Editing Fowler–Noll–Vo hash function

{{Short description|Non-cryptographic hash function}}
'''Fowler–Noll–Vo''' (or '''FNV''') is a [[non-cryptographic hash function]] created by Glenn Fowler, [[Landon Curt Noll]], and Kiem-Phong Vo<!-- Võ Kiềm Phong -->.

The basis of the FNV hash algorithm was taken from an idea sent as reviewer comments to the [[POSIX|IEEE POSIX P1003.2]] committee by Glenn Fowler and Phong Vo in 1991. In a subsequent ballot round, Landon Curt Noll improved on their algorithm. In an email message to Noll, they named it the ''Fowler/Noll/Vo'' or FNV hash.<ref>{{Cite web|url=http://www.isthe.com/chongo/tech/comp/fnv/index.html#history|title=FNV Hash - FNV hash history|website=www.isthe.com}}</ref>

==Overview==
The current versions are FNV-1 and FNV-1a, which supply a means of creating non-zero ''FNV offset basis''.  FNV currently{{As of when|date=August 2024}} comes in 32-, 64-, 128-, 256-, 512-, and 1024-bit variants.  For pure FNV implementations, this is determined solely by the availability of ''FNV primes'' for the desired bit length; however, the FNV webpage discusses methods of adapting one of the above versions to a smaller length that may  or may not be a power of two.<ref>{{Cite web|url=http://www.isthe.com/chongo/tech/comp/fnv/index.html#xor-fold|title=FNV Hash - Changing the FNV hash size - xor-folding|website=www.isthe.com}}</ref><ref>{{Cite web|url=http://www.isthe.com/chongo/tech/comp/fnv/index.html#other-folding|title=FNV Hash - Changing the FNV hash size - non-powers of 2|website=www.isthe.com}}</ref>

The FNV hash algorithms and reference FNV [[source code]]<ref name="FNV_prime">{{Cite journal|last1=Eastlake|first1=Donald|last2=Hansen|first2=Tony|last3=Fowler|first3=Glenn|last4=Vo|first4=Kiem-Phong|last5=Noll|first5=Landon|date=29 May 2019|title=The FNV Non-Cryptographic Hash Algorithm|url=https://tools.ietf.org/html/draft-eastlake-fnv-17.html|archive-url=|archive-date=|access-date=|website=tools.ietf.org}}</ref><ref>{{Cite web|url=http://www.isthe.com/chongo/tech/comp/fnv/index.html#FNV-source|title=FNV Hash - FNV source|website=www.isthe.com}}</ref> have been released into the [[public domain]].<ref>[http://www.isthe.com/chongo/tech/comp/fnv/index.html#public_domain FNV put into the public domain] on isthe.com</ref>

The [[Python programming language]] previously used a modified version of the FNV scheme for its default <code>hash</code> function. From Python 3.4, FNV has been replaced with [[SipHash]] to resist "[[Collision attack#Hash flooding|hash flooding]]" [[denial-of-service attack]]s.<ref>{{Cite web|url=https://www.python.org/dev/peps/pep-0456/|title=PEP 456 -- Secure and interchangeable hash algorithm|website=Python.org}}</ref>

FNV is not a [[cryptographic hash]].<ref name="FNV_prime"/>

==The hash==

One of FNV's key advantages is that it is very simple to implement.<ref name="FNV_gps">
{{cite web
| first = James
| last = Smith
| work = Golang Project Structure
| title = Hash Functions in Go
| url = https://golangprojectstructure.com/hash-functions-go-code/#implementing-the-fowler%e2%80%93noll%e2%80%93vo-fnv-hash-function
| date = 2022-05-29
| access-date = 2024-10-19
}}
</ref>  Start with an initial hash value of ''FNV offset basis''.  For each byte in the input, [[multiply]] ''hash'' by the ''FNV prime'', then [[XOR]] it with the byte from the input.  The alternate algorithm, FNV-1a, reverses the multiply and XOR steps.

