Which hashing algorithm is best for uniqueness and speed? Example (good) uses include hash dictionaries.

I know there are things like SHA-256 and such, but these algorithms are designed to be secure, which usually means they are slower than algorithms that are less unique. I want a hash algorithm designed to be fast, yet remain fairly unique to avoid collisions.

  • 9
    For what purpose, security or other? – Orbling Feb 19 '11 at 0:05
  • 16
    @Orbling, for implementation of a hash dictionary. So collisions should be kept to a minimal, but it has no security purpose at all. – Earlz Feb 19 '11 at 0:06
  • 4
    Note that you will need to expect at least some collisions in your hash table, otherwise the table will need to be enormous to be able to handle even a relatively small number of keys... – Dean Harding Feb 19 '11 at 1:14
  • 17
    Great post! Could you also check's Yann Collet's xxHash (creator or LZ4), which is twice as fast as Murmur? Homepage: code.google.com/p/xxhash More info: fastcompression.blogspot.fr/2012/04/… – user55191 May 29 '12 at 12:35
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    @zvrba Depends on the algorithm. bcrypt is designed to be slow. – Izkata Oct 31 '13 at 19:20

11 Answers 11

up vote 2285 down vote accepted
+300

I tested some different algorithms, measuring speed and number of collisions.

I used three different key sets:

For each corpus, the number of collisions and the average time spent hashing was recorded.

I tested:

Results

Each result contains the average hash time, and the number of collisions

Hash           Lowercase      Random UUID  Numbers
=============  =============  ===========  ==============
Murmur            145 ns      259 ns          92 ns
                    6 collis    5 collis       0 collis
FNV-1a            152 ns      504 ns          86 ns
                    4 collis    4 collis       0 collis
FNV-1             184 ns      730 ns          92 ns
                    1 collis    5 collis       0 collis▪
DBJ2a             158 ns      443 ns          91 ns
                    5 collis    6 collis       0 collis▪▪▪
DJB2              156 ns      437 ns          93 ns
                    7 collis    6 collis       0 collis▪▪▪
SDBM              148 ns      484 ns          90 ns
                    4 collis    6 collis       0 collis**
SuperFastHash     164 ns      344 ns         118 ns
                   85 collis    4 collis   18742 collis
CRC32             250 ns      946 ns         130 ns
                    2 collis    0 collis       0 collis
LoseLose          338 ns        -             -
               215178 collis

Notes:

Do collisions actually happen?

Yes. I started writing my test program to see if hash collisions actually happen - and are not just a theoretical construct. They do indeed happen:

FNV-1 collisions

  • creamwove collides with quists

FNV-1a collisions

  • costarring collides with liquid
  • declinate collides with macallums
  • altarage collides with zinke
  • altarages collides with zinkes

Murmur2 collisions

  • cataract collides with periti
  • roquette collides with skivie
  • shawl collides with stormbound
  • dowlases collides with tramontane
  • cricketings collides with twanger
  • longans collides with whigs

DJB2 collisions

  • hetairas collides with mentioner
  • heliotropes collides with neurospora
  • depravement collides with serafins
  • stylist collides with subgenera
  • joyful collides with synaphea
  • redescribed collides with urites
  • dram collides with vivency

DJB2a collisions

  • haggadot collides with loathsomenesses
  • adorablenesses collides with rentability
  • playwright collides with snush
  • playwrighting collides with snushing
  • treponematoses collides with waterbeds

CRC32 collisions

  • codding collides with gnu
  • exhibiters collides with schlager

SuperFastHash collisions

  • dahabiah collides with drapability
  • encharm collides with enclave
  • grahams collides with gramary
  • ...snip 79 collisions...
  • night collides with vigil
  • nights collides with vigils
  • finks collides with vinic

Randomnessification

The other subjective measure is how randomly distributed the hashes are. Mapping the resulting HashTables shows how evenly the data is distributed. All the hash functions show good distribution when mapping the table linearly:

