A hash function is a mathematical algorithm that transforms input data into a fixed-size string of characters, and its properties include determinism, efficiency, and resistance to collisions.

A hash function is a fundamental component of many computer science applications, particularly in the context of data structures like hash tables and cryptographic systems. It is a mathematical algorithm that takes an input (or 'message') and produces a fixed-size string of characters, typically referred to as the hash value or hash code.

One of the key properties of a hash function is determinism, meaning that the same input will always produce the same output. This property is essential for ensuring consistency in data retrieval and storage. Additionally, hash functions are designed to be efficient, allowing for quick computation of the hash value for any given input.

Another crucial property of hash functions is their resistance to collisions. A collision occurs when two different inputs produce the same hash value, which can compromise the integrity of a hash table or cryptographic system. A good hash function minimizes the likelihood of collisions by ensuring a uniform distribution of hash values across the output space.

Other desirable properties of a hash function include pre-image resistance (making it infeasible to reverse-engineer the original input from its hash value) and second pre-image resistance (making it difficult to find a different input that produces the same hash value as a given input).

Understanding hash functions and their properties is vital for developing secure systems, optimizing data retrieval methods, and ensuring data integrity in various applications.