Fowler–Noll–Vo hash function

Fowler–Noll–Vo is a non-cryptographic hash function created by Glenn Fowler, Landon Curt Noll, and Kiem-Phong Vo.

The basis of the FNV hash algorithm was taken from an idea sent as reviewer comments to the 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 Landon, they named it the Fowler/Noll/Vo or FNV hash.^[1]

Overview

The current versions are FNV-1 and FNV-1a, which supply a means of creating non-zero FNV offset basis. FNV currently comes in 32-, 64-, 128-, 256-, 512-, and 1024-bit flavors. 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.^[2]^[3]

The FNV hash algorithms and reference FNV source code^[4]^[5] have been released into the public domain.^[6]

FNV is not a cryptographic hash.^[7]

The hash

One of FNV's key advantages is that it is very simple to implement. 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:^[8]^[9]

   hash = FNV_offset_basis
   for each byte_of_data to be hashed
   	hash = hash × FNV_prime
   	hash = hash XOR byte_of_data
   return hash

In the above pseudocode, all variables are unsigned integers. All variables, except for byte_of_data, have the same number of bits 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 FNV offset basis value: 14695981039346656037 (in hex, 0xcbf29ce484222325).
The FNV_prime is the 64-bit FNV prime value: 1099511628211 (in hex, 0x100000001b3).
The multiply returns the lower 64-bits of the product.
The XOR is an 8-bit operation that modifies only the lower 8-bits of the hash value.
The hash value returned is a 64-bit unsigned integer.

FNV-1a hash

The FNV-1a hash differs from the FNV-1 hash by only the order in which the multiply and XOR is performed:^[8]^[10]

   hash = FNV_offset_basis
   for each byte_of_data to be hashed
   	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 small change in order leads to slightly better avalanche characteristics.^[8]^[11]

FNV-0 hash (deprecated)

The FNV-0 hash differs from the FNV-1 hash only by the initialisation value of the hash variable:^[8]^[12]

   hash = 0
   for each byte_of_data to be hashed
   	hash = hash × FNV_prime
   	hash = hash XOR octet_of_data
   return hash

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

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.^[8]^[12]

FNV offset basis

There are several different FNV offset basis for various bit lengths. These FNV offset basis are computed by computing the FNV-0 from the following 32 octets when expressed in ASCII:

chongo <Landon Curt Noll> /\../\

which is one of Landon Curt Noll's signature lines. This is the only current practical use for the deprecated FNV-0.^[8]^[12]

FNV prime

An FNV prime is a prime number and is determined as follows:^[13]^[14]

For a given $s$ :

$s\in \mathbb {I} ^{*}~$ (i.e., s is an integer)
$4<s<11$

where $n$ is:

$n=2^{s}$

and where $t$ is:

$t=\left\lfloor {\frac {5+2^{s}}{12}}\right\rfloor$

NOTE:

\lfloor x\rfloor \,

is the floor function

then the n-bit FNV prime is the smallest prime number $p$ that is of the form:

256^{t}+2^{8}+\mathrm {b} \,

such that:

$0<b<2^{8}$
The number of one-bits in the binary number representation of $b$ is either 4 or 5
$p\mod (2^{40}-2^{24}-1)>(2^{24}+2^{8}+2^{7})$

Experimentally, FNV prime 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 n-bit hash space.^[13]^[14]

FNV hash parameters

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

FNV parameters ^[15]^[16]
Size in bits $n=2^{s}$	FNV prime	FNV offset basis
32	2²⁴ + 2⁸ + 0x93 = 16777619	2166136261 = 0x811c9dc5
64	2⁴⁰ + 2⁸ + 0xb3 = 1099511628211	14695981039346656037 = 0xcbf29ce484222325
128	2⁸⁸ + 2⁸ + 0x3b = 309485009821345068724781371	144066263297769815596495629667062367629 = 0x6c62272e07bb014262b821756295c58d
256	2¹⁶⁸ + 2⁸ + 0x63 = 374144419156711147060143317 175368453031918731002211	100029257958052580907070968620625704837 092796014241193945225284501741471925557 = 0xdd268dbcaac550362d98c384c4e576ccc8b153 6847b6bbb31023b4c8caee0535
512	2³⁴⁴ + 2⁸ + 0x57 = 358359158748448673689190764 890951084499463279557543925 583998256154206699388825751 26094039892345713852759	965930312949666949800943540071631046609 041874567263789610837432943446265799458 293219771643844981305189220653980578449 5328239340083876191928701583869517785 = 0xb86db0b1171f4416dca1e50f309990acac87d0 59c90000000000000000000d21e948f68a34c192 f62ea79bc942dbe7ce182036415f56e34bac982a ac4afe9fd9
1024	2⁶⁸⁰ + 2⁸ + 0x8d = 501645651011311865543459881 103527895503076534540479074 430301752383111205510814745 150915769222029538271616265 187852689524938529229181652 437508374669137180409427187 316048473796672026038921768 4476157468082573	14197795064947621068722070641403218320 88062279544193396087847491461758272325 22967323037177221508640965212023555493 65628174669108571814760471015076148029 75596980407732015769245856300321530495 71501574036444603635505054127112859663 61610267868082893823963790439336411086 884584107735010676915 = 0x5f7a76758ecc4d32e56d5a591028b74b29fc 4223fdada16c3bf34eda3674da9a21d9000000 00000000000000000000000000000000000000 00000000000000000000000000000000000000 00000000000000000004c6d7eb6e7380273451 0a555f256cc005ae556bde8cc9c6a93b21aff4 b16c71ee90b3

The prefix "0x" on numbers means that the subsequent numbers are in hexadecimal.

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:^[7]

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, 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").^[17]

External links

Landon Curt Noll's webpage on FNV (with table of base & prime parameters)
Internet draft by Fowler, Noll, Vo, and Eastlake (IETF Informational Internet Draft)
FNV-1 and FNV-1a Calculator in-browser (all bit lengths supported for verification)

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[1] FNV hash history

[2] Changing the FNV hash size – xor-folding

[3] Changing the FNV hash size – non-powers of 2

[4] The Source Code

[5] FNV source

[6] FNV put into the public domain on isthe.com

[not_crypto_hash-7] 1 2 Why is FNV Non-Cryptographic?

[FNV_basics-8] 1 2 3 4 5 6 FNV Basics

[9] The core of the FNV hash

[10] FNV-1a alternate algorithm

[11] Avalanche

[FNV0-12] 1 2 3 FNV-0 historic note

[FNV_prime-13] 1 2 FNV Primes

[FNV_prime_remarks-14] 1 2 A few remarks on FNV primes

[FNV_constants-15] FNV Constants

[16] Parameters of the FNV hash

[17] Other Hash Sizes and XOR Folding