Enter image description here

Or as a Hilbert Map (XKCD is always relevant):

Enter image description here

Except when hashing number strings ("1", "2", ..., "216553") (for example, zip codes), where patterns begin to emerge in most of the hashing algorithms:

SDBM:

Enter image description here

DJB2a:

Enter image description here

FNV-1:

Enter image description here

All except FNV-1a, which still look pretty random to me:

Enter image description here

In fact, Murmur2 seems to have even better randomness with Numbers than FNV-1a:

Enter image description here

When I look at the FNV-1a "number" map, I think I see subtle vertical patterns. With Murmur I see no patterns at all. What do you think?


The extra * in the above table denotes how bad the randomness is. With FNV-1a being the best, and DJB2x being the worst:

      Murmur2: .
       FNV-1a: .
        FNV-1: ▪
         DJB2: ▪▪
        DJB2a: ▪▪
         SDBM: ▪▪▪
SuperFastHash: .
          CRC: ▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪
     Loselose: ▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪
                                        ▪
                                 ▪▪▪▪▪▪▪▪▪▪▪▪▪
                        ▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪
          ▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪

I originally wrote this program to decide if I even had to worry about collisions: I do.

And then it turned into making sure that the hash functions were sufficiently random.

FNV-1a algorithm

The FNV1 hash comes in variants that return 32, 64, 128, 256, 512 and 1024 bit hashes.

The FNV-1a algorithm is:

hash = FNV_offset_basis
for each octetOfData to be hashed
    hash = hash xor octetOfData
    hash = hash * FNV_prime
return hash

Where the constants FNV_offset_basis and FNV_prime depend on the return hash size you want:

Hash Size    Prime                       Offset
===========  =========================== =================================
32-bit       16777619                    2166136261
64-bit       1099511628211               14695981039346656037
128-bit      309485009821345068724781371 144066263297769815596495629667062367629
256-bit
    prime: 2^168 + 2^8 + 0x63 = 374144419156711147060143317175368453031918731002211
    offset: 100029257958052580907070968620625704837092796014241193945225284501741471925557
512-bit
    prime: 2^344 + 2^8 + 0x57 = 35835915874844867368919076489095108449946327955754392558399825615420669938882575126094039892345713852759
    offset: 9659303129496669498009435400716310466090418745672637896108374329434462657994582932197716438449813051892206539805784495328239340083876191928701583869517785
1024-bit
    prime: 2^680 + 2^8 + 0x8d = 5016456510113118655434598811035278955030765345404790744303017523831112055108147451509157692220295382716162651878526895249385292291816524375083746691371804094271873160484737966720260389217684476157468082573
    offset: 1419779506494762106872207064140321832088062279544193396087847491461758272325229673230371772250864096521202355549365628174669108571814760471015076148029755969804077320157692458563003215304957150157403644460363550505412711285966361610267868082893823963790439336411086884584107735010676915

See the main FNV page for details.

As a practical matter:

  • 32-bit UInt32,
  • 64-bit UInt64, and
  • 128-bit Guid can be useful

All my results are with the 32-bit variant.

FNV-1 better than FNV-1a?

No. FNV-1a is all around better. There was more collisions with FNV-1a when using the English word corpus:

Hash    Word Collisions
======  ===============
FNV-1   1
FNV-1a  4

Now compare lowercase and uppercase:

Hash    lowercase word Collisions  UPPERCASE word collisions
======  =========================  =========================
FNV-1   1                          9
FNV-1a  4                          11

In this case FNV-1a isn't "400%" worse than FN-1, only 20% worse.

I think the more important takeaway is that there are two classes of algorithms when it comes to collisions:

  • collisions rare: FNV-1, FNV-1a, DJB2, DJB2a, SDBM
  • collisions common: SuperFastHash, Loselose

And then there's the how evenly distributed the hashes are:

  • outstanding distribution: Murmur2, FNV-1a, SuperFastHas
  • excellent distribution: FNV-1
  • good distribution: SDBM, DJB2, DJB2a
  • horrible distribution: Loselose

Update

Murmur? Sure, why not


Update

@whatshisname wondered how a CRC32 would perform, added numbers to the table.

