Compute message digest of data of any size
Fixed length output:128-512 bits
Easy to compute H(m)
Given H(m), no easy way to find m
One-way function
Given m1, it is computationally infeasible to find m2 = m1 s.t. H(m2) = H(m1)
weak collision resistant
Computionally infeasible to find m1=m2 s.t. H(m1)=h(m2)
strong collision resistant
Requirements for a practical application of a hash function
The one way property
Hash functions are unique to each message
Sender: Message with encrypted hash code
-> generate an un-encrypted hash code
-> create an alternate message
-> Receiver: Forged message with encrypted hash code
Hash Function Weaknesses
-> Pigeonhole principle
-> The Birthday Paradox
n = numbers of pigeons
m = number of holes
n = m There is one pigeon per hole
n > m Then at least one hole must have more than one pigeon
