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<title>MurmurHash</title>

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MurmurHash

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MurmurHash is a <a href="Non-cryptographic_hash_function" title="Non-cryptographic hash function">non-cryptographic hash function</a> suitable for general hash-based lookup.<a href="#cite_note-Hadoop-1">[1]</a><a href="#cite_note-2">[2]</a><a href="#cite_note-3">[3]</a> It was created by Austin Appleby in 2008<a href="#cite_note-4">[4]</a> and, as of 8 January 2016,<a href="#cite_note-5">[5]</a> is hosted on <a href="GitHub" title="GitHub">GitHub</a> along with its test suite named SMHasher. It also exists in a number of variants,<a href="#cite_note-Murmur160-6">[6]</a> all of which have been released into the public domain. The name comes from two basic operations, multiply (MU) and rotate (R), used in its inner loop.

Unlike <a href="Cryptographic_hash_function" title="Cryptographic hash function">cryptographic hash functions</a>, it is not specifically designed to be difficult to reverse by an adversary, making it unsuitable for cryptographic purposes.

<div class="mw-heading mw-heading2"><h2 id="Variants">Variants</h2></div>

<div class="mw-heading mw-heading3"><h3 id="MurmurHash1">MurmurHash1</h3></div>

The original MurmurHash was created as an attempt to make a faster function than <a href="Jenkins_hash_function#lookup3" title="Jenkins hash function">Lookup3</a>.<a href="#cite_note-7">[7]</a> Although successful, it had not been tested thoroughly and was not capable of providing 64-bit hashes as in Lookup3. Its design would be later built upon in MurmurHash2, combining a multiplicative hash (similar to the <a href="Fowler%E2%80%93Noll%E2%80%93Vo_hash_function" title="Fowler–Noll–Vo hash function">Fowler–Noll–Vo hash function</a>) with an <a href="Xorshift" title="Xorshift">Xorshift</a>.

<div class="mw-heading mw-heading3"><h3 id="MurmurHash2">MurmurHash2</h3></div>

MurmurHash2<a href="#cite_note-8">[8]</a> yields a 32- or 64-bit value. It comes in multiple variants, including some that allow incremental hashing and aligned or neutral versions.

<ul><li>MurmurHash2 (32-bit, x86)—The original version; contains a flaw that weakens collision in some cases.<a href="#cite_note-9">[9]</a></li>

<li>MurmurHash2A (32-bit, x86)—A fixed variant using <a href="Merkle%E2%80%93Damg%C3%A5rd_construction" title="Merkle–Damgård construction">Merkle–Damgård construction</a>. Slightly slower.</li>

<li>CMurmurHash2A (32-bit, x86)—MurmurHash2A, but works incrementally.</li>

<li>MurmurHashNeutral2 (32-bit, x86)—Slower, but endian- and alignment-neutral.</li>

<li>MurmurHashAligned2 (32-bit, x86)—Slower, but does aligned reads (safer on some platforms).</li>

<li>MurmurHash64A (64-bit, x64)—The original 64-bit version. Optimized for 64-bit arithmetic.</li>

<li>MurmurHash64B (64-bit, x86)—A 64-bit version optimized for 32-bit platforms. It is not a true 64-bit hash due to insufficient mixing of the stripes.<a href="#cite_note-10">[10]</a></li></ul>

The person who originally found the flaw in MurmurHash2 created an unofficial 160-bit version of MurmurHash2 called MurmurHash2_160.<a href="#cite_note-11">[11]</a>

<div class="mw-heading mw-heading3"><h3 id="MurmurHash3">MurmurHash3</h3></div>

The current version, completed April 3, 2011, is MurmurHash3,<a href="#cite_note-12">[12]</a><a href="#cite_note-Horvath-13">[13]</a> which yields a 32-bit or 128-bit hash value. When using 128-bits, the x86 and x64 versions do not produce the same values, as the algorithms are optimized for their respective platforms. MurmurHash3 was released alongside SMHasher, a hash function test suite.

<div class="mw-heading mw-heading2"><h2 id="Implementations">Implementations</h2></div>

