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Hash Functions

We often want a succinct representation of some data with the expectation that we are referring to the same data.

A "fingerprint".

Hash functions can play this role by converting input data of any size into a fixed-size string of characters.

blake2_256("Hello, World!") = 0x511bc81dde11180838c562c82bb35f3223f46061ebde4a955c27b3f489cf1e03

The input to a hash function is sometimes referred to as a "pre-image".

This output is commonly referred to as the "hash", "digest", "checksum", or "fingerprint".

These functions are widely used for various purposes, including:

  • data integrity verification
  • password storage
  • digital signatures
  • and more!

Key Properties of Hash Functions

When designing and choosing a hash function, we look for the following properties:

  • Can accept unbounded size input.
  • Always maps to a bounded, fixed-size output.
  • Is fast to compute.

Cryptographic Hash Functions

There is a subset of hash functions which are called "cryptographic hash functions", which have emphasis on these additional properties:

  • Is irreversible, i.e. computable only in one direction
  • Pre-image resistance
    • Given a hash value h, it should be difficult to find any message m such that h = hash(m).
    • This concept is related to that of a one-way function. Functions that lack this property are vulnerable to pre-image attacks.
  • Second pre-image resistance (attacker controls one input)
    • Given an input m1, it should be difficult to find a different input m2 such that hash(m1) = hash(m2).
    • This property is sometimes referred to as weak collision resistance. Functions that lack this property are vulnerable to second-preimage attacks.
  • Collision resistance (attacker controls both inputs)
    • It should be difficult to find two different messages m1 and m2 such that hash(m1) = hash(m2).
      • Such a pair is called a cryptographic hash collision.
    • This property is sometimes referred to as strong collision resistance. It requires a hash value at least twice as long as that required for pre-image resistance; otherwise collisions may be found by a birthday attack.

An example of a cryptographic hash function is Blake2_256, which takes a binary input of an arbitrary size and outputs 256 bits.

Learn more at: https://en.wikipedia.org/wiki/Cryptographic_hash_function

Non-Cryptographic Hash Functions

Non-cryptographic hash functions provide weaker guarantees in exchange for performance. They are OK to use in specific scenarios and when you know that the input is not malicious.

An example of a non-cryptographic hash function is XXHash. Note the performance increase for XXHash over Blake2:

Hash Name Width Bandwidth (GB/s) Small Data Velocity Quality Comment
XXH64 64 19.4 GB/s 71.0 10
Blake2 256 1.1 GB/s 5.1 10 Cryptographic

From: https://github.com/Cyan4973/xxHash#benchmarks

Scale of Hashes

Hash functions can vary in output size, but for the purposes of this illustration let's assume we are working with a cryptographic 256-bit hash like Blake2_256.

There are 2^256 possible unique hashes, which is around 10^77.

The number of atoms in the universe is estimated to be around 10^80 to 10^85.

As you can see, this immense scale allows hash functions to have the key properties listed above which make them secure to use in modern cryptography.

Hash Functions on Blockchains

Hash functions, like all software, is a constantly evolving space. Different blockchains use different hash functions based on the time they were developed and the properties they were after.

  • Bitcoin: SHA2-256 & RIPMD-160
  • Ethereum: Keccak-256 (though others supported via EVM)
  • Polkadot: Blake2 & xxHash (though others supported via host functions)

Practical Uses

Hash functions are being used all around you and in nearly all parts of the internet. Here are just a few examples of how they are being used.

Hash File

  1. Data Integrity:

    Hash functions are employed to verify the integrity of data. By comparing the hash value of the original data with the hash value calculated after data transfer, users can detect any changes or corruption.

  2. Password Storage:

    Hash functions secure passwords by storing only their hash values. During authentication, the system compares the stored hash with the hash of the entered password, eliminating the need to store actual passwords.

  3. Digital Signatures:

    In digital signatures, hash functions play a role in creating a unique identifier for a piece of data. The hash value is then encrypted with a private key to generate the digital signature.

Examples

You can find examples to play with hash functions here:

https://www.shawntabrizi.com/substrate-js-utilities/

  • Blake2 a String
  • XXHash a String

Another great resource is:

https://andersbrownworth.com/blockchain/