Network Working Group Glenn Fowler
INTERNET-DRAFT AT&T Labs Research
Intended Status: Informational Landon Curt Noll
Cisco Systems
Kiem-Phong Vo
AT&T Labs Research
Donald Eastlake
Huawei Technologies
Expires: September 6, 2011 March 7, 2011
The FNV Non-Cryptographic Hash Algorithm
Abstract
FNV (Fowler/Noll/Vo) is a fast, non-cryptographic hash algorithm with
good dispersion. The purpose of this document is to make information
on FNV and open source code performing FNV conveniently available to
the Internet community.
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G. Fowler, L. Noll, K. Vo & D. Eastlake [Page 1]
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Table of Contents
1. Introduction............................................3
2. FNV Basics..............................................4
2.1 FNV Primes.............................................4
2.2 FNV offset_basis.......................................5
2.3 FNV Endianism..........................................5
3. Other Hash Sizes and XOR Folding........................6
4. FNV Constants...........................................7
5. The Source Code.........................................9
5.1 FNV C Header...........................................9
5.2 FNV C Code.............................................9
5.3 FNV Test Code..........................................9
6. Security Considerations................................10
7. IANA Considerations....................................10
8. References.............................................11
8.1 Normative References..................................11
8.2 Informative References................................11
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1. Introduction
The FNV hash algorithm is based on 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 suggested an
improvement on their algorithm. Some people tried this hash and found
that it worked rather well. In an EMail message to Landon, they named
it the "Fowler/Noll/Vo" or FNV hash. [FNV]
FNV hashes are designed to be fast while maintaining a low collision
rate. Their speed allows one to quickly hash lots of data while
maintaining a reasonably low collision rate. The high dispersion of
the FNV hashes makes them well suited for hashing nearly identical
strings such as URLs, hostnames, filenames, text, IP addresses, etc.
However, they are not suitable for cryptographic use. (For some hash
algorithms more suitable for cryptographic use see [RFCsha].)
The FNV hash is widely used, for example in DNS servers, database
indexing hashes, major web search / indexing engines, netnews history
file Message-ID lookup functions, anti-spam filters, a spellchecker
programmed in Ada 95, flatassembler's open source x86 assembler -
user-defined symbol hashtree, non-cryptographic file fingerprints,
computing Unique IDs in DASM (DTN Applications for Symbian Mobile-
phones), Microsoft's hash_map implementation for VC++ 2005, the
realpath cache in PHP 5.x (php-5.2.3/TSRM/tsrm_virtual_cwd.c), and
many other uses.
FNV hash algorithms and source code have been released into the
public domain. The authors of the FNV algorithm took deliberate steps
to disclose the algorithm in a public forum soon after it was
invented. More than a year passed after this public disclosure and
the authors deliberatley took no steps to patent the FNV algorithm.
Therefore, it is safe to say that the FNV authors have no patent
claims on the FNV algorithm as published.
If you use an FNV function in an application, you are kindly
requested to send an EMail about it to: fnv-mail@asthe.com
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2. FNV Basics
This document focuses on the FNV-1a function whose pseudo-code is as
follows:
hash = offset_basis
for each octet_of_data to be hashed
hash = hash xor octet_of_data
hash = hash * FNV_Prime
return hash
In the pseudo-code above, hash is a power-of-two number of bits (32,
64, ... 1024) and offset_basis and FNV_Prime depend on the size of
hash.
The FNV-1 algorithm is the same, including the values of offset_basis
and FNV_Prime, except that the order of the two lines with the "xor"
and multiply operations are reversed. Operational experience
indicates better hash dispersion for small amounts of data with
FNV-1a. FNV-0 is the same as FNV-1 but with offset_basis set to zero.
FNV-1a is suggested for general use.
2.1 FNV Primes
The theory behind FNV_Prime's is beyond the scope of this document
but the basic property to look for is how an FNV_Prime would impact
dispersion. Now, consider any n-bit FNV hash where n is >= 32 and
also a power of 2. For each such an n-bit FNV hash, an FNV_Prime p is
defined as:
The smallest prime of the form p = 2**t + 2**8 + b where:
- t is an integer such that:
If n == 32, then t == int((3/4)*n) == 24, or
If n >= 64, then t == 8*int((n+5)/12).
- b is an integer such that:
0 < b < 2**8, and
The number of one-bits in b is 4 or 5
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.
Per the above constraints, an FNV_Prime should have only 6 or 7 one-
bits in it. Therefore, some compilers may seek to improve the
performance of a multiplication with an FNV_Prime by replacing the
multiplication with shifts and adds. However, note that the
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performance of this substitution is highly hardware-dependent and
should be done with care. FNV_Primes were selected primarily for the
quality of resulting hash function, not for compiler optimization.
