Which function maps data of arbitrary size to a fixed-size value?

The function that maps data of arbitrary size to a fixed-size value is the hash function. Hash functions take input data, regardless of its length, and produce a fixed-length string or number, known as a hash value or digest. This characteristic is essential in various applications like data integrity verification, digital signatures, and password storage.

Hash functions can efficiently produce the same output for identical inputs, which allows for quick comparison of data without needing to inspect the entire dataset. Additionally, the fixed-size output simplifies storage and comparison processes. The collision resistance property of many hash functions—meaning it is difficult to find two different inputs that produce the same hash value—adds a layer of security, making them valuable in cryptography and data integrity checks.

In contrast, encryption transforms data into a format that is unreadable without a decryption key, focusing on confidentiality rather than fixed-size outputs. Checksums serve to quickly detect errors in data transmissions by producing a simple numeric representation of data but are not necessarily secure or cryptographically strong. Key derivation functions are specialized for generating keys from password inputs and typically output keys of certain sizes based on security needs rather than hashing arbitrary data sizes.