Introduction to Cryptography

1

• Introduction to Cryptography

2
Structure of Presentation

• Terminology
• Properties of Messages (sent between the sender
  and receiver)
• Cryptographic Algorithms
• Restricted Cryptographic Algorithms
• Modern Cryptographic Algorithms
• Cryptanalysis

3
Structure of Presentation

• Security of Algorithms
• Complexity of An Attack
• Steganography
• Cipher (Algorithm) Types
• Substitution Ciphers and
• Transposition (Shuffling) Ciphers
• Well-Known Cryptographic Algorithms

4
Terminology

• Sender and Receiver
• A sender who wants to send a message to a
  receiver.
• Messages
• A message plaintext (or cleartext).

5
Terminology

• Encryption
• The process of disguising a message to hide its
  substance (content).
• Ciphertext
• An encrypted message.

6
Terminology

• Decryption
• The process of turning ciphertext back into
  plaintext -- or recovering the plaintext.

Original Plaintext
Plaintext
Ciphertext
Encryption
Decryption
Encryption and Decryption Process
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Terminology

• Cryptography
• The art and science of keeping messages secure.
• Cryptographers
• Persons who apply cryptography.

8
Terminology

• Cryptanalysis
• The art and science of breaking ciphertext.
• Cryptanalysts
• Persons who apply cryptanalysis.

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Terminology

• Cryptology
• A branch of mathematics consisting of both
  cryptography and cryptanalysis.
• Cryptologists
• Persons who apply cryptology.

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Notations

• M plaintext,
• Plaintext can be a stream of bits, a text file, a
  bitmap, a stream of digitised voice, a digital
  video.
• C ciphertext.

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Notations

• E(M) C,
• where E is the encryption function, operating on
  M to produce the ciphertext C.
• D(C) M, (inversion function)
• where D is the decryption function.

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3 Properties of Messages

• Authentication
• The receiver is able to ascertain where the
  message really comes from.
• Integrity
• The receiver is able to verify that the message
  has not been modified or tampered.
• Nonrepudiation
• The sender should not be able to deny that s/he
  does not send this message.

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Cryptographic Algorithms

• Cryptographic algorithms (or ciphers)
• The mathematical function for encryption and
  decryption.
• One is for encryption and the other is for
  decryption.

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Restricted Cryptographic Algorithms (old time)

• Restricted cryptographic algorithms
• Keep the specific way that algorithm works a
  secret. (old time algorithms)
• Disadvantages of restricted algorithms
• If used in a user group and one happens to reveal
  the secret of the algorithm, everyone else must
  change this algorithm.
• No quality control or standardisation. Every
  group must have their own secret algorithm.

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Modern Cryptographic Algorithms (single/symmetric
key)

• Have a key K which can be one of the values in a
  keyspace so the functions are
• E-k (M) C, D-k (C) M

Key K
Original Plaintext
Key K
Plaintext
Ciphertext
Encryption
Decryption
Encryption and Decryption with a Key
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Modern Cryptographic Algorithms (asymmetric keys)

• Have an encryption key K-1 and a decryption key
  K-2 in a keyspace so the functions become
• E-k-1 (M) C, D-k-2 (C) M

Key K-2
Original Plaintext
Key K-1
Plaintext
Ciphertext
Encryption
Decryption
Encryption and Decryption with Two Keys
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Features of Modern Cryptographic Algorithms

• Modern algorithms are based on keys, not the
  confidential details of a specific algorithm.
• The algorithm is thus publishable and analysable.
• The algorithm can be used with mass-produced
  products. (safe enough)
• The algorithm doesnt care whether eavesdroppers
  will know its details and implementation.

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Symmetrical Algorithms

• They are conventional algorithms
• The decryption key is the same as the encryption
  key.
• The symmetrical algorithms are also called
  secret-key, single-key, one-key algorithms.
• The sender and receiver agree on an identical
  key. The key must remain secret.
• E-k (M) C, D-k (C) M

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Symmetrical Algorithms

• There are 2 categories of these algorithms
• Stream algorithms (ciphers)
• Operate on the plaintext in a single bit (or
  byte) at a time - bit by bit.
• Block algorithms (ciphers)
• Operate on the plaintext in groups of bits at a
  time.
• The typical block size is 64 bits.

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Public-Key (PK) Algorithms

• These algorithms are also called asymmetric
  algorithms.
• The encryption and decryption keys are different.

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Public-Key (PK) Algorithms

• They are called so because the encryption key can
  be made public and given to peers and only a
  specific person with its decryption key can
  decrypt the message.
• By these algorithms, the encryption key held by
  peers is often called public key and the
  decryption key is often called private/secret key.

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Digital Signature Use withPK Algorithms

• Sometimes, messages will be encrypted (signed)
  with the private key and decrypted (verified) by
  peers with its public key.

