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In hash tables, since hash collisions are inevitable, hash tables have mechanisms of dealing with them, known as collision resolutions. Two of the most common strategies are open addressing and separate chaining. The cache-conscious collision resolution is another strategy that has been discussed in the past for string hash tables.
This is exploited by birthday attacks on cryptographic hash functions and is the reason why a small number of collisions in a hash table are, for all practical purposes, inevitable. The theory behind the birthday problem was used by Zoe Schnabel [ 18 ] under the name of capture-recapture statistics to estimate the size of fish population in lakes.
This is exactly the probability of collision we would expect if the hash function assigned truly random hash codes to every key. Sometimes, the definition is relaxed by a constant factor, only requiring collision probability O ( 1 / m ) {\displaystyle O(1/m)} rather than ≤ 1 / m {\displaystyle \leq 1/m} .
A hash function is used to map each key into the cell of T where that key should be stored, typically scrambling the keys so that keys with similar values are not placed near each other in the table. A hash collision occurs when the hash function maps a key into a cell that is already occupied by a different key. Linear probing is a strategy ...
A birthday attack is a bruteforce collision attack that exploits the mathematics behind the birthday problem in probability theory. This attack can be used to abuse communication between two or more parties. The attack depends on the higher likelihood of collisions found between random attack attempts and a fixed degree of permutations ...
A hash of n bits can be broken in 2 n/2 time steps (evaluations of the hash function). Mathematically stated, a collision attack finds two different messages m1 and m2, such that hash(m1) = hash(m2). In a classical collision attack, the attacker has no control over the content of either message, but they are arbitrarily chosen by the algorithm.
A universal hashing scheme is a randomized algorithm that selects a hash function h among a family of such functions, in such a way that the probability of a collision of any two distinct keys is 1/m, where m is the number of distinct hash values desired—independently of the two keys. Universal hashing ensures (in a probabilistic sense) that ...
With SUHA however, we can state that because of an assumed uniform hashing, each element has an equal probability of mapping to a slot. Since no particular slot should be favored over another, the 30 elements should hash into the 10 slots uniformly. This will produce a hash table with, on average, 10 chains each of length 3