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: October 5, 2013 April 6, 2013
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.
Status of This Memo
This Internet-Draft is submitted to IETF in full conformance with the
provisions of BCP 78 and BCP 79.
Distribution of this document is unlimited. Comments should be sent
to the authors.
Internet-Drafts are working documents of the Internet Engineering
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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 Headers..........................................9
5.2 FNV C Code.............................................9
5.3 FNV Test Code..........................................9
6. Security Considerations................................10
6.1 Why is FNV Non-Cryptographic?.........................10
7. IANA Considerations....................................11
8. Acknowledgements.......................................11
9. References.............................................12
9.1 Normative References..................................12
9.2 Informative References................................12
Appendix A: Work Comparison with SHA-1....................13
Appendix B: Previous IETF Reference to FNV................14
Appendix C: A Few Test Vectors............................15
Appendix Z: Change Summary................................16
Author's Address..........................................18
G. Fowler, L. Noll, K. Vo & D. Eastlake [Page 2]
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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. 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. Their speed allows one to quickly
hash lots of data while maintaining a reasonably low collision rate.
However, they are generally not suitable for cryptographic use. (See
Section 6.1.)
The FNV hash is widely used, for example in DNS servers, the Twitter
service, 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.
A study has recommended FNV in connetion with the IPv6 Flow Label
field [IPv6flow].
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 deliberately 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
G. Fowler, L. Noll, K. Vo & D. Eastlake [Page 3]
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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:
When s is an integer and 4 < s < 11, then FNV_Prime is the
smallest prime p of the form:
256**int((5 + 2^s)/12) + 2**8 + b
where b is an integer such that:
0 < b < 2**8
The number of one-bits in b is 4 or 5
and where p mod (2**40 - 2**24 - 1) > (2**24 + 2**8 + 2**7).
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.
G. Fowler, L. Noll, K. Vo & D. Eastlake [Page 4]
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The case where s < 5 is not considered because the resulting hash
quality is too low. Such small hashes can, if desired, be derived
from a 32 bit FNV hash by XOR folding (see Section 3). The case where
s > 10 is not considered because of the doubtful utility of such
large FNV hashes and because the criteria for such large FNV_Primes
is more complex, due to the sparsity of such large primes, and would
needlessly clutter the criteria given above.
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
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 32 octets representing
the following character string in [ASCII]:
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.
G. Fowler, L. Noll, K. Vo & D. Eastlake [Page 5]
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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 [RFC6234], 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
G. Fowler, L. Noll, K. Vo & D. Eastlake [Page 6]
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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
G. Fowler, L. Noll, K. Vo & D. Eastlake [Page 7]
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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 Headers
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.
6.1 Why is FNV Non-Cryptographic?
A full discussion of cryptographic hash requirements and strength is
beyond the scope of this document. However, here are three
characteristics of FNV that would generally be considered to make it
non-cryptographic:
1. Work Factor - To make brute force inversion hard, a cryptographic
hash should be computationally expensive, especially for a general
purpose processor. But FNV is designed to be very inexpensive on a
general-purpose processor. (See Appendix A.)
2. Sticky State - A cryptographic hash should not have a state in
which it can stick for a plausible input pattern. But, in the very
unlikely event that the FNV hash variable becomes zero and the
input is a sequence of zeros, the hash variable will remain at
zero until there is a non-zero input byte and the final hash value
will be unaffected by the length of that sequence of zero input
bytes. Of course, for the common case of fixed length input, this
would not be significant because the number of non-zero bytes
would vary inversely with the number of zero bytes and for some
types of input runs of zeros do not occur. Furthermore, the
inclusion of even a little unpredictable input may be sufficient
to stop an adversary from inducing a zero hash variable.
3. Diffusion - Every output bit of a cryptographic hash should be an
equally complex function of every input bit. But it is easy to see
that the least significant bit of a direct FNV hash is the XOR of
the least significant bits of every input byte and does not depend
on any other input bit. While more complex, the second least
significant bit of an FNV hash has a similar weakness. If these
properties are considered a problem, they can be easily fixed by
XOR folding (see Section 3).
Nevertheless, none of the above have proven to be a problem in actual
practice for the many applications of FNV.
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7. IANA Considerations
This document requires no IANA Actions. RFC Editor Note: please
delete this section before publication.
8. Acknowledgements
The contributions of the following are gratefully acknowledged:
Frank Ellermann, Bob Moskowitz, and Stefan Santesson.
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9. References
Below are the normative and informative references for this document.
9.1 Normative References
[ASCII] - American National Standards Institute (formerly United
States of America Standards Institute), "USA Code for
Information Interchange", ANSI X3.4-1968, 1968. ANSI X3.4-1968
has been replaced by newer versions with slight modifications,
but the 1968 version remains definitive for the Internet.
9.2 Informative References
[FNV] - FNV web site:
http://www.isthe.com/chongo/tech/comp/fnv/index.html
[IEEE] - http://www.ieee.org
[IPv6flow] - https://researchspace.auckland.ac.nz/bitstream/handle/
2292/13240/flowhashRep.pdf
[RFC3174] - Eastlake 3rd, D. and P. Jones, "US Secure Hash Algorithm
1 (SHA1)", RFC 3174, September 2001.
