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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?] 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.²³

The FNV hash algorithms and reference FNV source code⁴⁵ have been released into the public domain.⁶

The Python programming language previously used a modified version of the FNV scheme for its default hash function. From Python 3.4, FNV has been replaced with SipHash to resist "hash flooding" denial-of-service attacks.⁷

FNV is not a cryptographic hash.⁸

The hash

One of FNV's key advantages is that it is very simple to implement.⁹ 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:¹⁰¹¹

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 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 value: 14695981039346656037 (in hex, 0xcbf29ce484222325).
• The FNV_prime is the 64-bit 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 only by the order in which the multiply and XOR is performed:¹²¹³

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 characteristics.¹⁴¹⁵

FNV-0 hash (deprecated)

The FNV-0 hash differs from the FNV-1 hash only by the initialisation value of the hash variable:¹⁶¹⁷

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 0.¹⁸

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.¹⁹²⁰

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 octets when expressed in ASCII:

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

This is one of Landon Curt Noll's signature lines. This is the only current practical use for the deprecated FNV-0.²¹²²

FNV prime

An FNV prime is a prime number and is determined as follows:²³²⁴

For a given integer s such that 4 < s < 11, let n = 2s and t = ⌊(5 + n) / 12⌋; then the n-bit FNV prime is the smallest prime number p that is of the form

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

such that:

• 0 < b < 28,
• the number of one-bits in the binary representation of b is either 4 or 5, and
• p mod (240 − 224 − 1) > 224 + 28 + 27.

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 n-bit hash space.²⁵²⁶

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 ²⁷²⁸

Size in bits n = 2 s {\displaystyle n=2^{s}}	Representation	FNV prime	FNV offset basis
32	Expression	224 + 28 + 0x93
	Decimal	16777619	2166136261
	Hexadecimal	0x01000193	0x811c9dc5
64	Expression	240 + 28 + 0xb3
	Decimal	1099511628211	14695981039346656037
	Hexadecimal	0x00000100000001b3	0xcbf29ce484222325
128	Representation	288 + 28 + 0x3b
	Decimal	309485009821345068724781371	144066263297769815596495629667062367629
	Hexadecimal	0x0000000001000000000000000000013b	0x6c62272e07bb014262b821756295c58d
256	Representation	2168 + 28 + 0x63
	Decimal	374144419156711147060143317175368453031918731002211	100029257958052580907070968620625704837092796014241193945225284501741471925557
	Hexadecimal	0x0000000000000000000001000000000000000000000000000000000000000163	0xdd268dbcaac550362d98c384c4e576ccc8b1536847b6bbb31023b4c8caee0535
512	Representation	2344 + 28 + 0x57
	Decimal	35835915874844867368919076489095108449946327955754392558399825615420669938882575126094039892345713852759	9659303129496669498009435400716310466090418745672637896108374329434462657994582932197716438449813051892206539805784495328239340083876191928701583869517785
	Hexadecimal	0x0000000000000000 00000000000000000000000001000000 00000000000000000000000000000000 00000000000000000000000000000000 0000000000000157	0xb86db0b1171f4416 dca1e50f309990acac87d059c9000000 0000000000000d21e948f68a34c192f6 2ea79bc942dbe7ce182036415f56e34b ac982aac4afe9fd9
1024	Representation	2680 + 28 + 0x8d
	Decimal	5016456510113118655434598811035278955030765345404790744303017523831112055108147451509157692220295382716162651878526895249385292291816524375083746691371804094271873160484737966720260389217684476157468082573	14197795064947621068722070641403218320880622795441933960878474914617582723252296732303717722150864096521202355549365628174669108571814760471015076148029755969804077320157692458563003215304957150157403644460363550505412711285966361610267868082893823963790439336411086884584107735010676915
	Hexadecimal	0x0000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000100000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 000000000000018d	0x0000000000000000 005f7a76758ecc4d32e56d5a591028b7 4b29fc4223fdada16c3bf34eda3674da 9a21d900000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 000000000004c6d7eb6e73802734510a 555f256cc005ae556bde8cc9c6a93b21 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:²⁹