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Cryptanalysis

• The aim of cryptography is to keep the plaintext
  or the key, or both secret from
• eavesdroppers, adversaries, attackers,
  interceptors, interlopers, intruders, opponents,
  or simply enemies.
• Cryptanalysis the science of recovering the
  plaintext without access to (or knowing) the key.
• Successful cryptanalysis may recover both the
  plaintext and key.

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Cryptanalysis Assumption

• Related terms
• An attempted cryptanalysis is called an attack.
• The loss of a key through noncryptanalytic means
  is called a compromise.
• Assumption
• Cryptanalysts have complete details of the
  cryptographic algorithm and its implementation.

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Cryptanalytic Attacks

• Ciphertext-only attack
• Cryptanalysts have access to
• the ciphertext of many messages which have been
  encrypted by the same encryption algorithm.
• Their job is
• to recover the plaintext of those encrypted
  messages and/or
• even deduce the key(s) used to encrypt the
  messages.

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Cryptanalytic Attacks

• Known-plaintext attack (more knowledge)
• Cryptanalysts have access to
• the ciphertext of many messages and
• the plaintext of those messages.
• but dont know the pair of which ciphertext
  belongs to which plaintext.
• Their job is to deduce
• the key(s) used to encrypt those messages.
• an algorithm to decrypt any new encrypted
  messages.

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Cryptanalytic Attacks

• Chosen-plaintext attack (even more knowledge)
• Cryptanalysts have access to
• the ciphertext of many messages and
• the associated plaintext of those messages.
• Thus they know the corresponding pairs of
  ciphertext and plaintext.
• They also have ability/knowledge to select
  specific plaintext blocks to encrypt.
• This is probably to make any fraudulent things on
  messages sent.

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Cryptanalytic Attacks

• Chosen-plaintext attack (even more knowledge)
• Their job is to deduce
• the key(s) used to encrypt those messages and
• an algorithm to decrypt any new encrypted
  messages.

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Cryptanalytic Attacks

• Chosen-ciphertext attack
• Cryptanalysts have access to their decrypted
  plaintexts.
• Thus they know the corresponding pairs of
  ciphertext and plaintext.
• E.g., they have access to the tamperproof box
  that does automatic decryption.
• They can choose different ciphertexts to be
  decrypted (I dont know the rationale in doing
  this).

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Cryptanalytic Attacks

• Chosen-ciphertext attack
• Their job is to deduce
• the keys used to encrypt those messages.

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Cryptanalytic Attacks

• Chosen-key attack
• Cryptanalysts have some knowledge about the
  relationship between different keys.
• This approach is obscure in reason and not very
  practical.

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Cryptanalytic Attacks

• Rubber-hose attack
• Cryptanalysts threaten, blackmail, or torture
  someone until they give him the key.
• Purchase-key attack
• E.g., bribe authorised people to get the key.
• The two are very powerful attacks and often the
  best way to break an algorithm.

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Security of Algorithms

• Different algorithms have different degrees of
  security.
• You are probably safe when
• the cost required to break an algorithm is higher
  than the value of the encrypted data.
• the time required to break an algorithm is longer
  than the time the encrypted data must remain
  secret.
• the amount of data encrypted with a key is less
  than the amount of data necessary to break the
  algorithm.

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Security of Algorithms (ease in breaking an
algorithm)

• Degrees of ease in breaking an algorithm in
  decreasing order.
• 1. Total break (easiest)
• A cryptanalyst finds the key to decrypt the
  message.
• 2. Global deduction (harder to achieve)
• A cryptanalyst finds an alternate algorithm
  equivalent to D-k (C) without knowing the key K.

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Security of Algorithms

• 3. Instance (or local) deduction
• A cryptanalyst finds the plaintext of an
  intercepted ciphertext.
• 4. Information deduction (hardest to achieve)
• A cryptanalyst gains some information about the
  key or plaintext.
• This gained information could be
• a few bits of the key, or
• some information about the form of the plaintext.

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Security of Algorithms

• An algorithm is unconditionally secure.
• If no matter how much ciphertext a cryptanalyst
  has, there is not enough information to recover
  the plaintext.
• Breaking an algorithm may employ a brute-force
  attack
• Try every possible key one by one, and
• Check whether the resulting plaintext is
  meaningful.

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Security of Algorithms

• An algorithm is computationally secure or strong.
• It is computationally infeasible to break it.
• That is, it cant be broken with any available
  resources either now or in the future.

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Complexity of An Attack

• Data complexity
• the amount of data needed as input to an attack.
• Processing (work factor) complexity
• the time needed to perform an attack.
• Storage requirements
• the amount of memory needed to perform an attack.
• Rule of thumb
• the complexity of an attack is taken to be the
  minimum of those three factors.