2.2 FNV offset_basis
The offset_basis values for the n-bit FNV-1a algorithms are computed
by applying the n-bit FNV-0 algorithm to the following 32 octets:
chongo /\../\
The \'s in the above string are not C-style escape characters. In C-
string notation, these 32 octets are:
"chongo /\\../\\"
2.3 FNV Endianism
For persistent storage or interoperability between different hardware
platforms, an FNV hash shall be represented in the little endian
format. That is, the FNV hash will be stored in an array hash[N] with
N bytes such that its integer value can be retrieved as follows:
unsigned char hash[N];
for ( i = N-1, value = 0; i >= 0; --i )
value = value << 8 + hash[i];
Of course, when FNV hashes are used in a single process or a group of
processes sharing memory on processors with compatible endian-ness,
the natural endianness of those processors can be used regardless of
its type, little, big, or some other exotic form.
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3. Other Hash Sizes and XOR Folding
Many hash uses require a hash that is not one of the FNV sizes for
which constants are provided in Section 4. If a larger hash size is
needed, please contact the authors of this document.
Most hash applications make use of a hash that is a fixed size binary
field. Assume that k bits of hash are desired and k is less than 1024
but not one of the sizes for which constants are provided in Section
4. The recommended technique is to take the smallest FNV hash of size
S, where S is larger than k, and calculate the desired hash using xor
folding as shown below. The final bit masking operation is logically
unnecessarily if the size of hash is exactly the number of desired
bits.
temp = FNV_S ( data-to-be-hashed )
hash = ( temp xor temp>>k ) bitwise-and ( 2**k - 1 )
Hash functions are a trade-off between speed and strength. For
example, a somewhat stronger hash may be obtained for exact FNV sizes
by calculating an FNV twice as long as the desired output ( S = 2*k )
and performing such data folding using a k equal to the size of the
desired output. However, if a much stronger hash, for example one
suitable for cryptographic applications, is wanted, algorithms
designed for that purpose, such as those in [RFCsha] should be used.
If it is desired to obtain a hash result that is a value between 0
and max, where max is a not a power of two, simply choose an FNV hash
size S such that 2**S > max. Then calculate the following:
FNV_S mod ( max+1 )
The resulting remainder will be in the range desired but will suffer
from a bias against large values with the bias being larger if 2**S
is only a little bigger than max. If this bias is acceptable, no
further processing is needed. If this bias is unacceptable, it can be
avoided by retrying for certain high values of hash, as follows,
before applying the mod operation above:
X = ( int( ( 2**S - 1 ) / ( max+1 ) ) ) * ( max+1 )
while ( hash >= X )
hash = ( hash * FNV_Prime ) + offset_basis
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4. FNV Constants
The FNV Primes are as follows:
32 bit FNV_Prime = 2**24 + 2**8 + 0x93 = 16,777,619
= 0x01000193
64 bit FNV_Prime = 2**40 + 2**8 + 0xB3 = 1,099,511,628,211
= 0x00000100 000001B3
128 bit FNV_Prime = 2**88 + 2**8 + 0x3B =
309,485,009,821,345,068,724,781,371
= 0x00000000 01000000 00000000 0000013B
256 bit FNV_Prime = 2**168 + 2**8 + 0x63 =
374,144,419,156,711,147,060,143,317,175,368,453,031,918,731,002,211 =
0x0000000000000000 0000010000000000 0000000000000000 0000000000000163
512 bit FNV_Prime = 2**344 + 2**8 + 0x57 = 35,
835,915,874,844,867,368,919,076,489,095,108,449,946,327,955,754,392,
558,399,825,615,420,669,938,882,575,126,094,039,892,345,713,852,759 =
0x0000000000000000 0000000000000000 0000000001000000 0000000000000000
0000000000000000 0000000000000000 0000000000000000 0000000000000157
1024 bit FNV_Prime = 2**680 + 2**8 + 0x8D = 5,
016,456,510,113,118,655,434,598,811,035,278,955,030,765,345,404,790,
744,303,017,523,831,112,055,108,147,451,509,157,692,220,295,382,716,
162,651,878,526,895,249,385,292,291,816,524,375,083,746,691,371,804,
094,271,873,160,484,737,966,720,260,389,217,684,476,157,468,082,573 =
0x0000000000000000 0000000000000000 0000000000000000 0000000000000000