The canonical implementation is in <a href="C%2B%2B" title="C++">C++</a>, but there are efficient ports for a variety of popular languages, including <a href="Python_(programming_language)" title="Python (programming language)">Python</a>,<a href="#cite_note-14">[14]</a> <a href="C_(programming_language)" title="C (programming language)">C</a>,<a href="#cite_note-15">[15]</a> <a href="Go_(programming_language)" title="Go (programming language)">Go</a>,<a href="#cite_note-16">[16]</a> <a href="C_Sharp_(programming_language)" title="C Sharp (programming language)">C#</a>,<a href="#cite_note-Horvath-13">[13]</a><a href="#cite_note-17">[17]</a> <a href="D_(programming_language)" title="D (programming language)">D</a>,<a href="#cite_note-18">[18]</a> <a rel="nofollow" class="external text" href="https://github.com/tkaemming/lua-murmurhash3">Lua</a>, <a href="Perl" title="Perl">Perl</a>,<a href="#cite_note-19">[19]</a> <a href="Ruby_(programming_language)" title="Ruby (programming language)">Ruby</a>,<a href="#cite_note-20">[20]</a> <a href="Rust_(programming_language)" title="Rust (programming language)">Rust</a>,<a href="#cite_note-21">[21]</a><a href="#cite_note-22">[22]</a> <a href="PHP" title="PHP">PHP</a>,<a href="#cite_note-23">[23]</a><a href="#cite_note-24">[24]</a> <a href="Common_Lisp" title="Common Lisp">Common Lisp</a>,<a href="#cite_note-25">[25]</a> <a href="Haskell_(programming_language)" class="mw-redirect" title="Haskell (programming language)">Haskell</a>,<a href="#cite_note-26">[26]</a> <a href="Elm_(programming_language)" title="Elm (programming language)">Elm</a>,<a href="#cite_note-27">[27]</a> <a href="Clojure" title="Clojure">Clojure</a>,<a href="#cite_note-28">[28]</a> <a href="Scala_(programming_language)" title="Scala (programming language)">Scala</a>,<a href="#cite_note-29">[29]</a> <a href="Java_(programming_language)" title="Java (programming language)">Java</a>,<a href="#cite_note-30">[30]</a><a href="#cite_note-31">[31]</a> <a href="Erlang_(programming_language)" title="Erlang (programming language)">Erlang</a>,<a href="#cite_note-32">[32]</a> <a href="Swift_(programming_language)" title="Swift (programming language)">Swift</a>,<a href="#cite_note-33">[33]</a> <a href="Object_Pascal" title="Object Pascal">Object Pascal</a>,<a href="#cite_note-34">[34]</a> <a href="Kotlin_(programming_language)" title="Kotlin (programming language)">Kotlin</a>,<a href="#cite_note-35">[35]</a> <a href="JavaScript" title="JavaScript">JavaScript</a>,<a href="#cite_note-36">[36]</a> and <a href="OCaml" title="OCaml">OCaml</a>.<a href="#cite_note-37">[37]</a>

It has been adopted into a number of open-source projects, most notably <a href="Libstdc%2B%2B" class="mw-redirect" title="Libstdc++">libstdc++</a> (ver 4.6), <a href="Nginx" title="Nginx">nginx</a> (ver 1.0.1),<a href="#cite_note-38">[38]</a> <a href="Rubinius" title="Rubinius">Rubinius</a>,<a href="#cite_note-39">[39]</a> libmemcached (the <a href="C_(programming_language)" title="C (programming language)">C</a> driver for <a href="Memcached" title="Memcached">Memcached</a>),<a href="#cite_note-40">[40]</a> <a href="Npm_(software)" class="mw-redirect" title="Npm (software)">npm</a> (nodejs package manager),<a href="#cite_note-41">[41]</a> maatkit,<a href="#cite_note-42">[42]</a> <a href="Hadoop" class="mw-redirect" title="Hadoop">Hadoop</a>,<a href="#cite_note-Hadoop-1">[1]</a> Kyoto Cabinet,<a href="#cite_note-43">[43]</a> <a href="Apache_Cassandra" title="Apache Cassandra">Cassandra</a>,<a href="#cite_note-44">[44]</a><a href="#cite_note-45">[45]</a> <a href="Apache_Solr" title="Apache Solr">Solr</a>,<a href="#cite_note-46">[46]</a> <a href="Vowpal_Wabbit" title="Vowpal Wabbit">vowpal wabbit</a>,<a href="#cite_note-47">[47]</a> <a href="Elasticsearch" title="Elasticsearch">Elasticsearch</a>,<a href="#cite_note-48">[48]</a> <a href="Google_Guava" title="Google Guava">Guava</a>,<a href="#cite_note-49">[49]</a> <a href="Apache_Kafka" title="Apache Kafka">Kafka</a>,<a href="#cite_note-50">[50]</a> and <a rel="nofollow" class="external text" href="https://access.redhat.com/documentation/en-us/red_hat_enterprise_linux/7/html/storage_administration_guide/vdo-integration">RedHat Virtual Data Optimizer (VDO)</a>.<a href="#cite_note-51">[51]</a>

<div class="mw-heading mw-heading2"><h2 id="Vulnerabilities">Vulnerabilities</h2></div>

Hash functions can be vulnerable to <a href="Collision_attack" title="Collision attack">collision attacks</a>, where a user can choose input data in such a way so as to intentionally cause hash collisions. Jean-Philippe Aumasson and <a href="Daniel_J._Bernstein" title="Daniel J. Bernstein">Daniel J. Bernstein</a> were able to show that even implementations of MurmurHash using a randomized seed are vulnerable to so-called <a href="HashDoS" class="mw-redirect" title="HashDoS">HashDoS</a> attacks.<a href="#cite_note-52">[52]</a> With the use of <a href="Differential_cryptanalysis" title="Differential cryptanalysis">differential cryptanalysis</a>, they were able to generate inputs that would lead to a hash collision. The authors of the attack recommend using their own <a href="SipHash" title="SipHash">SipHash</a> instead.