===FNV-1 hash===

The FNV-1 hash algorithm is as follows:<ref name="FNV_basics">{{Cite journal|last1=Eastlake|first1=Donald|last2=Hansen|first2=Tony|last3=Fowler|first3=Glenn|last4=Vo|first4=Kiem-Phong|last5=<unknown-email-Landon-Noll>|first5=Landon Noll|date=June 4, 2020|title=The FNV Non-Cryptographic Hash Algorithm|url=https://tools.ietf.org/html/draft-eastlake-fnv-17.html|archive-url=|archive-date=|access-date=2020-06-04|website=tools.ietf.org|language=en}}</ref><ref>{{Cite web|title=FNV Hash - The core of the FNV hash|url=http://www.isthe.com/chongo/tech/comp/fnv/index.html#FNV-1|access-date=2020-06-04|website=www.isthe.com}}</ref>

 '''algorithm''' fnv-1 '''is'''
     ''hash'' := '''''FNV_offset_basis'''''
 
     '''for each''' ''byte_of_data'' to be hashed '''do'''
         ''hash'' := ''hash'' × '''''FNV_prime'''''
         ''hash'' := ''hash'' [[XOR]] ''byte_of_data''
 
     '''return''' ''hash'' 

In the above [[pseudocode]], all variables are [[signedness|unsigned]] [[integers]].  All variables, except for ''byte_of_data'', have the same number of [[bit]]s as the FNV hash.  The variable, ''byte_of_data'', is an 8-[[bit]] unsigned [[integer]].

As an example, consider the 64-[[bit]] FNV-1 hash:

* All variables, except for ''byte_of_data'', are 64-[[bit]] unsigned [[integers]].
* The variable, ''byte_of_data'', is an 8-[[bit]] unsigned [[integer]].
* The ''FNV_offset_basis'' is the 64-[[bit]] value: 14695981039346656037 (in hex, 0xcbf29ce484222325).
* The ''FNV_prime'' is the 64-[[bit]] value 1099511628211 (in hex, 0x100000001b3).
* The [[multiply]] returns the lower 64 [[bit]]s of the [[Product (mathematics)|product]].
* The [[XOR]] is an 8-[[bit]] operation that modifies only the lower 8-[[bit]]s of the hash value.
* The ''hash'' value returned is a 64-[[bit]] [[Signedness|unsigned]] [[Integer (computer science)|integer]].

===FNV-1a hash===

The FNV-1a hash differs from the FNV-1 hash only by the order in which the [[multiply]] and [[XOR]] is performed:<ref name=FNV_basics /><ref>{{Cite web|url=http://www.isthe.com/chongo/tech/comp/fnv/index.html#FNV-1a|title=FNV Hash - FNV-1a alternate algorithm|website=www.isthe.com}}</ref>

 '''algorithm''' fnv-1a '''is'''
     ''hash'' := '''''FNV_offset_basis'''''
 
     '''for each''' ''byte_of_data'' to be hashed '''do'''
         ''hash'' := ''hash'' [[XOR]] ''byte_of_data''
         ''hash'' := ''hash'' × '''''FNV_prime'''''
 
     '''return''' ''hash'' 
The above pseudocode has the same assumptions that were noted for the FNV-1 pseudocode.  The change in order leads to slightly better [[avalanche effect|avalanche characteristics]].<ref name=FNV_basics /><ref>{{Cite web|url=https://sites.google.com/site/murmurhash/avalanche|title=avalanche - murmurhash|website=sites.google.com}}</ref>

===FNV-0 hash (deprecated)===
The FNV-0 hash differs from the FNV-1 hash only by the initialisation value of the ''hash'' variable:<ref name= FNV_basics /><ref name=FNV0>{{Cite web|url=http://www.isthe.com/chongo/tech/comp/fnv/index.html#FNV-0|title=FNV Hash - FNV-0 Historic not|website=www.isthe.com}}</ref>

 '''algorithm''' fnv-0 '''is'''
     ''hash'' := 0
 
     '''for each''' ''byte_of_data'' to be hashed '''do'''
         ''hash'' := ''hash'' × '''''FNV_prime'''''
         ''hash'' := ''hash'' [[XOR]] ''byte_of_data''
 
     '''return''' ''hash''

The above pseudocode has the same assumptions that were noted for the FNV-1 pseudocode.

A consequence of the initialisation of the hash to 0 is that empty messages and all messages consisting of only the byte 0, regardless of their length, hash to 0.<ref name=FNV0 />

Use of the FNV-0 hash is [[deprecated]] except for the computing of the FNV offset basis for use as the FNV-1 and FNV-1a hash parameters.<ref name= FNV_basics /><ref name=FNV0 />

===FNV offset basis===

There are several different FNV offset bases for various bit lengths.  These offset bases are computed by computing the FNV-0 from the following 32 [[octet (computing)|octet]]s when expressed in [[ASCII]]:
: <pre>chongo <Landon Curt Noll> /\../\</pre>
This is one of [[Landon Curt Noll]]'s [[Signature block|signature lines]].  This is the only current practical use for the [[deprecated]] FNV-0.<ref name= FNV_basics /><ref name=FNV0 />

