### More Examples

### Definition(s) from the Web

- A hash algorithm turns an arbitrarily-large amount of data into a fixed-length hash. The same hash will always result from the same data, but modifying the data by even one bit will completely change the hash. Like all computer data, hashes are large numbers, and are usually written as hexadecimal. Bitcoin uses the SHA-256 hash algorithm to generate verifiably “random” numbers in a way that requires a predictable amount of CPU effort. Generating a SHA-256 hash with a value less than the current target solves a block and wins you some coins. Source
- A Hash or also called hash function is any algorithm that maps data of arbitrary length to data of a fixed length. The values returned by a hash function are called hash values, hash codes, hash sums, checksums or simply hashes. Recent development of internet payment networks and digital money, such as Bitcoin, also uses a form of ‘hashing’ for checksums, and has brought additional attention to the term. Source
- A hash function is any function that can be used to map data of arbitrary size to fixed-size values. The values returned by a hash function are called hash values, hash codes, digests, or simply hashes. The values are usually used to index a fixed-size table called a hash table. Use of a hash function to index a hash table is called hashing or scatter storage addressing.

Hash functions and their associated hash tables are used in data storage and retrieval applications to access data in a small and nearly constant time per retrieval, and require an amount of storage space only fractionally greater than the total space required for the data or records themselves. Hashing is a computationally and storage space efficient form of data access which avoids the non-linear access time of ordered and unordered lists and structured trees, and the often exponential storage requirements of direct access of state spaces of large or variable-length keys.

Use of hash functions relies on statistical properties of key and function interaction: worst case behavior is intolerably bad with a vanishingly small probability, and average case behavior can be nearly optimal (minimal collisions).

Hash functions are related to (and often confused with) checksums, check digits, fingerprints, lossy compression, randomization functions, error-correcting codes, and ciphers. Although the concepts overlap to some extent, each one has its own uses and requirements and is designed and optimized differently. The hash functions differ from the concepts numbered mainly in terms of data integrity. Source