> For the complete documentation index, see [llms.txt](https://battlezips.gitbook.io/battlezips/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://battlezips.gitbook.io/battlezips/theory/primitives/hash-functions.md).
# Hash Functions
A background and overview and background on various hash functions related to and imperative to zero knowledge cryptography
## What are hash functions?
Hash functions are functions that take in a an arbitrary input, often called a pre-image, and output a variable or fixed length string called a digest. They are often referred to as one way functions because while it is trivial to convert the pre-image to the digest it is computationally infeasible to reverse this process. This makes hashing functions ideal for data verification and storing sensitive data like passwords in a secure manner. Hash functions play an imperative role in zero knowledge cryptography
Pre-image (top) is converted to digest (bottom)
## SHA-3 / Keccak-256
Secure hashing algorithm 3 (SHA-3) is a versatile function used for many cryptographic tools like digital signatures, MAC codes, and key derivation functions. SHA-3 is a subset of a cryptographic family called keccak. The Ethereum blockchain uses keccak-256 where the 256 bits stands for a 256 bit digest. While versatile this family of hasing functions falls short of the requirements necessary for SNARK applications. For zero knowledge cryptography entire new functions had to be implemented.
## MiMC / MiMC Sponge
MiMC is a block cipher and hash function that came into existence in 2016. It was the first widely popular ZK friendly hashing function. It was inspired by a precursor called [LowMC](https://eprint.iacr.org/2016/687.pdf). Providing low multiplicative complexity, it is SNARK friendly and enables quick and efficient proving time. Many of the popular ZK libraries out there come with existing implementations of MiMC like [gnark](https://github.com/ConsenSys/gnark) and circom. The original MiMC implementation has inspired many attempted improvements like [GMiMC](https://eprint.iacr.org/2019/1107.pdf) as well as spawning a new type of ZK friendly hashing function called Poseidon.
## Poseidon
Poseidon is a low multiplicative complexity hash function that is based on a design strategy called Hades. It applies rounds on non-linear transformations to the input and rounds applying transformations to part of the input. The end result is decreased symmetry between the pre-image and digest to ensure it is exceedingly difficult to calculate. It is advantageous over MiMC by allowing for variable length hashes.
## Pedersen Commitments
Commitments play a key role in zero knowledge cryptography. Commitments allow a user to choose a certain value to apply to a problem. While the value is known to them, it is not known to anyone else until the committee chooses to reveal a value. The value is chosen in a "commit phase" and then verified when made transparent in the aptly named reveal phase.
