Hash function and Data Integrity

1
Hash function and Data Integrity

• Data integrity data are intact during the period
  of storage or transmission
• Two possibilities of losing data integrity
• error occurs during transmission
• modified by attacker during storage or
  transmission
• Solutions to them
• error detection/correction, such as CRC (Cyclic
  Redundancy Code) in every IP packet.
• Hash function, Message digest, or Message
  authentication code (MAC).

2
Hash functions

• A mapping h 0,1 ? 0,1n
• Message m, hash value h(m) (message digest)
• Store m in insecure place, but h(m) in safe place
• Transmission
• Send m along with h(m) (in an insecure channel)
• Send m in insecure manner, h(m) in secure manner
  (e.g., encrypt the h(m)).
• Keyed hashed function, called MAC.
• As discussed before, hash value can be used for
  signature

3
Requirements for hash function

• It must be difficult to solve the following three
  problems, (Page 119)
• Problem 4.1
• Problem 4.2
• Problem 4.3
• Birthday attack (birthday paradox)

4
Typical hash functions

• MD4, MD5
• SHA (Secure Hash Algorithm), page 135

5
Message Authentication Code (MAC)

• Since hash function is public, unkeyed hash value
  is not secure
• Combine secret key information into hash
  function, called MAC.
• Two ways
• Incorporate a secret key into unkeyed hash
  function
• Add the key at the beginning of message
  (problem?)
• Add the key to the end.
• Keyed hash function
• E.g., CBC-MAC (DES CBC mode)

6
PGM cryptosystem

• Symmetric group
• Permutation group
• Logarithmic signature of permutation group
• Tame and supertame
• PGM encryption decryption
• Example
• PGM public key cryptosystem ?