===FNV prime===

An ''FNV prime'' is a [[prime number]] and is determined as follows:<ref name="FNV_prime"/><ref name=FNV_prime_remarks>{{Cite web|url=http://www.isthe.com/chongo/tech/comp/fnv/index.html#fnv-prime|title=FNV Hash - A few remarks on FNV primes|website=www.isthe.com}}</ref>

For a given integer {{Mvar|s}} such that {{Math|4 < ''s'' < 11}}, let {{Math|1=''n'' = 2<sup>''s''</sup>}} and {{Math|1=''t'' = {{floor|(5 + ''n'') / 12}}}}; then the {{Mvar|n}}-[[bit]] FNV prime is the smallest [[prime number]] {{Mvar|p}} that is of the form
:<math>256^t + 2^8 + \mathrm{b}\,</math>

such that:
:* {{Math|0 < ''b'' < 2<sup>8</sup>}},
:* the number of one-bits in the [[binary number|binary]] representation of {{Mvar|b}} is either 4 or 5, and
:* {{Math|''p'' mod (2<sup>40</sup> &minus; 2<sup>24</sup> &minus; 1) > 2<sup>24</sup> + 2<sup>8</sup> + 2<sup>7</sup>}}.

Experimentally, FNV primes matching the above constraints tend to have better dispersion properties. They improve the polynomial feedback characteristic when an FNV prime multiplies an intermediate hash value. As such, the hash values produced are more scattered throughout the {{Mvar|n}}-[[bit]] hash space.<ref name=FNV_prime /><ref name= FNV_prime_remarks />

===FNV hash parameters===

The above FNV prime constraints and the definition of the FNV offset basis yield the following table of FNV hash parameters:

{| border="1" class="wikitable" style="text-align: center;" align="center"
|+ FNV parameters <ref name="FNV_prime"/><ref>{{Cite web|url=http://www.isthe.com/chongo/tech/comp/fnv/index.html#FNV-param|title=FNV Hash - Parameters of the FNV-1/FNV-1a hash|website=www.isthe.com}}</ref>
! Size in bits
<math>n = 2^s</math>
! Representation
! '''FNV prime''' 
! '''FNV offset basis'''
|-
|-
! rowspan="3" | 32
! Expression
| 2<sup>24</sup> + 2<sup>8</sup> + 0x93
|
|-
! Decimal
|16777619
|2166136261
|-
! [[Hexadecimal]]
|0x01000193
|0x811c9dc5
|-
! rowspan="3" | 64
! Expression
|2<sup>40</sup> + 2<sup>8</sup> + 0xb3
|
|-
! Decimal
|1099511628211
|14695981039346656037
|-
! Hexadecimal
|0x00000100000001b3
|0xcbf29ce484222325
|-
! rowspan="3" | 128
! Representation
|2<sup>88</sup> + 2<sup>8</sup> + 0x3b
|
|-
! Decimal
|309485009821345068724781371
|144066263297769815596495629667062367629
|-
! Hexadecimal
|0x0000000001000000000000000000013b
|0x6c62272e07bb014262b821756295c58d
|-
! rowspan="3" | 256
! Representation
|2<sup>168</sup> + 2<sup>8</sup> + 0x63
|
|-
! Decimal
|
374144419156711147060143317<br>
175368453031918731002211
|
100029257958052580907070968620625704837<br>
092796014241193945225284501741471925557
|-
! Hexadecimal
|
0x00000000000000000000010000000000<br>
00000000000000000000000000000163
|
0xdd268dbcaac550362d98c384c4e576ccc8b153<br>
6847b6bbb31023b4c8caee0535
|-
! rowspan="3" | 512
! Representation
|2<sup>344</sup> + 2<sup>8</sup> + 0x57
|
|-
! Decimal
|
358359158748448673689190764<br>
890951084499463279557543925<br>
583998256154206699388825751<br>
26094039892345713852759
|
965930312949666949800943540071631046609<br>
041874567263789610837432943446265799458<br>
293219771643844981305189220653980578449<br>
5328239340083876191928701583869517785
|-
! Hexadecimal
|
0x0000000000000000 0000000000000000<br>
0000000001000000 0000000000000000<br>
0000000000000000 0000000000000000<br>
0000000000000000 0000000000000157
|
0xb86db0b1171f4416 dca1e50f309990ac<br>
ac87d059c9000000 0000000000000d21<br>
e948f68a34c192f6 2ea79bc942dbe7ce<br>
182036415f56e34b ac982aac4afe9fd9
|-
! rowspan="3" | 1024
! Representation
|2<sup>680</sup> + 2<sup>8</sup> + 0x8d
|
|-
! Decimal
|
501645651011311865543459881103<br>
527895503076534540479074430301<br>
752383111205510814745150915769<br>
222029538271616265187852689524<br>
938529229181652437508374669137<br>
180409427187316048473796672026<br>
0389217684476157468082573
|
14197795064947621068722070641403218320<br>
88062279544193396087847491461758272325<br>
22967323037177221508640965212023555493<br>
65628174669108571814760471015076148029<br>
75596980407732015769245856300321530495<br>
71501574036444603635505054127112859663<br>
61610267868082893823963790439336411086<br>
884584107735010676915
|-
! Hexadecimal
|
0x0000000000000000 0000000000000000<br>
0000000000000000 0000000000000000<br>
0000000000000000 0000010000000000<br>
0000000000000000 0000000000000000<br>
0000000000000000 0000000000000000<br>
0000000000000000 0000000000000000<br>
0000000000000000 0000000000000000<br>
0000000000000000 000000000000018d
|
0x0000000000000000 005f7a76758ecc4d<br>
32e56d5a591028b7 4b29fc4223fdada1<br>
6c3bf34eda3674da 9a21d90000000000<br>
0000000000000000 0000000000000000<br>
0000000000000000 0000000000000000<br>
0000000000000000 000000000004c6d7<br>
eb6e73802734510a 555f256cc005ae55<br>
6bde8cc9c6a93b21 aff4b16c71ee90b3
|}