0000000000000000 0000010000000000 0000000000000000 0000000000000000
0000000000000000 0000000000000000 0000000000000000 0000000000000000
0000000000000000 0000000000000000 0000000000000000 000000000000018D
The FNV offset_basis values are as follows:
32 bit offset_basis = 2,166,136,261 = 0x811C9DC5
64 bit offset_basis = 14695981039346656037 = 0xCBF29CE4 84222325
128 bit offset_basis = 144066263297769815596495629667062367629 =
0x6C62272E 07BB0142 62B82175 6295C58D
256 bit offset_basis = 100,029,257,958,052,580,907,070,968,
620,625,704,837,092,796,014,241,193,945,225,284,501,741,471,925,557 =
0xDD268DBCAAC55036 2D98C384C4E576CC C8B1536847B6BBB3 1023B4C8CAEE0535
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512 bit offset_basis = 9,
659,303,129,496,669,498,009,435,400,716,310,466,090,418,745,672,637,
896,108,374,329,434,462,657,994,582,932,197,716,438,449,813,051,892,
206,539,805,784,495,328,239,340,083,876,191,928,701,583,869,517,785 =
0xB86DB0B1171F4416 DCA1E50F309990AC AC87D059C9000000 0000000000000D21
E948F68A34C192F6 2EA79BC942DBE7CE 182036415F56E34B AC982AAC4AFE9FD9
1024 bit offset_basis = 14,197,795,064,947,621,068,722,070,641,403,
218,320,880,622,795,441,933,960,878,474,914,617,582,723,252,296,732,
303,717,722,150,864,096,521,202,355,549,365,628,174,669,108,571,814,
760,471,015,076,148,029,755,969,804,077,320,157,692,458,563,003,215,
304,957,150,157,403,644,460,363,550,505,412,711,285,966,361,610,267,
868,082,893,823,963,790,439,336,411,086,884,584,107,735,010,676,915 =
0x0000000000000000 005F7A76758ECC4D 32E56D5A591028B7 4B29FC4223FDADA1
6C3BF34EDA3674DA 9A21D90000000000 0000000000000000 0000000000000000
0000000000000000 0000000000000000 0000000000000000 000000000004C6D7
EB6E73802734510A 555F256CC005AE55 6BDE8CC9C6A93B21 AFF4B16C71EE90B3
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5. The Source Code
The following sub-sections are intended, in later versions, to
include reference C source code and a test driver for FNV-1a.
5.1 FNV C Header
TBD
5.2 FNV C Code
TBD
5.3 FNV Test Code
TBD
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6. Security Considerations
This document is intended to provide convenient open source access by
the Internet community to the FNV non-cryptographic hash. No
assertion of suitability for cryptographic applications is made for
the FNV hash algorithms.
7. IANA Considerations
This document requires no IANA Actions. The RFC Editor should delete
this section before publication.
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8. References
Below are the normative and informative references for this document.
8.1 Normative References
None.
8.2 Informative References
[FNV] - FNV web site:
http://www.isthe.com/chongo/tech/comp/fnv/index.html
[RFCsha] - D. Eastlake, T. Hansen, "US Secure Hash Algorithms (SHA
and SHA based HMAC and HKDF)", draft-eastlake-sha2b-07.txt, in
RFC Editor queue.
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Appendix: Test Vectors
Below are a few test vectors in the form of ASCII strings and their
FNV32 and FNV64 hashes using the FNV-1a algorithm.
Strings without null (zero byte) termination:
String FNV32 FNV64
"" 0x811c9dc5 0xcbf29ce484222325
"a" 0xe40c292c 0xaf63dc4c8601ec8c
"foobar" 0xbf9cf968 0x85944171f73967e8
Strings including null (zero byte) termination:
String FNV32 FNV64
"" 0x050c5d1f 0xaf63bd4c8601b7df
"a" 0x2b24d044 0x089be207b544f1e4
"foobar" 0x0c1c9eb8 0x34531ca7168b8f38
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Author's Address
Glenn Fowler
AT&T Labs Research
180 Park Avenue
Florham Park, NJ 07932 USA
Email: gsf@research.att.com
URL: http://www.research.att.com/~gsf/
Landon Curt Noll
Cisco Systems
170 West Tasman Drive
San Jose, CA 95134 USA
Telephone: +1-408-424-1102
Email: fnv-rfc-mail@asthe.com
URL: http://www.isthe.com/chongo/index.html
Kiem-Phong Vo
AT&T Labs Research
180 Park Avenue
Florham Park, NJ 07932 USA
Email: kpv@research.att.com
URL: http://www.research.att.com/info/kpv/
Donald Eastlake
Huawei Technologies
155 Beaver Street
Milford, MA 01757 USA
Telephone: +1-508-333-2270
EMail: d3e3e3@gmail.com
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G. Fowler, L. Noll, K. Vo & D. Eastlake [Page 14]