<div class="mw-heading mw-heading2"><h2 id="Algorithm">Algorithm</h2></div>

<pre>algorithm Murmur3_32 is

// Note: In this version, all arithmetic is performed with unsigned 32-bit integers.

// In the case of overflow, the result is reduced modulo 232.

input: key, len, seed

c1 ← 0xcc9e2d51

c2 ← 0x1b873593

r1 ← 15

r2 ← 13

m ← 5

n ← 0xe6546b64

hash ← seed

for each fourByteChunk of key do

k ← fourByteChunk

k ← k × c1

k ← k ROL r1

k ← k × c2

hash ← hash XOR k

hash ← hash ROL r2

hash ← (hash × m) + n

with any remainingBytesInKey do

remainingBytes ← SwapToLittleEndian(remainingBytesInKey)

// Note: Endian swapping is only necessary on big-endian machines.

// The purpose is to place the meaningful digits towards the low end of the value,

// so that these digits have the greatest potential to affect the low range digits

// in the subsequent multiplication. Consider that locating the meaningful digits

// in the high range would produce a greater effect upon the high digits of the

// multiplication, and notably, that such high digits are likely to be discarded

// by the modulo arithmetic under overflow. We don't want that.

remainingBytes ← remainingBytes × c1

remainingBytes ← remainingBytes ROL r1

remainingBytes ← remainingBytes × c2

hash ← hash XOR remainingBytes

hash ← hash XOR len

hash ← hash XOR (hash >> 16)

hash ← hash × 0x85ebca6b

hash ← hash XOR (hash >> 13)

hash ← hash × 0xc2b2ae35

hash ← hash XOR (hash >> 16)

</pre>

A sample C implementation follows (for little-endian CPUs):

<div class="mw-highlight mw-highlight-lang-c mw-content-ltr" dir="ltr"><pre>static inline uint32_t murmur_32_scramble(uint32_t k) {

k *= 0xcc9e2d51;

k = (k << 15) | (k >> 17);

k *= 0x1b873593;

return k;

}

uint32_t murmur3_32(const uint8_t* key, size_t len, uint32_t seed)

{

uint32_t h = seed;

uint32_t k;

/* Read in groups of 4. */

for (size_t i = len >> 2; i; i--) {

// Here is a source of differing results across endiannesses.

// A swap here has no effects on hash properties though.

memcpy(&k, key, sizeof(uint32_t));

key += sizeof(uint32_t);

h ^= murmur_32_scramble(k);

h = (h << 13) | (h >> 19);

h = h * 5 + 0xe6546b64;

}

/* Read the rest. */

k = 0;

for (size_t i = len & 3; i; i--) {

k <<= 8;

k |= key[i - 1];

}

// A swap is *not* necessary here because the preceding loop already

// places the low bytes in the low places according to whatever endianness

// we use. Swaps only apply when the memory is copied in a chunk.

/* Finalize. */

h ^= len;

h ^= h >> 16;

h *= 0x85ebca6b;

h *= 0xc2b2ae35;

return h;

}

</pre></div>

<caption>Tests

</caption>

<th>Test string

</th>

<th>Seed value

</th>

<th>Hash value (hexadecimal)

</th>

<th>Hash value (decimal)

</th></tr>

<tr>

<td>

</td>

</td>

</td>

</td></tr>

<tr>

<td>

</td>

</td>

</td>

</td></tr>

<tr>

<td>

</td>

<td><code>0xffffffff</code>

</td>

</td>

</td></tr>

<tr>

<td>test

</td>

</td>

</td>

</td></tr>

<tr>

<td>test

</td>

</td>

</td>

</td></tr>

<tr>

<td>Hello, world!

</td>

</td>

</td>

</td></tr>

<tr>

<td>Hello, world!

</td>

</td>

</td>

</td></tr>

<tr>

<td>The quick brown fox jumps over the lazy dog

</td>

</td>

</td>

</td></tr>

<tr>

<td>The quick brown fox jumps over the lazy dog

</td>

</td>

</td>

</td></tr></tbody></table>

<ul><li><a href="Non-cryptographic_hash_functions" class="mw-redirect" title="Non-cryptographic hash functions">Non-cryptographic hash functions</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="https://github.com/aappleby/smhasher">Official SMHasher site</a></li></ul></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2025-06-13" href="https://en.wikipedia.org/wiki/?title=MurmurHash&oldid=1295314879">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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