CRC32 is pretty good. Few collisions, but slower, and the overhead of a 1k lookup table.

Snip all erroneous stuff about CRC distribution - my bad


Up until today I was going to use FNV-1a as my de facto hash-table hashing algorithm. But now I'm switching to Murmur2:

  • Faster
  • Better randomnessification of all classes of input

And I really, really hope there's something wrong with the SuperFastHash algorithm I found; it's too bad to be as popular as it is.

Update: From the MurmurHash3 homepage on Google:

(1) - SuperFastHash has very poor collision properties, which have been documented elsewhere.

So I guess it's not just me.

Update: I realized why Murmur is faster than the others. MurmurHash2 operates on four bytes at a time. Most algorithms are byte by byte:

for each octet in Key
   AddTheOctetToTheHash

This means that as keys get longer Murmur gets its chance to shine.


Update

GUIDs are designed to be unique, not random

A timely post by Raymond Chen reiterates the fact that "random" GUIDs are not meant to be used for their randomness. They, or a subset of them, are unsuitable as a hash key:

Even the Version 4 GUID algorithm is not guaranteed to be unpredictable, because the algorithm does not specify the quality of the random number generator. The Wikipedia article for GUID contains primary research which suggests that future and previous GUIDs can be predicted based on knowledge of the random number generator state, since the generator is not cryptographically strong.

Randomess is not the same as collision avoidance; which is why it would be a mistake to try to invent your own "hashing" algorithm by taking some subset of a "random" guid:

int HashKeyFromGuid(Guid type4uuid)
{
   //A "4" is put somewhere in the GUID.
   //I can't remember exactly where, but it doesn't matter for
   //the illustrative purposes of this pseudocode
   int guidVersion = ((type4uuid.D3 & 0x0f00) >> 8);
   Assert(guidVersion == 4);

   return (int)GetFirstFourBytesOfGuid(type4uuid);
}

Note: Again, I put "random GUID" in quotes, because it's the "random" variant of GUIDs. A more accurate description would be Type 4 UUID. But nobody knows what type 4, or types 1, 3 and 5 are. So it's just easier to call them "random" GUIDs.

All English Words mirrors

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    It would be really interesting to see how SHA compares, not because it's a good candidate for a hashing algorithm here but it would be really interesting to see how any cryptographic hash compares with these made for speed algorithms. – Michael May 25 '12 at 15:09
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    A new hash by the name of 'xxHash', by Yann Collet, was doing the rounds recently. I'm always suspicious of a new hash. It would be interesting to see it in your comparison, (if you aren't tired of people suggesting random hashes they've heard of to be added...) – th_in_gs May 29 '12 at 11:51
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    Indeed. The performance numbers announced by the xxHash project page look impressive, maybe too much to be true. Well, at least, it's an open-source project : code.google.com/p/xxhash – ATTracker May 29 '12 at 16:23
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    Hi Ian, my Delphi implementation of SuperFastHash is correct. When implementing I created a test set in C and Delphi to compare the results of my implementation and the reference implementation. There are no differences. So what you see is the actual badness of the hash... (That is why I also published a MurmurHash implementation: landman-code.blogspot.nl/2009/02/… ) – Davy Landman Jun 4 '12 at 8:58
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    Is the poster aware this is not just an awesome answer - this is the world's de facto reference resource on the subject? Anytime I need to deal with hashes, that solves my issue so fast and authoritatively that I don't ever need anything else. – MaiaVictor May 29 '14 at 11:53

If you are wanting to create a hash map from an unchanging dictionary, you might want to consider perfect hashing https://en.wikipedia.org/wiki/Perfect_hash_function - during the construction of the hash function and hash table, you can guarantee, for a given dataset, that there will be no collisions.

