The current study's objectives are to analyze a broad overview of hash function applications in cryptography and investigate the connections between digital signature applications and cryptographic hash functions. Applications of the hash function are widespread and used for a variety of purposes, including password hashing, file integrity verification, key derivation, time stamping, rootkit detection, and digital signatures. Cryptographic hash functions are a crucial tool used in many sections of data security. A digital signature is a code that is electronically associated with a document and includes the sender's information. As a result, the usefulness of the digital signature in validating digital messages or documents is great. Without mathematics, there would be no cryptographic hash functions. Mathematics is credited with computer science's success, or, to put it another way, it is because of mathematical science that computer science is understood and can be explained to everyone. The study's main goals are to explain hash functions to the reader, as well as some of their uses, including digital signatures, and to provide detailed examples of some hash functions and their creation. Keywords: Hash Function, Cryptography, Digital Stamping