Computer and Network Security

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Computer and Network Security

• Hashes (Chapter 5)

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Hash

• Also called message digest function or one-way
  function, mapping an arbitrary-length message to
  a fixed-length output (message digest)

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Randomness Requirement

• For an arbitrary change in the input, every bit
  in the output has 50 chance to change (about
  half the bits should differ)
• Computationally impractical to find two messages
  with the same digest
• Computationally impractical to find a message
  with a given message digest

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Digest Length

• If the digest length is n bits long, it takes
  O(2n/2) to find two messages with the same
  digest. (Page 119-120)

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What Hash Can Do

• Authentication
• Integrity (MAC)
• Privacy (Encryption)

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Authentication

• Page 123

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Encryption

• Generate one-time pad as b1, b2, b3,
• b1 MD(KIV),
• b2 MD(Kb1),
• b3 MD(Kb2),
• Then, XOR the message with the one-time pad bit
  sequence.

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Using Secure Key for Hashing
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MD2

• Input arbitrary number of octets
• Output 128-bit message digest
• Step 1 Pad the message to be a multiple of 16
  octets
• Step 2 Append a 16-octet checksum to the message
• Step 3 Process the message, 16 octets at a time,
  to produce the message digest.

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Step 1 Padding
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Step 2 Checksum
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MD2 ? Substitution Table
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Step 3 Produce Message Digest
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MD4, MD5, SHA-1

• Input arbitrary number of bits
• Output 128 bits for MD4 and MD5, 160 bits for
  SHA-1
• Step 1 Pad the message to be a multiple of 512
  bits (16 words, 64 octets)
• Step 2 Process the message, 512 bits at a time,
  to produce the message digest

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Step 1 Padding
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Step 2 Produce Message Digest
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SHA-1 Digest Function
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Problem of keyed hash digest(Key m)

• A problem maker gets m, digest(Key m)
• It first pads m according the used hash function,
  and then adds another message M at the end. The
  result is m pad M.
• digest(Key m pad M) can be calculated from
  digest(Key m pad), which is the intermediate
  digest.

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Solutions

• Use digest(m Key)
• HMAC

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More on Hash

• Exercise 1 variants of
• One encryption after XORing message blocks
• Use constant as key
• Exercise 2 use CBC for hash
• Is it secure?
• Use message blocks as keys

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More on Hash

• Secure Hash Construction from Block Cipher