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. 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 Task Force (IETF), its areas, and its working groups. Note that other groups may also distribute working documents as Internet- Drafts. Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress." The list of current Internet-Drafts can be accessed at The list of Internet-Draft Shadow Directories can be accessed at 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 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 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 /\../\ 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] 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 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 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 = 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] INTERNET-DRAFT FNV 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 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 TBD 5.2 FNV C Code TBD 5.3 FNV Test Code TBD 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 None. 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 Email: URL: Landon Curt Noll Cisco Systems 170 West Tasman Drive San Jose, CA 95134 USA Telephone: +1-408-424-1102 Email: URL: Kiem-Phong Vo AT&T Labs Research 180 Park Avenue Florham Park, NJ 07932 USA Email: URL: Donald Eastlake Huawei Technologies 155 Beaver Street Milford, MA 01757 USA Telephone: +1-508-333-2270 EMail: G. Fowler, L. Noll, K. Vo & D. Eastlake [Page 13] INTERNET-DRAFT FNV Copyright, Disclaimer, and Additional IPR Provisions Copyright (c) 2011 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 ( 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 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 14]