0.8 Hashing  (Page 12/13)

Hash functions that are truly random with uniform output (including most cryptographic hash functions) are good in that, on average, only one or two probes will be needed (depending on the load factor). Perhaps as important is that excessive collision rates with random hash functions are highly improbable—if not computationally infeasible for an adversary. However, a small, predictable number of collisions are virtually inevitable.

In many cases, a heuristic hash function can yield many fewer collisions than a random hash function. Heuristic functions take advantage of regularities in likely sets of keys. For example, one could design a heuristic hash function such that file names such as FILE0000.CHK, FILE0001.CHK, FILE0002.CHK, etc. map to successive indices of the table, meaning that such sequences will not collide. Beating a random hash function on "good" sets of keys usually means performing much worse on "bad" sets of keys, which can arise naturally—not just through attacks. Bad performance of a hash table's hash function means that lookup can degrade to a costly linear search.

Aside from minimizing collisions, the hash function for a hash table should also be fast relative to the cost of retrieving a record in the table, as the goal of minimizing collisions is minimizing the time needed to retrieve a desired record. Consequently, the optimal balance of performance characteristics depends on the application.

Error correction

Using a hash function to detect errors in transmission is straightforward. The hash function is computed for the data at the sender, and the value of this hash is sent with the data. The hash function is performed again at the receiving end, and if the hash values do not match, an error has occurred at some point during the transmission. This is called a redundancy check.

For error correction, a distribution of likely perturbations is assumed at least approximately. Perturbations to a string are then classified into large (improbable) and small (probable) errors. The second criterion is then restated so that if we are given H(x) and x+s, then we can compute x efficiently if s is small. Such hash functions are known as error correction codes. Important sub-class of these correction codes are cyclic redundancy checks and Reed-Solomon codes.

Audio identification

For audio identification such as finding out whether an MP3 file matches one of a list of known items, one could use a conventional hash function such as MD5, but this would be very sensitive to highly likely perturbations such as time-shifting, CD read errors, different compression algorithms or implementations or changes in volume. Using something like MD5 is useful as a first pass to find exactly identical files, but another more advanced algorithm is required to find all items that would nonetheless be interpreted as identical to a human listener. Though they are not common, hashing algorithms do exist that are robust to these minor differences. Most of the algorithms available are not extremely robust, but some are so robust that they can identify music played on loud-speakers in a noisy room. One example of this in practical use is the service Shazam. Customers call a number and place their telephone near a speaker. The service then analyses the music, and compares it to known hash values in its database. The name of the music is sent to the user. An open source alternative to this service is MusicBrainz which creates a fingerprint for an audio file and matches it to its online community driven database.