Cryptography

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Cryptography

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Activity

• What is cryptography ?

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Introduction

• Cryptography is the study of Encryption
• Greek kryptos means hidden and
  graphia means writtings
• Encryption is an ancient form of information
  protection. dates back 4,000 years.
• process by which plaintext is converted into
  ciphertext.
• Decryption is the inverse of Encryption.

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Introduction

• A sender S wanting to transmit message M to a
  receiver R
• To protect the message M, the sender first
  encrypts it into meaningless message M
• After receipt of M, R decrypts the message to
  obtain M
• M is called the plaintext
• What we want to encrypt
• M is called the ciphertext
• The encrypted output

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Introduction

• Notation
• Given
• PPlaintext
• CCipherText
• C EK (P) Encryption
• P DK ( C) Decryption

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Terminologies

• Cryptography Schemes for encryption and
  decryption
• Encryption algorithm technique or rules selected
  for encryption.
• Key is secret value used to encrypt and/or
  decrypt the text.
• Cryptanalysis The study of breaking the code.
• Cryptology Cryptography and cryptanalysis
  together constitute the area of cryptology.

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Encryption vs. C-I-A

• Encryption provides
• Confidentiality/Secrecy
• keeps our data secret.
• Integrity
• protect against forgery or tampering

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Cryptographic systems

• are characterized along three dimensions
• operations used for transforming
• Substitution Replace (bit, letter, group of bits
  letters
• Transposition Rearrange the order
• Product use multiple stages of both
• number of keys used
• Symmetric same key , secret-key, private-key
• Asymmetric different key , public-key
• way in which the plaintext is processed
• block cipher
• Stream cipher

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Transposition and Substitution

• Simple Simple Substitution
• Transposition

security
security
security
Encryption
Encryption
Encryption
cusetyri
tfdvsjuz
19 5 3 20 18 9 19 25
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Classical Substitution

• Caesar Cipher used by Julius Caesar's military
• substitutes each letter of the alphabet with the
  letter standing three places further down the
  alphabet

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Caesar cipher
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Activity

• Convert it ....to Caesar Ciphertext?
• Plaintext are you ready
• Ciphertext duh brx uhdgb

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
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
z
C
Plaintext
Ciphertext
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Caesar Cipher

• the algorithm can be expressed as, for each
  plaintext letter P, substitute ciphertext letter
  C.
• C E(3, p) (p 3) mod 26
• 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
• General Caesar algorithm as
• c E(k, p) (p k) mod (26)
• p D(k, c) (c k) mod (26)
• Where k is 1 to 25. Secret-key

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Classical Transposition

• Spartans cipher , fifth century B.C.
• Start the war today
• Rewrite it by reading down
• Srhaoytterdatwta

Encryption rearrange the text in 3 columns
S t a r t t h e w a r t o d a y
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Cryptanalysis

• objective to recover key not just message
• general approaches
• cryptanalytic attack
• exploits the characteristics of the algorithm
• brute-force attack
• try every possible key on a piece of ciphertext
• if either succeed all key use compromised

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Cryptanalytic Attacks

• ciphertext only
• only know algorithm ciphertext, is statistical,
  know or can identify plaintext .Most difficult
• 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

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More Definitions

• 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 (eg time needed
  for calculations is greater than age of
  universe), the cipher cannot be broken
• it either takes too long, or is too expensive,

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Cryptanalysis

• given a ciphertext Caesar cipher, then a
  brute-force is easy performed
• simply try all the 25 possible keys.
• Assuming language of the plaintext is known.
• Thus, Caesar cipher is far from secure.

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Introducing

• Alice
• Bob
• Trudy

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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
• but would be !!!WRONG!!!
• problem is language characteristics, statistical
  techniques

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Brute Force Search

• always possible to simply try every key
• assume either know / recognise plaintext
• impractical if we use an algorithm that employs
  a large number of keys.
• most basic attack, proportional to key size

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Language Redundancy and Cryptanalysis

• human languages are redundant
• 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

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English Letter Frequencies
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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

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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
  but
• direct contacts have been made with political
• representatives of the viet cong in moscow

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• Given this cipher text
• UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ
• VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX
• EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ
• Relative frequency of the letters in the text
• 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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• UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ
• t a e e te a
  that e e a a t
• VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX
• e t ta t ha e ee a e
  th t a
• EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ
• e e e tat e the t
• Continued analysis of frequencies plus trial and
  error should easily yield a solution from this
  point
• it was disclosed yesterday that several
  informal but
• direct contacts have been made with political
• representatives of the viet cong in moscow.

