Cryptographic hash functions are foundational to the construction of practical cryptographic systems. A hash function transforms input data of arbitrary length into a fixed-length message digest that is easy to compute but impossible to invert. Once a digest is produced, recovering the original message is computationally infeasible. Hash functions are widely used in cryptographic applications, including verifying data integrity, authenticating messages, generating deterministic randomness, and deriving keys for secure communication protocols.

This article provides a detailed design of the FIPS 202 standard. I'll begin by explaining the sponge construction and its security properties, then examine how SHA-3 achieves diffusion and irreversibility through its internal permutation. Along the way, I'll clarify which components of the design are reversible in isolation and why the overall construction remains a one-way function. Finally, the SHA-3 and SHAKE design will highlight that they are particularly well-suited for modern cryptographic systems, including post-quantum cryptography.