Chap' 2 Classical Encryption Techniques

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Chap. 2 Classical Encryption Techniques
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Cryptography
Introduction to Cryptography

• Cryptography is the study of secret (crypto-)
  writing (-graphy)
• Concerned with developing algorithms which may be
  used to
• Conceal the context of some message from all
  except the sender and recipient (privacy or
  secrecy), and/or
• Verify the correctness of a message to the
  recipient (authentication or integrity)
• Basis of many technological solutions to computer
  and communications security problems

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Basic Terminology
Introduction to Cryptography

• Cryptography
• The art or science encompassing the principles
  and methods of transforming message an
  intelligible into one that is unintelligible, and
  then retransforming that message back to its
  original form
• Plaintext
• The original intelligible message
• Ciphertext
• The transformed message
• Cipher
• An algorithm for transforming an intelligible
  message into one that is unintelligible by
  transposition and/or substitution methods
• Key
• Some critical information used by the cipher,
  known only to the sender receiver

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Introduction to Cryptography
Basic Terminology - 2

• Encipher (encode)
• Process of converting plaintext to ciphertext
  using a cipher and a key
• Decipher (decode)
• The process of converting ciphertext back into
  plaintext using a cipher and a key
• Cryptanalysis (codebreaking)
• The study of principles and methods of
  transforming an unintelligible message back into
  an intelligible message without knowledge of the
  key.
• Cryptology
• The field encompassing both cryptography and
  cryptanalysis

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Introduction to Cryptography
Basic Terminology - 3

• Encryption
• The mathematical function mapping plaintext to
  ciphertext using the specified key Y EK(X)
  or E(K, X)
• Decryption
• The mathematical function mapping ciphertext to
  plaintext using the specified key X DK(Y)
  or D(K, X) EK-1(Y)

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Introduction to Cryptography
Basic Terminology - 4

• Cryptographic system (Cryptosystem)
• A cryptosystem is a five-tuple (P, C, K, E, D),
  where following conditions are satisfied
• P is a finite set of possible plaintexts
• C is a finite set of possible ciphertexts
• K, the keyspace, is a finite set of possible keys
• For each K ? K, there is an encryption algorithm
  EK ? E and a corresponding decryption algorithm
  DK ? D. Each EK P ? C and DK C ? P are
  functions such that DK(EK(X)) X for every
  plaintext X ? P.

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Simplified Conventional Encryption Model
Conventional Encryption Model

• Requirements
• Strong encryption algorithm
• Share of the secret key in a secure fashion
• Conventional
• Secret-Key (? Public-Key)
• Single-Key (? Two-Key)
• Symmetric (? Asymmetric)

Kerchhoffs Principle Encryption algorithms
being used should be assumed to be publicly known
and the security of the algorithm should reside
only in the key chosen
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Conventional Cryptosystem Model
Conventional Encryption Model
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Cryptanalysis
Conventional Encryption Model

• Process of attempting to discover X or K or both.
• Various types of cryptanalytic attacks

Probable-word attack
Differential cryptanalysis
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Exhaustive Key Search
Conventional Encryption Model

• Brute-force attack
• Always theoretically possible to simply try every
  key
• Most basic attack, directly proportional to key
  size
• Assume either know or can recognize when
  plaintext is found
• Average Time Required for Exhaustive Key Search

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Unconditional and Computational Security
Conventional Encryption Model

• Unconditionally secure (Perfect secure)
• 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
• Computationally secure
• The cost of breaking the security exceeds the
  value of the secured service or information.
• The time required to break the security exceeds
  the useful lifetime of the information

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Classical Encryption Techniques
Classical Encryption Techniques

• Substitution Techniques
• Caesar Cipher
• Monoalphabetic Ciphers
• Playfair Cipher
• Hill Cipher
• Polyalphabetic Ciphers
• One-Time Pad
• Transposition (Permutation) Techniques
• Rail Fence Technique
• Block (Columnar) Transposition Technique
• Product Techniques
• Substitution and transposition ciphers are
  concatenated

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Caesar Cipher
Substitution Techniques

• 2000 years ago, by Julius Caesar
• A simple substitution cipher, known as Caesar
  cipher
• Replace each letter with the letter standing 3
  places further down the alphabet
• Plain meet me after the toga party
• Cipher PHHW PH DIWHU WKH WRJD SDUWB
• No key, just one mapping (translation)
• 0123456...
• Plain abcdefghijklmnopqrstuvwxyz
• Cipher DEFGHIJKLMNOPQRSTUVWXYZABC
• 3456789...
• ciE(3,pi)(pi3) mod 26
• piD(3,ci)(ci-3) mod 26

