10-5 notes - Exam Typed page for exam ASSUME o Average case...

Typed page for exam
• ASSUME
o Average case analysis
 (not malicious adversary)
 (Uniformly distributed random inputs)
o Simple uniform hashing
 For any given hash function, if given a key it will uniformly distribute
throughout the table
 The cost (in collisions) of find () in a chained hash table with n keys =
θ(n/m)
• Hash Function Choice
o Output should be uniform on (o…m-1)
o Avoid patters on typical inputs
• Idea #1
o Division Hashing
 H(k) = k mod m
• Diffusion
o Used in Cryptographic Hashing
o One change causes a huge change in output
o Advice
 Use a odd prime number for m
o Need good diffusion so you can protect yourself against stupidity
• Multiplicative hashing
o Let A be a constant, 0<A<1
o H(k) = math.floor(m(KA-int(KA)))
 (KA-int(KA)
• Returns a number between [0…1)
 m(KA-int(KA)
• Returns a number between [0…m)
 math.floor(m(KA-int(KA)))
• returns a int inclusive [0…m-1]
o Ideas:
 “A” should be irrational
 Between (1/2, 1)