

Example of Vigenère Cipher write the plaintext out
write 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: wearediscoveredsaveyourself
ciphertext:ZICVTWQNGRZGVTWAVZHCQYGLMGJ

Slide 41:

Aids simple aids can assist with en/decryption
a Saint-Cyr Slide is a simple manual aid
a slide with repeated alphabet
line up plaintext 'A' with key letter, eg 'C'
then read off any mapping for key letter
can bend round into a cipher disk
or expand into a Vigenère Tableau

Slide 42:

Security of Vigenère Ciphers have multiple ciphertext letters for each plaintext letter
hence letter frequencies are obscured
but not totally lost
start with letter frequencies
see if it looks monoalphabetic or not
if not, then need to determine number of alphabets, since then can attack each

Slide 43:

Frequencies After Polyalphabetic Encryption

Slide 44:

Frequencies After Polyalphabetic Encryption

Slide 45:

Homework 1 Due next class
Question 1:
What is the best “flattening” effect you can achieve by carefully selecting two monoalphabetic substitutions? Explain and give an example. What about three monoalphabetic substitutions?

Slide 46:

Kasiski Method method developed by Babbage / Kasiski
repetitions in ciphertext give clues to period
so find same plaintext a multiple of key length apart
which results in the same ciphertext
of course, could also be random fluke
e.g. repeated “VTW” in previous example
distance of 9 suggests key size of 3 or 9
then attack each monoalphabetic cipher individually using same techniques as before

Slide 47:

Example of Kasiski Attack Find repeated ciphertext trigrams (e.g., VTW)
May be result of same key sequence and same plaintext sequence (or not)
Find distance(s)
Common factors are likely key lengths
key: deceptivedeceptivedeceptive
plaintext: wearediscoveredsaveyourself
ciphertext:ZICVTWQNGRZGVTWAVZHCQYGLMGJ

Slide 48:

Autokey Cipher ideally want a key as long as the message
Vigenère proposed the autokey cipher
with keyword is prefixed to message as key
knowing keyword can recover the first few letters
use these in turn on the rest of the message
but still have frequency characteristics to attack
eg. given key deceptive
key: deceptivewearediscoveredsav
plaintext: wearediscoveredsaveyourself
ciphertext:ZICVTWQNGKZEIIGASXSTSLVVWLA

Slide 49:

Homophone Cipher rather than combine multiple monoalphabetic ciphers, can assign multiple ciphertext characters to same plaintext character
assign number of homophones according to frequency of plaintext character
Gauss believed he made unbreakable cipher using homophones
but still have digram/trigram frequency characteristics to attack
e.g., have 58 ciphertext characters, with each plaintext character assigned to ceil(freq/2) ciphertext characters – so e has 7 homophones, t has 5, a has 4, j has 1, q has 1, etc.

Slide 50:

Vernam Cipher ultimate defense is to use a key as long as the plaintext
with no statistical relationship to it
invented by AT&T engineer Gilbert Vernam in 1918
specified in U.S. Patent 1,310,719, issued July 22, 1919
originally proposed using a very long but eventually repeating key
used electromechanical relays

Slide 51:

One-Time Pad if a truly random key as long as the message is used, the cipher will be secure
called a One-Time pad (OTP)
is unbreakable since ciphertext bears no statistical relationship to the plaintext
since for any plaintext & any ciphertext there exists a key mapping one to other
can only use the key once though
problems in generation & safe distribution of key

Slide 52:

Transposition Ciphers now consider classical transposition or permutation ciphers
these hide the message by rearranging the letter order
without altering the actual letters used
can recognise these since have the same frequency distribution as the original text

Slide 53:

Rail Fence cipher write message letters out diagonally over a number of 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

Slide 54:

Row Transposition Ciphers is a more complex transposition
write letters of message out in rows over a specified number of columns
then reorder the columns according to some key before reading off the rows
Key: 4312567
Column Out 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

Slide 55:

Block Transposition Ciphers arbitrary block transposition may be used
specify permutation on block
repeat for each block of plaintext
Key: 4931285607
Plaintext: attackpost poneduntil twoamxyzab
Ciphertext: CTATTSKPAO DLEONIDUPT MBAWOAXYTZ

Slide 56:

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

Slide 57:

Rotor Machines before modern ciphers, rotor machines were most common complex ciphers in use
widely used in WW2
German Enigma, Allied Hagelin, Japanese Purple
implemented a very complex, varying substitution cipher
used a series of cylinders, each giving one substitution, which rotated and changed after each letter was encrypted
with 3 cylinders have 263=17576 alphabets

Slide 58:

Hagelin Rotor Machine

Slide 59:

Rotor Machine Principles

Slide 60:

Rotor Ciphers Each rotor implements some permutation between its input and output contacts
Rotors turn like an odometer on each key stroke (rotating input and output contacts)
Key is the sequence of rotors and their initial positions

Slide 61:

Steganography an alternative to encryption
hides existence of message
using only a subset of letters/words in a longer message marked in some way
using invisible ink
hiding in LSB in graphic image or sound file
hide in “noise”
has drawbacks
high overhead to hide relatively few info bits
advantage is can obscure encryption use

Slide 62:

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
steganography

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