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


   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]

INTERNET-DRAFT                                                       FNV

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

G. Fowler, L. Noll, K. Vo & D. Eastlake                         [Page 2]

INTERNET-DRAFT                                                       FNV

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:

G. Fowler, L. Noll, K. Vo & D. Eastlake                         [Page 3]

INTERNET-DRAFT                                                       FNV

2. FNV Basics

   This document focuses on the FNV-1a function whose pseudo-code is as

      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

   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

G. Fowler, L. Noll, K. Vo & D. Eastlake                         [Page 4]

INTERNET-DRAFT                                                       FNV

   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 <Landon Curt Noll> /\../\

   The \'s in the above string are not C-style escape characters. In C-
   string notation, these 32 octets are:

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

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]

INTERNET-DRAFT                                                       FNV

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

      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

G. Fowler, L. Noll, K. Vo & D. Eastlake                         [Page 6]

INTERNET-DRAFT                                                       FNV

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 =
                                 = 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,
   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,
   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]

INTERNET-DRAFT                                                       FNV

    512 bit offset_basis = 9,
   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,
   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

G. Fowler, L. Noll, K. Vo & D. Eastlake                         [Page 8]

INTERNET-DRAFT                                                       FNV

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


5.2 FNV C Code


5.3 FNV Test Code


G. Fowler, L. Noll, K. Vo & D. Eastlake                         [Page 9]

INTERNET-DRAFT                                                       FNV

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.

G. Fowler, L. Noll, K. Vo & D. Eastlake                        [Page 10]

INTERNET-DRAFT                                                       FNV

8. References

   Below are the normative and informative references for this document.

8.1 Normative References


8.2 Informative References

   [FNV] - FNV web site:

   [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.

G. Fowler, L. Noll, K. Vo & D. Eastlake                        [Page 11]

INTERNET-DRAFT                                                       FNV

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

G. Fowler, L. Noll, K. Vo & D. Eastlake                        [Page 12]

INTERNET-DRAFT                                                       FNV

Author's Address

   Glenn Fowler
   AT&T Labs Research
   180 Park Avenue
   Florham Park, NJ 07932 USA


   Landon Curt Noll
   Cisco Systems
   170 West Tasman Drive
   San Jose, CA 95134 USA

   Telephone:   +1-408-424-1102

   Kiem-Phong Vo
   AT&T Labs Research
   180 Park Avenue
   Florham Park, NJ 07932 USA


   Donald Eastlake
   Huawei Technologies
   155 Beaver Street
   Milford, MA 01757 USA

   Telephone:   +1-508-333-2270

G. Fowler, L. Noll, K. Vo & D. Eastlake                        [Page 13]

INTERNET-DRAFT                                                       FNV

Copyright, Disclaimer, and Additional IPR Provisions

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   document authors. All rights reserved.

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G. Fowler, L. Noll, K. Vo & D. Eastlake                        [Page 14]