  • 2
    Here's more about (minimal) Perfect Hashing burtleburtle.net/bob/hash/perfect.html including performance data, although it doesn't use the most current processor etc. – Ellie Kesselman May 29 '12 at 12:24
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    It's pretty obvious, but worth pointing out that in order to guarantee no collisions, the keys would have to be the same size as the values, unless there are constraints on the values the algorithm can capitalize on. – devios1 Apr 4 '13 at 20:34
  • I improved gperf and provide a nice frontend to most perfect hash generators at github.com/rurban/Perfect-Hash It's not yet finished, but already better then the existing tools. – rurban Aug 20 '14 at 6:05
  • @devios: I've recently learned that there are several hash table algorithms that guarantee no collisions, even when you use long strings as keys, strings much longer than the hash table index values generated by the hash function, without any constraints on those strings. See cs.stackexchange.com/questions/477/… . – David Cary Jun 8 '15 at 17:11
  • Exactly how large is this dataset supposed to be? can it support sizes of between 750GB to 50 terabytes or so? – MarcusJ Oct 13 '15 at 2:53

Here is a list of hash functions, but the short version is:

If you just want to have a good hash function, and cannot wait, djb2 is one of the best string hash functions i know. It has excellent distribution and speed on many different sets of keys and table sizes

unsigned long
hash(unsigned char *str)
{
    unsigned long hash = 5381;
    int c;

    while (c = *str++)
        hash = ((hash << 5) + hash) + c; /* hash * 33 + c */

    return hash;
}
  • 6
    Actually djb2 is zero sensitive, as most such simple hash functions, so you can easily break such hashes. It has a bad bias too many collisions and a bad distribution, it breaks on most smhasher quality tests: See github.com/rurban/smhasher/blob/master/doc/bernstein His cdb database uses it, but I wouldn't use it with public access. – rurban Aug 20 '14 at 6:03
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    DJB is pretty bad from a performance and distribution standpoint. I wouldn't use it today. – Conrad Meyer Oct 30 '16 at 21:32
  • @ConradMeyer I'd bet, DJB can be sped up by a factor of three just like in this question of mine and then it'd probably beat most usable algorithms. Concerning the distribution, I agree. A hash producing collisions even for two letter strings can't be really good. – maaartinus Jun 4 '17 at 0:42

CityHash by Google is the algorithm you are looking for. It is not good for cryptography but is good for generating unique hashes.

Read the blog for more details and the code is available here.

CityHash is written in C++. There also is a plain C port.

About 32-bit support:

All the CityHash functions are tuned for 64-bit processors. That said, they will run (except for the new ones that use SSE4.2) in 32-bit code. They won't be very fast though. You may want to use Murmur or something else in 32-bit code.

The SHA algorithms (including SHA-256) are designed to be fast.

In fact, their speed can be a problem sometimes. In particular, a common technique for storing a password-derived token is to run a standard fast hash algorithm 10,000 times (storing the hash of the hash of the hash of the hash of the ... password).

#!/usr/bin/env ruby
require 'securerandom'
require 'digest'
require 'benchmark'

def run_random_digest(digest, count)
  v = SecureRandom.random_bytes(digest.block_length)
  count.times { v = digest.digest(v) }
  v
end

Benchmark.bmbm do |x|
  x.report { run_random_digest(Digest::SHA256.new, 1_000_000) }
end

Output:

Rehearsal ------------------------------------
   1.480000   0.000000   1.480000 (  1.391229)
--------------------------- total: 1.480000sec