• 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").³⁰

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

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)

References

1. "FNV Hash - FNV hash history". www.isthe.com. http://www.isthe.com/chongo/tech/comp/fnv/index.html#history ↩

2. "FNV Hash - Changing the FNV hash size - xor-folding". www.isthe.com. http://www.isthe.com/chongo/tech/comp/fnv/index.html#xor-fold ↩

3. "FNV Hash - Changing the FNV hash size - non-powers of 2". www.isthe.com. http://www.isthe.com/chongo/tech/comp/fnv/index.html#other-folding ↩

4. Eastlake, Donald; Hansen, Tony; Fowler, Glenn; Vo, Kiem-Phong; Noll, Landon (29 May 2019). "The FNV Non-Cryptographic Hash Algorithm". tools.ietf.org. https://tools.ietf.org/html/draft-eastlake-fnv-17.html ↩

5. "FNV Hash - FNV source". www.isthe.com. http://www.isthe.com/chongo/tech/comp/fnv/index.html#FNV-source ↩

6. FNV put into the public domain on isthe.com http://www.isthe.com/chongo/tech/comp/fnv/index.html#public_domain ↩

7. "PEP 456 -- Secure and interchangeable hash algorithm". Python.org. https://www.python.org/dev/peps/pep-0456/ ↩

8. Eastlake, Donald; Hansen, Tony; Fowler, Glenn; Vo, Kiem-Phong; Noll, Landon (29 May 2019). "The FNV Non-Cryptographic Hash Algorithm". tools.ietf.org. https://tools.ietf.org/html/draft-eastlake-fnv-17.html ↩

9. Smith, James (2022-05-29). "Hash Functions in Go". Golang Project Structure. Retrieved 2024-10-19. https://golangprojectstructure.com/hash-functions-go-code/#implementing-the-fowler%e2%80%93noll%e2%80%93vo-fnv-hash-function ↩

10. Eastlake, Donald; Hansen, Tony; Fowler, Glenn; Vo, Kiem-Phong; , Landon Noll (June 4, 2020). "The FNV Non-Cryptographic Hash Algorithm". tools.ietf.org. Retrieved 2020-06-04. {{cite journal}}: |last5= has generic name (help) https://tools.ietf.org/html/draft-eastlake-fnv-17.html ↩

11. "FNV Hash - The core of the FNV hash". www.isthe.com. Retrieved 2020-06-04. http://www.isthe.com/chongo/tech/comp/fnv/index.html#FNV-1 ↩

12. Eastlake, Donald; Hansen, Tony; Fowler, Glenn; Vo, Kiem-Phong; , Landon Noll (June 4, 2020). "The FNV Non-Cryptographic Hash Algorithm". tools.ietf.org. Retrieved 2020-06-04. {{cite journal}}: |last5= has generic name (help) https://tools.ietf.org/html/draft-eastlake-fnv-17.html ↩

13. "FNV Hash - FNV-1a alternate algorithm". www.isthe.com. http://www.isthe.com/chongo/tech/comp/fnv/index.html#FNV-1a ↩

14. Eastlake, Donald; Hansen, Tony; Fowler, Glenn; Vo, Kiem-Phong; , Landon Noll (June 4, 2020). "The FNV Non-Cryptographic Hash Algorithm". tools.ietf.org. Retrieved 2020-06-04. {{cite journal}}: |last5= has generic name (help) https://tools.ietf.org/html/draft-eastlake-fnv-17.html ↩

15. "avalanche - murmurhash". sites.google.com. https://sites.google.com/site/murmurhash/avalanche ↩

