A hashing algorithm is a function

H: D → V

where D is a discrete data set and V is a discrete set of hash values. H has the properties that it is sensitive to small variations in D and uniformally distributes D in V. Usually the number of points in D is greater than the number of points in V but within several orders of magnitude.

Hashing algorithms are used for in error checking over a noisy communication channel. In this case, the sender sends the hashing function and computed hash value with the data. The recipient then uses the hash function on the data and compares it with the sent hash value. When a hashing algorithm is used in this context the hash value is also called a CheckSum.

Hashing algorithms are used in search algorithms. Large data sets can be factored by computing and storing the hash values of each record. Then to dermine if the data set contains a particular record, one only needs to only check the collection of records that have the same hash value as the hash value of one in question.