VIII' MESSAGE AUTHENTICATION AND HASH FUNCTIONS

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VIII. MESSAGE AUTHENTICATION AND HASH FUNCTIONS

• Introdution to the requirements for
  authentication and digital signature and the
  types of attacks to be countered. Then the basic
  approaches are surveyed.

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1.AUTHENTICATION REQUIREMENTS

• Disclosure Release of message contents to any
  person or process not possessing the appropriate
  cryptographic key.
• Traffic analysis Discovery of the pattern of
  traffic between parties.
• Masquerade Insertion of message into the
  network from a fraudulent source.
• Content modification Changes to the contents of
  a message, including insertion, deletion,
  transposition, and modification.

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1.AUTHENTICATION REQUIREMENTS

• Sequence modification Any modification to a
  sequence of messages between parties, including
  insertion, deletion, and reordering.
• Timing modification Delay or replay of
  messages.
• Repudiation Denial of receipt of message by
  destination or denial of transmission of message
  by source.

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2.AUTHENTICATION FUNCTIONS

• Authentication functions may be grouped into
  three classes
• Message encryption The ciphertext of the entire
  message serves as its authenticator.
• Message authentication code (MAC) A public
  function of the message and a secret key that
  produces a fixed-length value that serves as the
  authenticator.
• Hash function A public function that maps a
  message of any length into a fixed-length hash
  value, which serves as the authenticator.

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2.AUTHENTICATION FUNCTIONS

• Message Encryption
• Message encryption by itself can provide a
  measure of authentication.

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2.AUTHENTICATION FUNCTIONS
Source
Destination
M
M
E
D
(c) Public-key encryption authentication and
signature
M
M
E
D
D
E
(d) Public-key encryption confidentiality,
authentication and signature
Basic Uses of Message Encryption
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2.AUTHENTICATION FUNCTIONS

• Message Authentication Code
• generated a small fixed-size block of data by use
  of a secret key

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2.AUTHENTICATION FUNCTIONS
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2.AUTHENTICATION FUNCTIONS

• Hash function
• accepts a variable-size message M as input and
  produces a fixed-size hash code H(M)
• The hash code is a function of all the bits of
  the message and provides an error-detection
  capability

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2.AUTHENTICATION FUNCTIONS
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2.AUTHENTICATION FUNCTIONS
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2.AUTHENTICATION FUNCTIONS
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3.MESSAGE AUTHENTICATION CODES

• Requirements for MACs
• If an opponent observers M and Ck(M), it should
  be computationally infeasible for the opponent to
  construct a message M such that Ck(M) Ck(M)
• Ck(M) should be uniformly distributed In the
  sense that for randomly chosen messages, M and
  M, the probability that Ck(M) Ck(M) is 2-n,
  where n is the number of bits in the MAC.
• Let M be equal to some known transformation on
  M. That is M f(M). For example, f may involve
  inverting one or more specific bits.In that case,
  PrCk(M) Ck(M) 2-n.

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3.MESSAGE AUTHENTICATION CODES

• Message Authentication Code Based on DES
• ANSI Standard X9.17 MAC

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4.HASH FUNCTIONS

• Requirement for a Hash Function
• H can be applied to a block data of any size.
• H produces a fixed-length output.
• H(x) is relatively easy to compute for any given
  x, making both hardware and software
  implementations practical.
• For any given code h, it is computationally
  infeasible to find x such that H(x) h. (one-way
  property)
• For any given block x, it is infeasible to find y
  ? x with H(y) H(x). (weak collision resistance)
• It is infeasible to find any pair (x, y) such
  that H(x) H(y). (strong collision resistance)

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4.HASH FUNCTIONS

• Simple Hash Function
• Ci Ith bit of the hash code, 1lt I ltn
• m number of n-bit blocks in the input
• bij ith bit in jth block
• XOR operation

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4.HASH FUNCTIONS

• Birthday Attacks
• Message M
• Find an M such that H(M) H(M)
• On average, the opponent would have to try about
  263 message to find one that matches the hash
  code of the intercepted message
• By the birthday paradox, the level of effort
  required is only on the order of 232

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4.HASH FUNCTIONS

• Block Chaining Techniques
• Based on using a cipher block chaining technique
  without secrete key
• Meet in the middle attack

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5.SECURITY OF HASH FUNCTIONS AND MACS

• Brute-Force Attacks
• Hash Function
• One Way -gt 2n
• Weak collision resistance -gt 2n
• Strong collision resistance -gt2n/2
• Message Authentication Codes
• Min(2k, 2n)
• k key length
• n MAC length

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5.SECURITY OF HASH FUNCTIONS AND MACS

• Cryptanalysis
• An ideal hash of MAC algorithm require a
  cryptanalytic effort greater than or equal to the
  brute-force effort.
• Hash Functions
• Focuses on the internal structure of f
• Based on attempts to find efficient techniques
  for producing collisions for a single execution
  of f
• Message Authentication Codes
• Difficult to generalize