16. Eastlake, Donald; Hansen, Tony; Fowler, Glenn; Vo, Kiem-Phong; , Landon Noll (June 4, 2020). "The FNV Non-Cryptographic Hash Algorithm". tools.ietf.org. Retrieved 2020-06-04. {{cite journal}}: |last5= has generic name (help) https://tools.ietf.org/html/draft-eastlake-fnv-17.html ↩

17. "FNV Hash - FNV-0 Historic not". www.isthe.com. http://www.isthe.com/chongo/tech/comp/fnv/index.html#FNV-0 ↩

18. "FNV Hash - FNV-0 Historic not". www.isthe.com. http://www.isthe.com/chongo/tech/comp/fnv/index.html#FNV-0 ↩

19. Eastlake, Donald; Hansen, Tony; Fowler, Glenn; Vo, Kiem-Phong; , Landon Noll (June 4, 2020). "The FNV Non-Cryptographic Hash Algorithm". tools.ietf.org. Retrieved 2020-06-04. {{cite journal}}: |last5= has generic name (help) https://tools.ietf.org/html/draft-eastlake-fnv-17.html ↩

20. "FNV Hash - FNV-0 Historic not". www.isthe.com. http://www.isthe.com/chongo/tech/comp/fnv/index.html#FNV-0 ↩

21. Eastlake, Donald; Hansen, Tony; Fowler, Glenn; Vo, Kiem-Phong; , Landon Noll (June 4, 2020). "The FNV Non-Cryptographic Hash Algorithm". tools.ietf.org. Retrieved 2020-06-04. {{cite journal}}: |last5= has generic name (help) https://tools.ietf.org/html/draft-eastlake-fnv-17.html ↩

22. "FNV Hash - FNV-0 Historic not". www.isthe.com. http://www.isthe.com/chongo/tech/comp/fnv/index.html#FNV-0 ↩

23. Eastlake, Donald; Hansen, Tony; Fowler, Glenn; Vo, Kiem-Phong; Noll, Landon (29 May 2019). "The FNV Non-Cryptographic Hash Algorithm". tools.ietf.org. https://tools.ietf.org/html/draft-eastlake-fnv-17.html ↩

24. "FNV Hash - A few remarks on FNV primes". www.isthe.com. http://www.isthe.com/chongo/tech/comp/fnv/index.html#fnv-prime ↩

25. Eastlake, Donald; Hansen, Tony; Fowler, Glenn; Vo, Kiem-Phong; Noll, Landon (29 May 2019). "The FNV Non-Cryptographic Hash Algorithm". tools.ietf.org. https://tools.ietf.org/html/draft-eastlake-fnv-17.html ↩

26. "FNV Hash - A few remarks on FNV primes". www.isthe.com. http://www.isthe.com/chongo/tech/comp/fnv/index.html#fnv-prime ↩

27. Eastlake, Donald; Hansen, Tony; Fowler, Glenn; Vo, Kiem-Phong; Noll, Landon (29 May 2019). "The FNV Non-Cryptographic Hash Algorithm". tools.ietf.org. https://tools.ietf.org/html/draft-eastlake-fnv-17.html ↩

28. "FNV Hash - Parameters of the FNV-1/FNV-1a hash". www.isthe.com. http://www.isthe.com/chongo/tech/comp/fnv/index.html#FNV-param ↩

29. Eastlake, Donald; Hansen, Tony; Fowler, Glenn; Vo, Kiem-Phong; Noll, Landon (29 May 2019). "The FNV Non-Cryptographic Hash Algorithm". tools.ietf.org. Retrieved 2021-01-12. https://tools.ietf.org/html/draft-eastlake-fnv-17.html ↩

30. Eastlake, Donald; Hansen, Tony; Fowler, Glenn; Vo, Kiem-Phong; Noll, Landon (29 May 2019). "The FNV Non-Cryptographic Hash Algorithm". tools.ietf.org. https://tools.ietf.org/html/draft-eastlake-fnv-17.html ↩