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Generalized Caesar Cipher
Substitution Techniques

• Can use any shift from 1 to 25, i.e., replace
  each letter by a letter a fixed distance away
• ciE(k,pi)(pik) mod 26
• piD(k,ci)(ci-k) mod 26
• Shift cipher
• Key k
• Key letter the letter a plaintext A maps to
• e.g. a key letter of F means A maps to F, B to G,
  , Y to D, Z to E
• Hence have 26 (25 useful) ciphers
• Key space 26

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Substitution Techniques
Brute-Force Cryptanalysis of Caesar Cipher

• Ciphertext only attack
• Charateristics for success
• The encryption and decryption algorithms are
  known
• There are only 25 keys to try
• The language of the plaintext is known and easily
  recongnizable

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Affine Cipher
Substitution Techniques

• ciE(k,pi)(k1pik2) mod 26 gcd(k1,26)1
• piD(k,ci)(k1-1(ci-k2)) mod 26
• Key k (k1,k2)
• Number of keys ?(26) x 26 12 x 26 312
• ?(m) the number of integers in Zm that are
  relatively prime to m
• k1?1,3,5,7,9,11,15,17,19,21,23,25
• Caesar/Shift ciphers are special cases of affine
  ciphers

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Monoalphabetic Substitution Ciphers
Substitution Techniques

• Further generalization of the Caesar cipher,
• Plain abcdefghijklmnopqrstuvwxyz
• Cipher DEFGHIJKLMNOPQRSTUVWXYZABC
• is obtained by allowing any permutation of 26
  characters for the cipher
• Key size 26
• Key space 26! ? 4x1026
• Unique mapping of plaintext alphabet to
  ciphertext alphabet ? Monoalphabetic
• For a long time thought secure, but easily
  breakable by frequency analysis attack

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Relative Frequency of Letters in English Text
Substitution Techniques
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Frequency Statistics of Language
Substitution Techniques

• In addition to the frequency info of single
  letters, the frequency info of two-letter
  (digram) or three-letter (trigram) combinations
  can be used for the cryptanalysis
• Most frequent digrams
• TH, HE, IN, ER, AN, RE, ED, ON, ES, ST, EN, AT,
  TO, NT, HA, ND, OU, EA, NG, AS, OR, TI, IS, ET,
  IT, AR, TE, SE, HI, OF
• Most frequent trigrams
• THE, ING, AND, HER, ERE, ENT, THA, NTH, WAS, ETH,
  FOR, DTH

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Homophones
Substitution Techniques

• Monoalphabetic substitution ciphers are easy to
  break through letter frequency analysis
• Multiple substitutes (homophones) for a single
  letter can be used to hide the single-letter
  frequency information
• But even with homophones, multiple-letter
  patterns (e.g. digram frequencies) still survive
  in the ciphertext
• Two approaches for this problem
• Encrypt multiple letters of plaintext
• Playfair cipher
• Hill cipher
• Use multiple cipher alphabets
• Polyalphabetic cipher

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Playfair Cipher
Substitution Techniques

• Best-known multiple-letter substitution cipher
• Digram cipher (digram to digram, i.e., E(pipi1)
  cici1 through keyword-based 5x5 transformation
  table)
• Great advance over simple monoalphabetic
  cipher (26 letters ? 26x26676 digrams)
• Still leaves much of the structure of the
  plaintext language ? relatively easy to break
• Can be generalized to polygram cipher

Keyword monarchy Plaintext H S E A A R M
U Ciphertext B P I M R M C M
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Substitution Techniques
Relative Frequency of Occurrence of Letters
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Hill Cipher
Substitution Techniques

• Multi-letter cipher
• Takes m successive plaintext letters and
  substitutes for them m ciphertext letters
• 3x3 Hill cipher
• K
• C EK(P) KP P DK(C) K-1C K-1KP P
• m x m Hill cipher hides (m-1)-letter frequency
  info
• Strong against for the ciphertext-only attack,
  but easily broken with known plaintext attack
• with m plaintext-ciphertext pairs, each of length
  m K CP-1

c1 (k11p1 k12p2 k13p3) mod 26 c2 (k21p1
k22p2 k23p3) mod 26 c3 (k31p1 k32p2
k33p3) mod 26
k11 k12 k13 k21 k22 k23 k31 k32 k33
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Polyalphabetic Cipher
Substitution Techniques

• Typically a set of monoalphabetic substitution
  rules is used
• Key determines which rule to use