       user     system      total        real
   1.400000   0.000000   1.400000 (  1.382016)
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    It's relatively fast, sure, for a cryptographic hashing algorithm. But the OP just wants to store values in a hashtable, and I don't think a cryptographic hash function is really appropriate for that. – Dean Harding Feb 19 '11 at 1:10
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    The question brought up (tangentially, it now appears) the subject of the cryptographic hash functions. That's the bit I am responding to. – yfeldblum Feb 22 '11 at 13:14
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    Just to put people off the idea of "In particular, a common technique for storing a password-derived token is to run a standard fast hash algorithm 10,000 times" -- while common, that's just plain stupid. There are algorithms designed for these scenarios, e.g., bcrypt. Use the right tools. – TC1 Oct 14 '13 at 13:19
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    Cryptographic hashes are designed to have a high throughput, but that often means they have high setup, teardown, .rodata and/or state costs. When you want an algorithm for a hashtable, you usually have very short keys, and lots of them, but do not need the additional guarantees of a cryptographic has. I use a tweaked Jenkins’ one-at-a-time myself. – mirabilos Dec 6 '13 at 13:57
  • Thanks for the amazingly extensive work! Could you perhaps make the source for that available? I'd like to try out something, and it'd be generally helpful for people implementing hash algorithms. – Hans-Peter Störr Jun 14 '17 at 9:25

I've plotted a short speed comparison of different hashing algorithms when hashing files.

The individual plots only differ slightly in the reading method and can be ignored here, since all files were stored in a tmpfs. Therefore the benchmark was not IO-bound if you are wondering.

Algorithms include: SpookyHash, CityHash, Murmur3, MD5, SHA{1,256,512}.

Conclusions:

  • Non-cryptographic hash functions like Murmur3, Cityhash and Spooky are pretty close together. One should note that Cityhash may be faster on CPUs with SSE 4.2s CRC instruction, which my CPU does not have. SpookyHash was in my case always a tiny bit before CityHash.
  • MD5 seems to be a good tradeoff when using cryptographic hash functions, although SHA256 may be more secure to the collision vulnerabilities of MD5 and SHA1.
  • The complexity of all algorithms is linear - which is really not surprising since they work blockwise. (I wanted to see if the reading method makes a difference, so you can just compare the rightmost values).
  • SHA256 was slower than SHA512.
  • I did not investigate the randomness of the hash functions. But here is a good comparison of the hash functions that are missing in Ian Boyds answer. This points out that CityHash has some problems in corner cases.

The source used for the plots:

  • 1
    The linear scale graph cuts off the y-axis label which says what quantity it is plotting. I guess it probably would be "time in seconds", same as the logarithmic scale. It's worth fixing. – Craig McQueen Dec 13 '15 at 23:24

I know there are things like SHA-256 and such, but these algorithms are designed to be secure, which usually means they are slower than algorithms that are less unique.

The assumption that cryptographic hash functions are more unique is wrong, and in fact it can be shown to be often backwards in practice. In truth:

  1. Cryptographic hash functions ideally should be indistinguishable from random;
  2. But with non-cryptographic hash functions, it's desirable for them to interact favorably with likely inputs.

Which means that a non-cryptographic hash function may well have fewer collisions than a cryptographic one for "good" data set—data sets that it was designed for.

We can actually demonstrate this with the data in Ian Boyd's answer and a bit of math: the Birthday problem. The formula for the expected number of colliding pairs if you pick n integers at random from the set [1, d] is this (taken from Wikipedia):

n - d + d * ((d - 1) / d)^n

Plugging n = 216,553 and d = 2^32 we get about 5.5 expected collisions. Ian's tests mostly show results around that neighborhood, but with one dramatic exception: most of the functions got zero collisions in the consecutive numbers tests. The probability of choosing 216,553 32-bit numbers at random and getting zero collisions is about 0.43%. And that's just for one function—here we have five distinct hash function families with zero collisions!

So what we're seeing here is that the hashes that Ian tested are interacting favorably with the consecutive numbers dataset—i.e., they're dispersing minimally different inputs more widely than an ideal cryptographic hash function would. (Side note: this means that Ian's graphical assessment that FNV-1a and MurmurHash2 "look random" to him in the numbers data set can be refuted from his own data. Zero collisions on a data set of that size, for both hash functions, is strikingly nonrandom!)