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Steganography

• This is to hide secret messages in something
  else, e.g., other messages.
• Traditional ways of steganography
• invisible ink,
• a message hidden in a specific page of a book.

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Steganography

• More recent ways (which appear in public domain
  software)
• Hide secret messages in graphic images by
  replacing the least significant bit of each byte
  of the image with the bits of the message.
• Strip those bits out and combine them to form the
  message at the destination.
• The blended image wont change appreciably.

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Cipher Types

• In old times, cryptography is character-based.
• Its fundamental technique to scramble messages is
  either
• substitute characters for one another,
• transpose (shuffle) them with one another, or
• do both. (Many times do either of the two above.)

42
Cipher Types

• Cryptography nowadays works on bits, instead of
  characters but still use substitution and
  transposition to scramble messages.
• However, substitution is far more common than
  transposition.

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Substitution Ciphers

• Each character in the plaintext is substituted
  with another.
• The receiver then inverts the substitution on the
  ciphertext to recover the plaintext.
• There are 4 types of substitution ciphers
• Simple substitution (monoalphabetic) ciphers,
• Homophonic substitution ciphers,
• Polygram substitution ciphers, and
• Polyalphabetic substitution ciphers.

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Simple Substitution

• Simple substitution (monoalphabetic) ciphers
• They are one-to-one and thus easy to break.
• Each character in the plaintext is replaced with
  a character that appears in the ciphertext.

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Homophonic Substitution

• Homophonic substitution ciphers
• They are one-to-many and thus harder to break
  than simple substitution.
• A single character can map to a number of
  characters, e.g.
• A gt 5, 13, 25, 56
• B gt 7, 19, 31, 42

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Polygram Substitution

• Polygram substitution ciphers
• They are harder to break than simple
  substitution.
• Characters are encrypted in groups (blocks),
  e.g.,
• ABA gt RTQ,
• ABB gt SLL.

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Polyalphabetic Substitution

• Polyalphabetic substitution ciphers
• They are harder to break than simple
  substitution.
• They combine a number of simple substitution
  ciphers to produce the ciphertext.

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Simple Substitution Ciphers

• Caesar cipher
• Each character is replaced by
• (the char shifted to the right three positions)
  mod 26.
• A gt D, B gt E, , W gt Z,
• X gt A, Y gt B, Z gt C.
• ROT13
• It is commonly used on UNIX systems.
• Every letter is rotated (shifted) 13 positions.
• A gt N, B gt O, and so on.

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A Polyalphabetic Cypher (One Time Pads)

• A perfect encryption scheme (unbreakable) called
  one-time pad is polyalphabetic.
• A set of truly random key letters, written on a
  pad is created.
• The sender uses each key letter in the pad to
  encrypt exactly one character in the plaintext.
• The pad is used only one time. Any new message
  needed to send implies that a new pad is required.

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One-Time Pads

• The sender and receiver must have the same pad
  (key) and both destroy it when things are done.
  (a symmetric algorithm)
• Example A message
• O N E T I lt plaintext
• Suppose that the key from a pad is
• T B F R G lt pad
• I P K L P lt ciphertext
• This is done by applying (O T) mod 26 I, (N
  B) mod 26 P, (E F) mod 26 K, so on.

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A Polyalphabetic Cypher (XOR)

• Bit XOR operations are
• 0 0 0
• 0 1 1
• 1 0 1
• 1 1 0
• The plaintext is XORed with a keyword (key) to
  generate the ciphertext.
• XORing the ciphertext with the same keyword
  produces the original plaintext.
• This is a symmetric algorithm, i.e., share the
  same key for encryption and decryption.

52
Transposition (Shuffling) Ciphers

• The content of the plaintext remains the same but
  the order of characters in the plaintext is
  shuffled around, e.g.,
• cdef gt dfed,
• artg gt trga.

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Transposition (Shuffling) Ciphers

• Usually these cyphers require more memory than
  substitution to encrypt and decrypt messages.
• A simple columnar transposition cipher is one of
  the kind.
• Example Cleartext computergraphic
• columnar text ciphertext
• c o m p u
• t e r g r gt ctaoepmrhpgiurc
• a p h i c

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Well-Known Cryptographic Algorithms

• DES (Data Encryption Standard) is the most
  popular symmetric algorithm.
• DES is a U.S. and international standard.

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Well-Known Cryptographic Algorithms

• RSA (named for its creator--Rivest, Shamir, and
  Adleman) is the most popular public-key (PK)
  algorithm.
• It is asymmetric and used for both encryption and
  digital signatures.
• DSA (Digital Signature Algorithm, used as part of
  the Digital Signature Standard) is another PK
  algorithm.
• It is asymmetric and used only for digital
  signatures.