Hashers

This crate is a collection of hashing-related functionality, for use with Rust's std::collections::HashMap, HashSet, and so forth.

Additionally, there are benchmarks of the hash functions and a couple of statistical tests for hash quality.

Disclaimer

None of this is cryptographically secure. Attempting to use this for cryptographic purposes is not recommended. I am not a cryptographer; I don't even play one on TV.

Many (most? all?) of these functions are not designed to prevent collision-based denial of service attacks. Rust's default hash function is SipHash (1-3?), which is designed for that. Many of these functions are intended to be used for performance purposes where that form of security is not needed.

What's a Hasher?

A hash function, for our purposes here, is a function that takes as input another, general, value, and returns a number that is ideally unique to that value. This number can be used to store the value in an array and then locate it again later without searching the array; in other words, in O(1) time. More or less: there are a lot of other details. For more information, see Rust's HashMap and various information sources online.

In Rust specifically, std::hash::Hasher is a trait:

pub trait Hasher {
    fn finish(&self) -> u64;
    fn write(&mut self, bytes: &[u8]);

    fn write_u8(&mut self, i: u8) { ... }
    fn write_u16(&mut self, i: u16) { ... }
    ...
}

Hasher has two required methods, finish and write, and default implementations of other useful methods like write_u8 and write_u16, implemented by calling write. In use, an implementation of Hasher is created, data is fed to it using the various write methods, then the result is returned using the finish method to get the hash number out.

Using a custom hash function in Rust

Using a custom hash function with Rust's HashMap or HashSet has long been regarded as a deep mystery. Now, I will strip back the curtains of ignorance and reveal the secrets in all their unholy glory!

Or something like that. It's not really a big deal.

There are two ways to create a HashMap that uses a custom Hasher implementation: setting the hasher on a hash-map instance, and type-level hackery.

Explicitly telling a HashMap what Hasher to use

Everytime a value needs to be hashed, when inserting or querying the HashMap for example, a new Hasher instance is created. (Remember that the only methods in the Hasher trait update its state or return the final value.)

As a result, instead of passing in a Hasher, we have to pass an instance of another trait, std::hash::BuildHash. Rust's standard library currently has two implementations of that trait:

• std::collections::hash_map::RandomState, which creates instances of DefaultHasher, Rust's implementation of SIP-something using cryptographic keys to prevent denial-of-service attacks.
• std::hash::BuildHasherDefault, which can create instances of any Hasher implementation that also implements the Default trait.

All of the Hashers in this collection also implement Default.

use std::collections::HashMap;
use std::hash::BuildHasherDefault;

use hashers::fx_hash::FxHasher;

// BuildHasherDefault also implements Default---it's not really interesting.
let mut map =
  HashMap::with_hasher( BuildHasherDefault::<FxHasher>::default() );

map.insert(1, 2);
assert_eq!(map.get(&1), Some(&2));

Using types to specify what Hasher to use

As an alternative, HashMap has three type-level parameters: the type of keys, the type of values, and a type implementing std::hash::BuildHash. By default, the latter is RandomState, which securely creates DefaultHashers. By replacing RandomState, the Hashers used by the map can be determined by the HashMap's concrete type. std::hash::BuildHasherDefault is useful here, as well.

use std::collections::HashMap;
use std::hash::BuildHasherDefault;

use hashers::fnv::FNV1aHasher64;

// This could be more complicated.
fn gimmie_a_map() -> HashMap<i32,i32,BuildHasherDefault<FNV1aHasher64>> {
    HashMap::default()
}

let mut map = gimmie_a_map();

map.insert(1,2);
assert_eq!(map.get(&1), Some(&2));

A more complicated example is the anagrams-hashmap.rs example program included with this module.

About this crate

This collection of Hashers is based on:

• http://www.cse.yorku.ca/~oz/hash.html Oz's Hash functions. (oz)
• http://www.burtleburtle.net/bob/hash/doobs.html Bob Jenkins' (updated) 1997 Dr. Dobbs article. (jenkins)
• http://burtleburtle.net/bob/hash/spooky.html Jenkin's SpookyHash. (jenkins::spooky_hash)
• Rust's builtin DefaultHasher (SIP 1-3?) (default)
• https://github.com/cbreeden/fxhash A fast, non-secure, hashing algorithm derived from an internal hasher in FireFox. (fx_hash)
• http://www.isthe.com/chongo/tech/comp/fnv/ The Fowler/Noll/Vo hash algorithm. (fnv)
• https://hbfs.wordpress.com/2015/11/17/and-a-good-one-hash-functions-part vi/ Steven Pigeon's Bricolage hash algorithm.
• Two "null" hashers: NullHasher returns 0 for all inputs and PassThroughHasher returns the last 8 bytes of the data.

Each sub-module implements one or more Hashers plus a minimal testing module. As well, the module has a benchmarking module for comparing the Hashers and some example programs using statistical tests to prod the various Hashers.

Example programs

chi2

The chi-squared test is used to determine whether there is a significant difference between the expected frequencies and the observed frequencies in one or more categories. -- Chi-squared test

This program attempts to compute the hash values for one of a number of data sets, then simulates using those values in a 128-bucket hash table (a 2^7 - 1 mask) and tries to determine if the hash buckets are uniformly distributed. I think. I'm not a statistician and apparently not much of a programmer any more. Sorry.

Anyway, it shows what may be the chi2 test of the lower bits of the hash values for a number of samples and for each Hasher. Numbers closer to 0 are better, and between 3.0 and -3.0 are apparently "ok." Maybe.

The samples are:

• 1000 uniformly distributed 6-byte binary values.
• 1000 uniformly distributed 6-byte alphanumeric (ASCII) values.
• 1000 generated identifiers of the form 'annnnn'.
• The words from data/words.txt

kolmogorov-smirnov

The Kolmogorov–Smirnov statistic quantifies a distance between the empirical distribution function of the sample and the cumulative distribution function of the reference distribution. -- Kolmogorov–Smirnov test.

Ok, this one I have a bit more confidence in. It hashes the same samples as the chi2 program, then attempts to determine how far from uniformly distributed the 64-bit hash values are, reporting values between 0.0 and 1.0. Lower values are better. 32-bit hashes like DJB2 trivially fail this test, though, although they may be fine for HashMaps with much less than 2^32 entries.

anagrams-hashmap

This program finds the number of words that can be made from the letters "asdwtribnowplfglewhqagnbe", based on the anagrams dictionary in data/anadict.txt. (There are 7440 of them.) It uses implementations of HashMap and HashSet parameterized by Hashers, and reports the time taken by each hasher as well as a comparison with DefaultHasher.

For more information, check out my ancient series of blog posts:

• https://maniagnosis.crsr.net/2013/02/creating-letterpress-cheating-program.html
• https://maniagnosis.crsr.net/2014/01/letterpress-cheating-in-rust-09.html
• https://maniagnosis.crsr.net/2016/01/letterpress-cheating-in-rust-16-how.html And others.