[RFC6194] - Polk, T., Chen, L., Turner, S., and P. Hoffman, "Security
Considerations for the SHA-0 and SHA-1 Message-Digest
Algorithms", RFC 6194, March 2011.
[RFC6234] - Eastlake 3rd, D. and T. Hansen, "US Secure Hash
Algorithms (SHA and SHA-based HMAC and HKDF)", RFC 6234, May
2011.
G. Fowler, L. Noll, K. Vo & D. Eastlake [Page 12]
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Appendix A: Work Comparison with SHA-1
This section provides a simplistic rough comparison of the level of
effort required per input byte to compute FNV-1a and SHA-1 [RFC3174].
Ignoring transfer of control and conditional tests and equating all
logical and arithmetic operations, FNV requires 2 operations per
byte, an XOR and a multiply.
SHA-1 is a relatively weak cryptographic hash producing a 160-bit
hash. It that has been partially broken [RFC6194]. It is actually
designed to accept a bit vector input although almost all computer
uses apply it to an integer number of bytes. It processes blocks of
512 bits (64 bytes) and we estimate the effort involved in SHA-1
processing a full block. Ignoring SHA-1 initial set up, transfer of
control, and conditional tests, but counting all logical and
arithmetic operations, including counting indexing as an addition,
SHA-1 requires 1,744 operations per 64 bytes block or 27.25
operations per byte. So by this rough measure, it is a little over 13
times the effort of FNV for large amounts of data. However, FNV is
commonly used for small inputs. Using the above method, for inputs of
N bytes, where N is <= 55 so SHA-1 will take one block (SHA-1
includes padding and an 8-byte length at the end of the data in the
last block), the ratio of the effort for SHA-1 to the effort for FNV
will be 872/N. For example, with an 8 byte input, SHA-1 will take 109
times as much effort as FNV.
Stronger cryptographic functions than SHA-1 generally have an even
high work factor.
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Appendix B: Previous IETF Reference to FNV
FNV-1a was referenced in draft-ietf-tls-cached-info-08.txt that has
since expired. It was later decided that it would be better to use a
cryptographic hash for that application.
Below is the Jave code for FNV64 from that TLS draft include by the
kind permission of the author:
/**
* Java code sample, implementing 64 bit FNV-1a
* By Stefan Santesson
*/
import java.math.BigInteger;
public class FNV {
static public BigInteger getFNV1aToByte(byte[] inp) {
BigInteger m = new BigInteger("2").pow(64);
BigInteger fnvPrime = new BigInteger("1099511628211");
BigInteger fnvOffsetBasis =
new BigInteger("14695981039346656037");
BigInteger digest = fnvOffsetBasis;
for (byte b : inp) {
digest = digest.xor(BigInteger.valueOf((int) b & 255));
digest = digest.multiply(fnvPrime).mod(m);
}
return digest;
}
}
G. Fowler, L. Noll, K. Vo & D. Eastlake [Page 14]
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Appendix C: A Few 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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Appendix Z: Change Summary
RFC Editor Note: Please delete this appendix on publication.
From -00 to -01
1. Add Security Considerations section on why FNV is non-
cryptographic.
2. Add Appendix A on a work factor comparison with SHA-1.
3. Add Appendix B concerning previous IETF draft referenced to FNV.
4. Minor editorial changes.
From -01 to -02
1. Correct FNV_Prime determination criteria and add note as to why s
< 5 and s > 10 are not considered.
2. Add acknowledgements list.
3. Add a couple of references.
4. Minor editorial changes.
From -02 to -03
1. Replace direct reference to US-ASCII standard with reference to
RFC 20.
2. Update dates and verion number.
3. Minor editing changes.
From -03 to -04
1. Change reference to RFC 20 back to a reference to the ANSI 1968
ASCII standard.
2. Minor addition to Section 6, point 3.
G. Fowler, L. Noll, K. Vo & D. Eastlake [Page 16]
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3. Update dates and version number.
4. Minor editing changes.
From -04 to -05
1. Add Twitter as a use example and IPv6 flow hash study reference.
2. Update dates and version number.
G. Fowler, L. Noll, K. Vo & D. Eastlake [Page 17]
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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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Copyright, Disclaimer, and Additional IPR Provisions
Copyright (c) 2013 IETF Trust and the persons identified as the
document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents
(http://trustee.ietf.org/license-info) in effect on the date of
publication of this document. Please review these documents
carefully, as they describe your rights and restrictions with respect
to this document. Code Components extracted from this document must
include Simplified BSD License text as described in Section 4.e of
the Trust Legal Provisions and are provided without warranty as
described in the Simplified BSD License. This Internet-Draft is
submitted to IETF in full conformance with the provisions of BCP 78
and BCP 79.
G. Fowler, L. Noll, K. Vo & D. Eastlake [Page 19]