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Vigenère cipher
Substitution Techniques

• Best-known polyalphabetic ciphers
• Each key letter determines one of 26 Caesar
  (shift) ciphers
• ci E(pi) pi ki mod(key length) mod 26
• Example
• Keyword is repeated to make a key as long as the
  plaintext
• (Kasiski Test) Given a sufficient amount of
  ciphertext, common sequences are repeated,
  exposing the period (keyword length) ? Target of
  the cryptanalysis

Key deceptivedeceptivedeceptive Plaintext weare
discoveredsaveyourself Cipheretxt ZICVTWQNGRZGVTW
AVZHCQYGLMGJ
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Substitution Techniques
Vigenère cipher - 2
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Vigenère cipher - 3
Substitution Techniques

• If the keyword length is N, then Vigenère cipher,
  in effect, consists of N monoalphabetic
  substitution ciphers ?
  Consider each of the ciphers separately
• Improvement over the Playfair cipher, but
  language structure and frequency information
  still remain
• Vigenère autokey system after key is exhausted,
  use plaintext for running key (to eliminate the
  periodic nature)
• Key and plaintext share the same frequency
  distribution of letters ? a statistical technique
  can be used for the cryptanalysis, (e.g., e
  enciphered with e would occur with a frequency of
  (0.1275)2 ? 0.0163, t enciphered with t would
  occur with a frequency of (0.0925)2 ? 0.0086,
  etc.)

Key deceptivewearediscoveredsav Plaintext weare
discoveredsaveyourself Cipheretxt ZICVTWQNGKZEIIG
ASXSTSLVVWLA
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One-Time Pad
Substitution Techniques

• Perfect substitution cipher
• Improved Vernam cipher
• Use a random key (pad) which is as long as the
  message, with no repetitions.
• Key distribution is a problem
• Or, random key stream generation is a problem
• With such key, plaintext and ciphertext are
  statistically independent
• Unconditionally secure (Unbreakable)

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Transposition (Permutation) Techniques
Transposition Techniques

• Hide the message by rearranging the letter order
  without altering the actual letters used
• Rail Fence Cipher
• Write message on alternate rows, and read off
  cipher row by row
• Example
• Block (Columnar) Transposition Ciphers
• Message is written in rectangle, row by row, but
  read off column by column The order of columns
  read off is the key
• Example
• Generalization multiple transpositions ? More
  secure

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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Rotor Machines
Rotor Machines

• Mechanical cipher machines, extensively used in
  WWII Germany (Enigma), Japan (Purple), Sweden
  (Hagelin)

• Each rotor corresponds to a substitution cipher
• A one-rotor machine produces a polyalphabetic
  cipher with period 26
• Output of each rotor is input to next rotor
• After each symbol, the fast rotor is rotated
• After a full rotation, the adjacent rotor is
  rotated (like odometer)
• - An n rotor machine produces a polyalphabetic
  cipher with period 26n

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Rotor Machines
Three-Rotor Machines
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Steganography
Steganography

• The art of covered writing
• Security by obscurity
• Hide messages in other messages
• Conceal the existence of message
• Conceal what you are communicating (Sending
  encrypted messages would make you a spy)
• Character marking. Overwrite with a pencil
• Invisible ink, - Pin punctures, - First letter
  of each word
• Letter position on page, - Drawings, - Codes
• Typewriter correction ribbon
• Microdots
• Digital steganography
• Spread spectrum

Covert channel or Subliminal channel
Digital Watermarking
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Steganography
Steganography - Example
News Eight Weather Tonight increasing snow.
Unexpected precipitation Smothers Eastern towns.
Be extremely cautious and use snowtires
especially heading east. The highways are
knowingly slippery. Highway evacuation is
suspected. Police report emergency situations in
downtown ending near Tuesday First letter of
each word yields Newt is upset because he thinks
he is President This example was
created by Neil F. Johnson, and was published in
Steganography,Technical Report TR_95_11_nfj,
1995. URL  http//www.jjtc.com/pub/tr_95_11_
nfj/ From WWII German spy (Kahn) Apparently
neutrals protest is thoroughly discounted and
ignored. Isman hard hit. Blockade issue affects
pretext for embargo on by products, ejecting
suets and vegetable Oils. Second letter of
each word yields Pershing sails from NY June 1.
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Steganography
Steganography - Exercise
What is the message embedded in the left figure?
(Prob. 2.1)
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Chapter 2 Homework

• Problems 2.1, 2.4, 2.8, 2.11, 2.14(a), 2.17, 2.19
• Due date 17 March 2006