==Non-cryptographic hash==

The FNV hash was designed for fast [[hash table]] and [[checksum]] use, not [[cryptography]]. The authors have identified the following properties as making the algorithm unsuitable as a [[cryptographic hash function]]:<ref>{{Cite journal|last1=Eastlake|first1=Donald|last2=Hansen|first2=Tony|last3=Fowler|first3=Glenn|last4=Vo|first4=Kiem-Phong|last5=Noll|first5=Landon|date=29 May 2019|title=The FNV Non-Cryptographic Hash Algorithm|url=https://tools.ietf.org/html/draft-eastlake-fnv-17.html|archive-url=|archive-date=|access-date=2021-01-12|website=tools.ietf.org|language=en}}</ref>

* '''Speed of computation''' – As a hash designed primarily for hashtable and checksum use, FNV-1 and FNV-1a were designed to be fast to compute. However, this same speed makes finding specific hash values (collisions) by brute force faster.
* '''Sticky state''' – Being an iterative hash based primarily on multiplication and XOR, the algorithm is sensitive to the number zero. Specifically, if the hash value were to become zero at any point during calculation, and the next byte hashed were also all zeroes, then the hash would not change. This makes colliding messages trivial to create given a message that results in a hash value of zero at some point in its calculation. Additional operations, such as the addition of a third constant prime on each step, can mitigate this but may have detrimental effects on [[avalanche effect]] or random distribution of hash values.
* '''Diffusion''' – The ideal secure hash function is one in which each byte of input has an equally-complex effect on every bit of the hash. In the FNV hash, the ones place (the rightmost bit) is always the XOR of the rightmost bit of every input byte. This can be mitigated by XOR-folding (computing a hash twice the desired length, and then XORing the bits in the "upper half" with the bits in the "lower half").<ref name="FNV_prime"/>

A structural weakness of FNV-1a arises from its use of XOR before multiplication, which can cause predictable relationships between hashes of related inputs. For example, the following identity holds in both the 32-bit and 64-bit variants:

 fnv1a("some-string-a") [[XOR]] fnv1a("some-id-1231") = fnv1a("some-string-b") [[XOR]] fnv1a("some-id-1232")

because the differing characters ('a' vs 'b', and '1' vs '2') differ by the same bit pattern. This illustrates how certain bitwise symmetries in input can lead to unintended hash correlations. XOR-folding does not remove this weakness.

==See also==
* [[Bloom filter]] (application for fast hashes) 
* [[Non-cryptographic hash functions]]

==References==
{{reflist|30em}}

==External links==
* [http://www.isthe.com/chongo/tech/comp/fnv/index.html Landon Curt Noll's webpage on FNV] (with table of base & prime parameters)
* [https://datatracker.ietf.org/doc/html/draft-eastlake-fnv-17 Internet draft by Fowler, Noll, Vo, and Eastlake] (IETF Informational Internet Draft)

{{DEFAULTSORT:Fowler-Noll-Vo hash function}}
[[Category:Hash function (non-cryptographic)]]
[[Category:Public-domain software with source code]]