Conventional Cryptography

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Conventional Cryptography

• Classical Encryption Techniques

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Topics

• Introduction to Cryptography
• Encryption / Decryption
• Basic Terminologies
• Cryptography Types
• Classical Cryptographic Techniques
• Stenography
• Mono-alphabetic Poly-alphabetic
• Caesar Cipher
• Transposition Cipher
• OTPs
• Rotor Machines

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Encryption / Decryption

• The process of disguising a message (plaintext)
  into an unintelligible form (ciphertext) by an
  encryption algorithm and a secret variable,
  called a key
• The process of transforming ciphertext back into
  plaintext using the encryption algorithm and a key

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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.
• Cryptography may be part of a security solution,
  but it is never the whole solution. At best, it
  transforms a more general security problem into a
  key management problem.

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Crypto Systems Classification

• Two requirements for secure use of symmetric
  encryption
• a strong encryption algorithm
• a secret key known only to sender / receiver
• Y EK(X)
• X DK(Y)
• Assume encryption algorithm is known
• Implies a secure channel to distribute key
• The way in which the plaintext is processed
• Block cipher
• Stream cipher

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History of Cryptography

• Ancient Cipher
• Have a history of some 4000 years
• Ancient Egyptians encoded some hieroglyphic
  writings on monuments
• Ancient Hebrews enciphered certain words in the
  scriptures using the ATBASH cipher
• Greek writings show the first discussions of the
  use of secret writings.

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Hieroglyphic Writings
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Basic Terminologies

• cryptology
• the field encompassing both cryptography and
  cryptanalysis
• cryptography
• the art or science encompassing the principles
  and methods of transforming an intelligible
  message into one that is unintelligible, and then
  retransforming that message back to its original
  form.
• cryptanalysis (codebreaking)
• the study of principles and methods of
  transforming an unintelligible message back into
  an intelligible message without knowledge of the
  key.
• plaintext
• the original intelligible message
• ciphertext
• the transformed message

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Basic Terminologies (Contd.)

• cipher
• Mathematical algorithm for transforming an
  intelligible message into unintelligible by
  transposition and/or substitution methods
• key
• Critical information used by the cipher, known
  only to the sender receiver
• encipher (encrypt)
• the process of converting plaintext to ciphertext
  using a cipher and a key
• decipher (decrypt)
• the process of converting ciphertext back into
  plaintext using a cipher and a key
• code
• an algorithm for transforming an intelligible
  message into an unintelligible one using a
  code-book

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Symbols Used
P plaintext C ciphertext E encryption
function D decryption function E(P) C
encrypting plaintext yields ciphertext D(C) P
decrypting ciphertext yields plaintext D(E(P))
P decrypting encrypted plaintext yields plaintext
K Key
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Cryptographic Concept

• Encryption C EK(P)
• Decryption P EK-1(C)
• EK is chosen from a family of transformations
  known as a cryptographic system.
• The parameter that selects the individual
  transformation is called the key K, selected from
  a keyspace K.

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The Key !

• All modern algorithms use a key to control
  encryption and decryption
• The key used for decryption can be different from
  the encryption key, but for most algorithms they
  are the same.

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Key Management Problems

• Key management is the hardest part of
  cryptography
• Two classes of keys
• Short-term session keys (sometimes called
  ephemeral keys)
• Generated automatically and invisibly
• Used for one message or session and discarded
• Long-term keys
• Generated explicitly by the user
• Long-term keys are used for two purposes
• Authentication (including access control,
  integrity, and non-repudiation)
• Confidentiality (encryption)
• Establish session keys
• Protect stored data

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Key Lifetimes and Key Compromise

• Authentication keys
• Public keys may have an long lifetime (decades)
• Conventional keys have shorter lifetimes (a year
  or two)
• If the key is compromised
• Revoke the key
• Effects of compromise
• Authentication Signed documents are rendered
  invalid unless time-stamped.
• Confidentiality All data encrypted with it is
  compromised.

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Cryptography Types

• Symmetric cryptography
• Use the same key for encryption and decryption
• Asymmetric cryptography
• More popularly known as Public Key Cryptography
• Use different keys for encryption and decryption

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Symmetric Cryptography
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Asymmetric Cryptography
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Cryptanalysis

• Cryptanalysis is the process of breaking an
  encrypted message without knowledge of key
• Several different types of attacks can be
  identified
• Ciphertext only
• only known algorithm and some ciphertext
• use statistical attacks only
• Purpose is to recover plaintext and/or key
• must be able to identify when have plaintext
• Known plaintext
• know (or strongly suspect) some
  plaintext-ciphertext pairs
• use this knowledge in attacking cipher and
  recover key

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Cryptanalytic Attacks Contd..

