> For the complete documentation index, see [llms.txt](https://satoshichain.gitbook.io/satoshi-chain/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://satoshichain.gitbook.io/satoshi-chain/background/3.1-cryptographic-hash-functions.md).

# 3.1 Cryptographic Hash Functions

An essential tool in blockchain technology is the cryptographic function that ensures transaction integrity and immutability. The hash function is the mathematical algorithm that produces a fixed size numerical output (called fingerprint or digest) consisting of input data. More specifically, a hash function can be denoted as: \
\
`H:{0,1}*→ {0,1}ᵏ` \
\
A hash function takes on the input of any size and produces a fixed k length output. In addition, it must satisfy the following properties: \
● It is easy to compute H regardless of input data size. \
● Given any h, it is computationally infeasible to find an input x such that H(x) = h. \
● Given any x, it is also computationally infeasible to find y such that H(y) = H(x) and x≠ y. \
● It is computationally infeasible to find any (x, y) such that H(x) = H(y) and x≠ y. 

{% hint style="info" %}
SHA-256 and Keccak-256 are widely used in several blockchains, and they produce a hash (output) of 256 bits in size.
{% endhint %}


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