This is not a surprise because this is a desirable behavior for many uses of hash functions. For example, hash table keys are often very similar; Ian's answer mentions a problem MSN once had with ZIP code hash tables. This is a use where collision avoidance on likely inputs wins over random-like behavior.

Another instructive comparison here is the contrast in the design goals between CRC and cryptographic hash functions:

  • CRC is designed to catch errors resulting from noisy communications channels, which are likely to be a small number of bit flips;
  • Crypto hashes are designed to catch modifications made by malicious attackers, who are allotted limited computational resources but arbitrarily much cleverness.

So for CRC it is again good to have fewer collisions than random in minimally different inputs. With crypto hashes, this is a no-no!

It depends on the data you are hashing. Some hashing works better with specific data like text. Some hashing algorithms were specificaly designed to be good for specific data.

Paul Hsieh once made fast hash. He lists source code and explanations. But it was already beaten. :)

Use SipHash. It has many desirable properties:

  • Fast. An optimized implementation takes around 1 cycle per byte.

  • Secure. SipHash is a strong PRF (pseudorandom function). This means that it is indistinguishable from a random function (unless you know the 128-bit secret key). Hence:

    • No need to worry about your hash table probes becoming linear time due to collisions. With SipHash, you know that you will get average-case performance on average, regardless of inputs.

    • Immunity to hash-based denial of service attacks.

    • You can use SipHash (especially the version with a 128-bit output) as a MAC (Message Authentication Code). If you receive a message and a SipHash tag, and the tag is the same as that from running SipHash with your secret key, then you know that whoever created the hash was also in possession of your secret key, and that neither the message nor the hash have been altered since.

  • 1
    Isn't SipHash overkill unless you need security? Requires a 128-bit key which is just a glorified hash seed. Not to mention MurmurHash3 has 128-bit output and SipHash only has a 64-bit output. Obviously the larger digest has a lower collision chance. – bryc Apr 2 at 0:37
  • @bryc The difference is that SipHash will continue to be well-behaved, even on malicious input. A hash table based on SipHash can be used for data from potentially hostile sources, and can use an algorithm such as linear probing that is very sensitive to the details of the hash function. – Demi Apr 2 at 1:21

Java uses this simple multiply-and-add algorithm:

The hash code for a String object is computed as

 s[0]*31^(n-1) + s[1]*31^(n-2) + ... + s[n-1]

using int arithmetic, where s[i] is the i​-th character of the string, n is the length of the string, and ^ indicates exponentiation. (The hash value of the empty string is zero.)

There are probably much better ones out there but this is fairly widespread and seems to be a good trade-off between speed and uniqueness.

  • 12
    I wouldn't use the exact same one used here, as it's still relatively easy to produce collisions with this. It's definitely not terrible, but there are much better ones out there. And if there's no significant reason to be compatible with Java, it should not be chosen. – Joachim Sauer Apr 23 '12 at 12:51
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    If you still choose this way of hashing for some reason, you could at least use a better prime like 92821 as a multiplicator. That reduces collisions much. stackoverflow.com/a/2816747/21499 – Hans-Peter Störr Jul 1 '14 at 6:30

First of all, why do you need to implement your own hashing? For most tasks you should get good results with data structures from a standard library, assuming there's an implementation available (unless you're just doing this for your own education).

As far as actual hashing algorithms go, my personal favorite is FNV. 1

Here's an example implementation of the 32-bit version in C:

unsigned long int FNV_hash(void* dataToHash, unsigned long int length)
{
  unsigned char* p = (unsigned char *) dataToHash;
  unsigned long int h = 2166136261UL;
  unsigned long int i;

  for(i = 0; i < length; i++)
    h = (h * 16777619) ^ p[i] ;

  return h;
}
  • 2
    The FNV-1a variant is slightly better with randomness. Swap the order of the * and ^: h = (h * 16777619) ^ p[i] ==> h = (h ^ p[i]) * 16777619 – Ian Boyd Apr 23 '12 at 15:04

protected by ChrisF May 29 '12 at 12:38

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