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Cryptograph cont

• Playfair cipher
• Polyalphabetic ciphers
• Vigenère cipher
• Vernam cipher
• One-timepad
• More on Transposition
• Rail fence cipher
• Message in rectangle ( row transposition )
• Rotor machine

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Playfair Cipher

• A.k.a Playfair square
• A manual symmetric encryption technique
• It was the first literal digraph substitution
  cipher.
• The scheme was invented in 1854 by Charles
  Wheatstone, but bears the name of Lord Playfair
  who promoted the use of the cipher.
• Used in WWI and WWII

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Playfair Key Matrix

• a 5X5 matrix of letters based on a keyword
• fill in letters of keyword (no duplicates, i j)
  
• fill rest of matrix with other letters
• eg. using the keyword (key) simple

s i/j m p l
e a b c d
f g h k n
o q r t u
v w x y z
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Playfair Cipher

• Use filler letter to separate repeated letters
• eg. "balloon" encrypts as "ba lx lo on" Encrypt
  two letters together
• Same row gtfollowed letters
• ac--bd
• Same columngt letters under
• qw--wi
• Otherwisegtsquares corner at same row
• ar--bq

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Activity

• Q construct the playfair matrix using the
  keyword MONARCHY ?
• Plaintext Ethiopia
• Ciphertext

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
klbfhvsb
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Security of Playfair Cipher

• security much improved over monoalphabetic
• But, still has much of plaintext structure.
• it can be broken, given a few hundred letters
• With ciphertext only, possible to analyse
  frequency of occurrence of digrams (pairs of
  letters)
• Obtaining the key is relatively straightforward
  if both plaintext and ciphertext are known.

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• Polyalphabetic ciphers

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Polyalphabetic ciphers

• using multiple substitution 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

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Vigenere Cipher

• simplest polyalphabetic substitution cipher
• meaning that instead of there being a one-to-one
  relationship between each letter and its
  substitute, there is a one-to-many relationship
  between each letter and its substitutes.
• The encipherer chooses a keyword and repeats it
  until it matches the length of the plaintext

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Vigenère Cipher

• Basically multiple Caesar ciphers
• key is multiple letters long
• K k1 k2 ... kd
• ith letter specifies ith alphabet to use
• use each alphabet in turn, repeating from start
  after d letters in message
• Plaintext THISPROCESSCANALSOBEEXPRESSED Keyword
  CIPHERCIPHERCIPHERCIPHERCIPHE
• Ciphertext VPXZTIQKTZWTCVPSWFDMTETIGAHLH

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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

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Activity

• Q encrypt the given plaintext letter using
  Vigenère Cipher use keyword deceptive
• plaintext wearediscoveredsaveyourself
  
• Key
• Ciphertext

• deceptivedeceptivedeceptive
• zicvtwqngrzgvtwavzhcqyglmgj

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Security of Vigenère Ciphers

• have multiple ciphertext letters for each
  plaintext letter
• hence letter frequencies are masked
• but not totally lost
• start with letter frequencies
• see if look monoalphabetic or not
• if not, then need to determine number of
  alphabets, since then can attach each

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Kasiski Method

• method developed by Babbage / Kasiski
• repetitions in ciphertext give clues to period
• so find same plaintext an exact period apart
• which results in the same ciphertext.
• eg repeated VTW in previous activity
• suggests size of 3 or 9
• then attack each monoalphabetic cipher
  individually using same techniques as before

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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
• ciphertextZICVTWQNGKZEIIGASXSTSLVVWLA

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Vernam Cipher

• ultimate defense is to use a key as long as the
  plaintext
• with no statistical relationship to it
• invented by ATT engineer Gilbert Vernam in 1918
• Originally proposed using a very long but
  eventually repeating key
• His system works on binary data (bits rather than
  letters)

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One-Time Pad

• if a truly random key as long as the message is
  used, the cipher will be secure.
• 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

