Remember from last Tuesday

1
Remember from last Tuesday

• RSA cryptosystem
• Encryption (Public)

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Remember from last Tuesday

• Alice
• M
• E(M)
• D(E(M))

• The Bank
• M
• E(M)

M D(E(M)) ? M ? D(E(M)) ?
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But what about

• John,
• Please loan Alice 128,370.
• The Bank will guarantee it.
• -The Bank

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Digesting the message

• Alice
• M
• E(Digest(M))
• D(E(Digest(M)))

• The Bank
• M
• Digest(M)
• E(Digest(M))

Digest(M) D(E(Digest(M))) ? Digest(M) ?
D(E(Digest(M))) ?
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Hash Functions
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What is hash?

• hash
• \hash\
• transitive verb
• from French hacher, from Old French hachier, from
  hache battle-ax, of Germanic origin
• ca. 1590
• 1a to chop (as meat and potatoes) into small
  pieces
• 1b confuse, muddle
• 2 to talk about  review often used with over
  or out

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What is hash?

• hash
• noun
• ca 1663
• 1 chopped food specifically  chopped meat
  mixed with potatoes and browned
• 2 a restatement of something that is already
  known
• 3a hodgepodge, jumble
• 3b a confused muddle project

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What is hash?

• Hans Peter Luhn of IBM appears to have been the
  first to use the concept
• memo dated January 1953
• Robert Morris
• survey paper in CACM (Commuication of the
  Association for Computing Machinery) (1968?)
• elevated the term from technical jargon to formal
  terminology.
• SHA-1 (a type of hash function)
• domain is "flattened" and "chopped" into "words"
  which are then "mixed"

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What is hash?

• Mathworld
• A hash function projects a value from a set with
  many (or even an infinite number of) members to a
  value from a set with a fixed number of (fewer)
  members.
• Hash functions are not reversible.
• Wikipedia
• Any well-defined procedure or mathematical
  function for turning some kind of data into a
  relatively small integer.
• A fingerprint of a larger object

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Examples of Hash Functions

• MD5 (Message-Digest algorithm 5)
• SHA-1 (Secure Hash Algorithm-1)

http//scriptserver.mainframe8.com/md5.php
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Properties of CryptographicHash Functions

• Preimage Resistant
• Difficult to find message m given H(m)y
• Random but still Deterministic
• Second Preimage Resistant
• Weak-collision Resistant
• Given m, difficult to find n s.t. H(m)H(n)
• Collision Resistant
• Stong-collision Resistant
• Difficult to find m and n s.t. H(m)H(n)
• Birthday Attack

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Collisions in MD5

• A 128-bit hash can have 3.4 x 1038 possible
  values
• 340,282,366,920,938,463,463,374,607,431,768,211,45
  6
• Guessing a collision in MD5 is less likely than a
  million people correctly guess all the California
  Lottery numbers every day for a billion trillion
  years.

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Hash Tables

• Assigns memory locations
• Speeds searches
• Ex Social Security Numbers
• Must choose m intelligently
• Good distribution
• Minimal collisions

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Ex Social Security Numbers

• Choices for m
• Powers of 10
• relies on last several digits
• A number dividing
• same digits rearranged leads to collision
• Prime which approximates number of memory
  locations
• 5000 memory locations m4969

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Ex Social Security Numbers

• Collision Resolution Option 1
• Link memory locations together and search within
  in bucket
• Collision Resolution Option 2
• If occupied, define a set of new functions H1,
  H2, H3, to find a new memory location

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Ex Social Security Numbers

• All memory locations checked
• Leads to clustering
• Double Hashing
• , where m-2 is
  also prime

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Ex Social Security Numbers
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Other uses of hash functions

• Storing passwords
• File integrity
• Duplicates
• Near duplicates
• Geometric hashing
• Audio identification

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Hash Function in the News

• MD5
• Replaced MD4 in 1991
• Flaw found in 1996
• SHA-1 suggested (160 bit vs 128 bit)
• Flaw found in 2004 (also found in SHA-1)
• Collision algorithm found in 2007

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SHA-3?

• In 2007 the National Institute of Standards
  and Technology announced a contest to design a
  hash function which will be given the name SHA-3
  and be the subject of a Federal Information
  Processing Standard.

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