• Chosen plaintext (differential cryptanalysis)
• can select plaintext and obtain corresponding
  ciphertext more powerful than known plaintext
  attack
• Picks patterns that may reveal info/structure of
  key
• Chosen ciphertext (less probable attack)
• can select ciphertext and obtain corresponding
  plaintext
• Chosen plaintext-ciphertext (Chosen Text)
• can select plaintext and obtain corresponding
  ciphertext, or select ciphertext and obtain
  plaintext

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Cipher Security

• unconditional security
• With all computing power 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 within the
  useful lifetime of the information

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Key Strengths
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Stegnography

• Simply takes one piece of information and hides
  it within another.
• Stenography can also be used to place a hidden
  "trademark" in images, audio, and software, a
  technique referred to as watermarking.
• More
• http//members.tripod.com/steganography/stego/info
  .htm
• http//www.belmont.cc.oh.us/Majors/Steno.html

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Classical Cryptographic Techniques

• Two basic components in classical ciphers
• substitution and transposition
• Substitution ciphers - has letters replaced by
  others
• Monoalphabetic
• Polyalphabetic
• Transposition ciphers - has letters arranged in a
  different order

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Caesar Cipher History

• A Monoalphabetic Substitution Cipher
• 2000 years ago Julius Ceasar used a simple
  substitution cipher, now known as the Caesar
  cipher
• First attested use in military affairs (Gallic
  Wars)
• General Caeser Algorithm
• C E(p) (p k) mod (26)
• p D(C) (C k) mod (26)
• Replace each letter by 3rd letter on, eg.
• e.g. SSUET is cipher as V V X H W

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Ceasar Cipher (contd.)

• More generally can use any shift from 1 to 25
• i.e. replace each letter of message by a letter a
  fixed distance away
• Specify key letter as the letter a plaintext A
  maps to
• e.g. a key letter of F means
• A map A to F, B to G, ... Y to D, Z to E
• i.e. shift letters by 5 places
• Hence have 25 useful ciphers

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Example Caesar Cipher

• Replace each letter of message by a letter a
  fixed distance away
• e.g. use the 3rd letter on
• L FDPH L VDZ L FRQTXHUHG (Cipher)
• i came i saw i conquered (Plain)
• i.e. Mapping in above case is as
• ABCDEFGHIJKLMNOPQRSTUVWXYZ
• DEFGHIJKLMNOPQRSTUVWXYZABC
• Caesar Cipher as
• Encryption Ek i -gt i k mod 26
• Decryption Dk i -gt i - k mod 26

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Cryptanalysis Caesar Cipher

• Exhaustive key search
• Given some ciphertext, just try every shift of
  letters
• LIZHZLVKWRUHSODFHOHWWHUV Original Ciphertext
  KHYGYKUJVQTGRNCEGNGVVGTU Shift 1
  JGXFXJTIUPSFQMBDFMFUUFST Shift 2
  IFWEWISHTOREPLACELETTERS Shift 3
  PlaintextHEVDVHRGSNQDOKZBDKDSSDQR Shift 4
  GDUCUGQFRMPCNJYACJCRRCPQ Shift 5MJAIAMWLXSVITPEGI
  PIXXIVW Shift 25
• Class Room Task
• Break ciphertext "GCUA VQ DTGCM"

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Arbitrary Substitution

• A dramatic increase in the key space is achieved
  by allowing an arbitrary substitution.
• There will be 26! or greater than 4 x 1026
  possible keys.
• The cryptanalysis can be exploited after looking
  at the regularities of the language.
• This approach is referred as Frequency
  Distribution Cryptanalysis.

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Playfair Cipher

• Invented by Sir Charles Wheatstone, in 1854.
• Developed for Telegraph Secrecy
• Based on the 55 matrix of letters constructed
  using a keyword.
• The matrix is constructed by filling in the
  letters of the keyword (minus duplicates).
• Then filling in the remainder of the matrix with
  the remaining letters in alphabetic order.
• More
• http//raphael.math.uic.edu/jeremy/crypt/contrib/
  hong.html
• http//members.magnet.at/wilhelm.m.plotz/Doc/Playf
  air.html
• http//www.math.temple.edu/renault/cryptology/pla
  yfair.html
• http//www.mactech.com/progchallenge/9909Challenge
  .html

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Playfair Rules of Enciphering

• Repeating plaintext letters are separated by a
  filler letter, such as x.
• BALOON as BA LX LO ON
• Plaintext letters that fall in same row of the
  matrix are each replaced by the letter to the
  right.
• AR in arch as RM
• Plaintext letters that fall in same column are
  each replaced by the letter beneath.
• MU in mute as CM
• Otherwise, each plaintext letter is replaced by
  the letter that lies in its corresponding row and
  column.
• SH in shell as PB
• Refer to the matrix given in Text book on page 34.