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One-time Pad Encryption
e000 h001 i010 k011 l100 r101 s110
t111
Encryption Plaintext ? Key Ciphertext
h e i l h i t l e r
001 000 010 100 001 010 111 100 000 101
Plaintext
111 101 110 101 111 100 000 101 110 000
110 101 100 001 110 110 111 001 110 101
s r l h s s t h s r
Key
Ciphertext
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One-time Pad Decryption
e000 h001 i010 k011 l100 r101 s110
t111
Decryption Ciphertext ? Key Plaintext
s r l h s s t h s r
110 101 100 001 110 110 111 001 110 101
Ciphertext
111 101 110 101 111 100 000 101 110 000
001 000 010 100 001 010 111 100 000 101
h e i l h i t l e r
Key
Plaintext
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One-time Pad
Double agent claims sender used following key
s r l h s s t h s r
110 101 100 001 110 110 111 001 110 101
Ciphertext
101 111 000 101 111 100 000 101 110 000
011 010 100 100 001 010 111 100 000 101
k i l l h i t l e r
key
Plaintext
e000 h001 i010 k011 l100 r101 s110
t111
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One-time Pad
Or sender is captured and claims the key is
s r l h s s t h s r
110 101 100 001 110 110 111 001 110 101
Ciphertext
111 101 000 011 101 110 001 011 101 101
001 000 100 010 011 000 110 010 011 000
h e l i k e s i k e
Key
Plaintext
e000 h001 i010 k011 l100 r101 s110
t111
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One-time pad

• the only cryptosystem that exhibits what is
  referred to as perfect secrecy
• Drawbacks
• it requires secure exchange of the one-time pad
  material, which must be as long as the message
• pad disposed of correctly and never reused
• In practice
• Generate a large number of random keys,
• Exchange the key material securely between the
  users before sending an one-time enciphered
  message,
• Keep both copies of the key material for each
  message securely until they are used, and
• Securely dispose of the key material after use,
  thereby ensuring the key material is never
  reused.

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• Strength
• Is unconditionally secure provided key is truly
  random

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Random numbers needed

• If the key material is generated by a
  deterministic program then it is not actually
  random
• Why not to generate keystream from a smaller
  (base) key?
• Use some pseudo-random function to do this
• Although this looks very attractive, it proves to
  be very very difficult in practice to find a good
  pseudo-random function that is cryptographically
  strong
• This is still an area of much research

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Key Management

• Using secret channel
• Encrypt the key
• Third trusted party
• The sender and the receiver generate key

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More Transposition 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

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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 depth 2
• 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
• Plain msg "meet me after the toga party"

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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 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

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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

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Information Security Principles
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10 generally accepted basic principles

• Principle 1There is no such thing as
  absolute Security
• Given enough time, tools, skills and inclination
  a hacker can break through any security measure
  .
• E.g. safes vaults are usually rated according
  to their resistance to attacks.
• How long would it take ?

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• Principle 2 C-I-A
• All information security tries to address at
  least one of the three
• Protect the Confidentiality of data
• Preserve Integrity of data
• Promote the Availability of data

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CIA Triad
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• Principle 3 Defense in depth
• Layered security approach

• Prevent
• Detect
• Response
• E.g. Bank
• Human guard/door lock
• CCTV/Motion sensor
• Alarm/Tear gas

• E.g Internet attached devices
• Firewall(IPS)
• IDS/Traffic analyzer
• Auto traffic block

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• Principle 4 people are easy to be tricked
  into giving up secrets.
• Studies have proved it !
• Pen for password study.
• I love you virus.

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• Principle 5 Security through Obscurity
• If hackers dont know how software is secured,
  does it make security is better ?
• WRONG!!!!!
• Leads to false sense of security !

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• Principle 6 Security Riskmanagement
• Careful balance of the above two.
• E.g buy 500 safe to secure 200 jewelry
• Risk analysis
• Mitigate
• Insurance
• Accept
• Likely hood/consequence

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• Principle 7 3 types of security controls
• Preventive
• Detective
• Responsive

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• Principle 8 people, process technology
• All are needed to adequately secure a system
• E.g firewall with out process
• Dual control
• Separation of duties

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• Principle 9Open disclosure of vulnerabilities is
  good for security!
• To disclose or not to disclose
• that is the question !
• E.g. Automobile defects

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• The ethical Question is how should that valuable
  information be disseminated to the good guys
  while keeping it away from the bad guys!
• Anyhow Hackers know about most vulnerability long
  before the public!
• Problem shared is half solved!

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• Principle 10 Complexity is the enemy of
  security.
• With too many interfaces b/n programs and other
  systems, the interface became difficult to
  secure.