In cryptography and cybersecurity, hash functions are indispensable for encrypting data, preserving data integrity, and verifying digital signatures. Employed within hash tables, these functions efficiently map data from arbitrary sizes to fixed sizes, crucial for various security applications. This paper delves into the essential characteristics that hash functions must exhibit: pre-image resistance, to ensure that the original data cannot be derived from the hash value; collision resistance, to avoid different inputs producing identical outputs; and bit sensitivity, where minor changes in input significantly alter the output. Predominantly built on the Merkle-Damgard construction, current implementations include Message Digest (MD) algorithms and Secure Hash Algorithms (SHA). Despite the advancements, this paper identifies persistent challenges in attaining the pinnacle of security and efficiency, underscoring the need for ongoing research and development in cryptographic hash functions.
