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John Smith and Sandra Dee share the same hash value of 02, causing a hash collision. In computer science, a hash collision or hash clash [1] is when two distinct pieces of data in a hash table share the same hash value. The hash value in this case is derived from a hash function which takes a data input and returns a fixed length of bits. [2]
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 ...
In words, when given an x, it is not possible to find another x' such that the hashing function would create a collision. A hash function has strong collision resistance when, given a hashing function H, no arbitrary x and x' can be found where H(x)=H(x'). In words, no two x's can be found where the hashing function would create a collision.
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 ...
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} .
Real-world applications for the birthday problem include a cryptographic attack called the birthday attack, which uses this probabilistic model to reduce the complexity of finding a collision for a hash function, as well as calculating the approximate risk of a hash collision existing within the hashes of a given size of population.
Linear probing is a component of open addressing schemes for using a hash table to solve the dictionary problem.In the dictionary problem, a data structure should maintain a collection of key–value pairs subject to operations that insert or delete pairs from the collection or that search for the value associated with a given key.