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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 ...
Perfect hash function. In computer science, a perfect hash function h for a set S is a hash function that maps distinct elements in S to a set of m integers, with no collisions. In mathematical terms, it is an injective function. Perfect hash functions may be used to implement a lookup table with constant worst-case access time.
Alice chooses a secret integer a = 4, then sends Bob A = g a mod p. A = 5 4 mod 23 = 4 (in this example both A and a have the same value 4, but this is usually not the case) Bob chooses a secret integer b = 3, then sends Alice B = g b mod p. B = 5 3 mod 23 = 10; Alice computes s = B a mod p. s = 10 4 mod 23 = 18; Bob computes s = A b mod p. s ...
Formally, a message authentication code (MAC) system is a triple of efficient [4] algorithms (G, S, V) satisfying: G (key-generator) gives the key k on input 1 n, where n is the security parameter. S (signing) outputs a tag t on the key k and the input string x. V (verifying) outputs accepted or rejected on inputs: the key k, the string x and ...
A standard technique is to use a modulo function on the key, by selecting a divisor M which is a prime number close to the table size, so h(K) ≡ K (mod M). The table size is usually a power of 2. This gives a distribution from {0, M − 1}. This gives good results over a large number of key sets.
Modular exponentiation can be performed with a negative exponent e by finding the modular multiplicative inverse d of b modulo m using the extended Euclidean algorithm. That is: c = be mod m = d−e mod m, where e < 0 and b ⋅ d ≡ 1 (mod m). Modular exponentiation is efficient to compute, even for very large integers.
Extendible hashing. Extendible hashing is a type of hash system which treats a hash as a bit string and uses a trie for bucket lookup. [1] Because of the hierarchical nature of the system, re-hashing is an incremental operation (done one bucket at a time, as needed). This means that time-sensitive applications are less affected by table growth ...
Bloom filter used to speed up answers in a key-value storage system. Values are stored on a disk which has slow access times. Bloom filter decisions are much faster. However some unnecessary disk accesses are made when the filter reports a positive (in order to weed out the false positives).