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Hill Cipher

• Developed by the mathematician Lester Hill in
  1929.
• Implemented in the form of a machine using gears
  and chains like those used with bicycles.
• The fact that it is impractical for hand use,
  while it predates the computer age.
• More
• http//math.vassar.edu/Classes/280/matrixcode.html
  
• http//home.ecn.ab.ca/jsavard/crypto/ro020103.htm
  

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Polyalphabetic Cipher

• An approach to improving security is to use
  multiple cipher alphabets, hence the name
  Polyalphabetic ciphers
• Makes cryptanalysis harder since have more
  alphabets to guess and because flattens frequency
  distribution
• Use a key to select which alphabet is used for
  each letter of the message
• ith letter of key specifies ith alphabet to use
• Use each alphabet in turn
• Repeat from start after end of key is reached

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Polyalphabetic Substitution
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Vigenère Cipher

• Simplest Polyalphabetic substitution cipher is
  the Vigenère Cipher
• 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
• Describe this mathematically as the function
• Encryption is done using
• Eki(a) a -gt a ki (mod 26)
• Decryption is done using
• Dki(a) a -gt a - ki (mod 26)

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Vigenère Cipher Contd..

• Write the plaintext out
• Under it write the keyword in repetition
• Use each key letter in turn as a Caesar cipher
  key
• Encrypt the corresponding plaintext letter
• Example
• Plaintext THISPROCESSCANALSOBEEXPRESSED
• Keyword CIPHERCIPHERCIPHERCIPHERCIPHE
• Plaintext VPXZTIQKTZWTCVPSWFDMTETIGAHLH

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Vernam Cipher

• Introduced by an ATT engineer named Gilbert
  Vernam.
• Uses a keyword that is as long as the plaintext.
• The key has no statistical relationship to the
  plain text.
• This system works on binary data rather than
  letters.
• Mathematical representation
• Pi Ci XOR ki

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Transposition Ciphers

• Referred as classical Transposition or
  Permutation ciphers
• These hide the message by rearranging the letter
  order without altering the actual letters used.
• Scheme uses writing message in a rectangle, row
  by row, and reading the message off, column by
  column, but permute the order of the columns.
• The order of the columns then becomes the key to
  the algorithm.
• The transposition cipher can be made
  significantly more secure by performing more than
  one stage of transposition.

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Rail Fence Cipher

• Write message with letters on alternate rows (of
  depth n).
• Read off cipher row by row
• Plain I A E S W C N U R D C M I A I O Q
  E E
• Cipher IAESW CNURD CMIAI OQEE

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Rail Fence CipherGeometric Figure
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Scytale Cipher

• An early Greek transposition cipher .
• A strip of paper was wound round a staff.
• Message written along staff in rows, then paper
  removed.
• Leaving a strip of seemingly random letters.
• Not very secure as key was width of paper staff.

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Scytale Cipher (contd.)
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Reverse (Mirror) Cipher

• Write the message backwards
• Plain I CAME I SAW I CONQUERED
• Cipher DEREU QNOCI WASIE MACI

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Key Concepts for Transposition

• In a transposition cipher the key idea is,
• Write the message out in columns according to
  some rule
• Read the letters off to form the ciphertext
  according to another rule
• Key used to find order to
• Read off the cipher
• Write in the plaintext, or
• Both

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Row Transposition ciphers

• Group the message and shuffle letters within each
  group.
• More formally write letters across rows.
• Then re-order the columns before reading off the
  rows.
• Always have an equivalent pair of keys (Read off
  vs. Write In)

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Row Transposition ciphers E.g.
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Example 2
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Example 3
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What is a One Time Pad? OTPs

• An improvement to the Vernam Cipher.
• It is the only currently known unconditionally
  secure encryption system.
• Other are cryptographically secure which means
  that they have a cost associated with breaking,
  this cost will be very high, but it would
  theoretically be possible to break if enough
  compute time could be gathered.
• OTPs are provably unconditionally secure.
• Example Statement in C-language
• main(i,c)intcfor(cfopen(c1,"r")(igetchar(
  ))putchar(getc(c)i))

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How Does It Work?

• Basically you have your random OTP, which both
  you and your intended recipient have. You have a
  message M, and you compute the ciphertext C by
  XORing the message with the OTP
• C M XOR OTP
• You send the ciphertext to your recipient, the
  recipient knowing the OTP also can recover the
  message by computing the reverse, XORing the
  ciphertext C with the OTP
• M C XOR OTP
• You must never re-use the OTP, other wise it
  wouldn't be a "One-Time" pad anymore, and it
  would loose it's unbreakable properties as
  information would start to be leaked.

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Rotor Machines

• A rotor is a small disk of insulating material.
• Consist of 26 equally-spaced electrical contacts
  in a circle on each side.
• The contacts on one side are connected to the
  contacts on the other side in a scrambled order.
• Enigma A Unique Rotor Machine
• Enigma Rotor Machine, one of a very important
  class of cipher machines, heavily used during 2nd
  world war,
• Comprised a series of rotor wheels with internal
  cross-connections, providing a substitution using
  a continuously changing alphabet.

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