MurmurHash

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MurmurHash is a non-cryptographic hash function suitable for general hash-based lookup. [1] [2] [3] It was created by Austin Appleby in 2008 [4] and is currently hosted on GitHub along with its test suite named 'SMHasher'. It also exists in a number of variants, [5] 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.

Contents

Unlike cryptographic hash functions, it is not specifically designed to be difficult to reverse by an adversary, making it unsuitable for cryptographic purposes.

Variants

MurmurHash1

The original MurmurHash was created as an attempt to make a faster function than Lookup3. [6] Although successful, it hadn't been tested thoroughly and wasn't capable of providing 64-bit hashes as in Lookup3. It had a rather elegant design, that would be later built upon in MurmurHash2, combining a multiplicative hash (similar to Fowler–Noll–Vo hash function) with a Xorshift.

MurmurHash2

MurmurHash2 [7] yields a 32-bit or 64-bit value. It came in multiple variants, including some that allowed incremental hashing and aligned or neutral versions.

The person who originally found the flaw[ clarification needed ] in MurmurHash2 created an unofficial 160-bit version of MurmurHash2 called MurmurHash2_160. [10]

MurmurHash3

The current version is MurmurHash3, [11] [12] 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.

Implementations

The canonical implementation is in C++, but there are efficient ports for a variety of popular languages, including Python, [13] C, [14] Go, [15] C#, [12] [16] D, [17] Lua, Perl, [18] Ruby, [19] Rust, [20] PHP, [21] [22] Common Lisp, [23] Haskell, [24] Elm, [25] Clojure, [26] Scala, [27] Java, [28] [29] Erlang, [30] Swift, [31] Object Pascal, [32] Kotlin, [33] JavaScript. [34] and OCaml, [35]

It has been adopted into a number of open-source projects, most notably libstdc++ (ver 4.6), nginx (ver 1.0.1), [36] Rubinius, [37] libmemcached (the C driver for Memcached), [38] npm (nodejs package manager), [39] maatkit, [40] Hadoop, [1] Kyoto Cabinet, [41] Cassandra, [42] [43] Solr, [44] vowpal wabbit, [45] Elasticsearch, [46] Guava, [47] Kafka [48] and RedHat Virtual Data Optimizer (VDO). [49]

Vulnerabilities

Hash functions can be vulnerable to collision attacks, where a user can choose input data in such a way so as to intentionally cause hash collisions. Jean-Philippe Aumasson and Daniel J. Bernstein were able to show that even implementations of MurmurHash using a randomized seed are vulnerable to so-called HashDoS attacks. [50] With the use of differential cryptanalysis they were able to generate inputs that would lead to a hash collision. The authors of the attack recommend to use their own SipHash instead.

Algorithm

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 ← seedfor each fourByteChunk of keydo         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)

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

staticinlineuint32_tmurmur_32_scramble(uint32_tk){k*=0xcc9e2d51;k=(k<<15)|(k>>17);k*=0x1b873593;returnk;}uint32_tmurmur3_32(constuint8_t*key,size_tlen,uint32_tseed){uint32_th=seed;uint32_tk;/* Read in groups of 4. */for(size_ti=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_ti=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.h^=murmur_32_scramble(k);/* Finalize. */h^=len;h^=h>>16;h*=0x85ebca6b;h^=h>>13;h*=0xc2b2ae35;h^=h>>16;returnh;}
Tests
Test stringSeed valueHash value (hexadecimal)Hash value (decimal)
0x000000000x000000000
0x000000010x514E28B71,364,076,727
0xffffffff0x81F16F392,180,083,513
test0x000000000xba6bd2133,127,628,307
test0x9747b28c0x704b81dc1,883,996,636
Hello, world!0x000000000xc0363e433,224,780,355
Hello, world!0x9747b28c0x24884CBA612,912,314
The quick brown fox jumps over the lazy dog0x000000000x2e4ff723776,992,547
The quick brown fox jumps over the lazy dog0x9747b28c0x2FA826CD799,549,133

See also

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References

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  3. ↑ "Couceiro et al" (PDF) (in Portuguese). p. 14. Retrieved 13 January 2012.
  4. ↑ Tanjent (tanjent) wrote,3 March 2008 13:31:00. "MurmurHash first announcement". Tanjent.livejournal.com. Retrieved 13 January 2012.{{cite web}}: CS1 maint: numeric names: authors list (link)
  5. ↑ "MurmurHash2-160". Simonhf.wordpress.com. 25 September 2010. Retrieved 13 January 2012.
  6. ↑ "MurmurHash1" . Retrieved 12 January 2019.
  7. ↑ "MurmurHash2 on Github".
  8. ↑ "MurmurHash2Flaw" . Retrieved 15 January 2019.
  9. ↑ "MurmurHash3 (see note on MurmurHash2_x86_64)" . Retrieved 15 January 2019.
  10. ↑ "MurmurHash2_160" . Retrieved 12 January 2019.
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  12. 1 2 Horvath, Adam (10 August 2012). "MurMurHash3, an ultra fast hash algorithm for C# / .NET".
  13. ↑ "pyfasthash in Python" . Retrieved 13 January 2012.
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  25. ↑ "Elm". package.elm-lang.org. Retrieved 12 June 2019.
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  28. ↑ Murmur3, part of Guava
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  31. ↑ Daisuke T (7 February 2019). "MurmurHash-Swift". GitHub.com. Retrieved 10 February 2019.
  32. ↑ GitHub - Xor-el/HashLib4Pascal: Hashing for Modern Object Pascal
  33. ↑ "goncalossilva/kotlinx-murmurhash". GitHub.com. 10 December 2021. Retrieved 14 December 2021.
  34. ↑ raycmorgan (owner). "Javascript implementation by Ray Morgan". Gist.github.com. Retrieved 13 January 2012.
  35. ↑ INRIA. "OCaml Source". GitHub.com.
  36. ↑ "nginx" . Retrieved 13 January 2012.
  37. ↑ "Rubinius" . Retrieved 29 February 2012.
  38. ↑ "libMemcached". libmemcached.org. Retrieved 21 October 2015.
  39. ↑ "switch from MD5 to murmur".
  40. ↑ "maatkit". 24 March 2009. Retrieved 13 January 2012.
  41. ↑ "Kyoto Cabinet specification". Fallabs.com. 4 March 2011. Retrieved 13 January 2012.
  42. ↑ "Partitioners". apache.org. 15 November 2013. Retrieved 19 December 2013.
  43. ↑ "Introduction to Apache Cassandra™ + What's New in 4.0 by Patrick McFadin. DataStax Presents". YouTube. 10 April 2019.
  44. ↑ "Solr MurmurHash2 Javadoc".
  45. ↑ "hash.cc in vowpalwabbit source code".
  46. ↑ "Elasticsearch 2.0 - CRUD and routing changes".
  47. ↑ "Guava Hashing.java".
  48. ↑ "Kafka DefaultPartitioner.java".
  49. ↑ Virtual Data Optimizer source code
  50. ↑ "Breaking Murmur: Hash-flooding DoS Reloaded".
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