## The FNV Non-Cryptographic Hash Algorithm

draft-eastlake-fnv-08

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Authors | Glenn Fowler , Landon Noll , Kiem-Phong Vo , Donald Eastlake | ||

Last updated | 2014-10-06 | ||

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Network Working Group Glenn Fowler INTERNET-DRAFT Google Intended Status: Informational Landon Curt Noll Cisco Systems Kiem-Phong Vo Google Donald Eastlake Huawei Technologies Expires: April 5, 2015 October 6, 2014 The FNV Non-Cryptographic Hash Algorithm <draft-eastlake-fnv-08.txt> 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 http://www.ietf.org/1id-abstracts.html. The list of Internet-Draft Shadow Directories can be accessed at http://www.ietf.org/shadow.html. 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-1a Code............................................9 5.1.1 FNV32 Code...........................................9 5.1.2 FNV64 C Code.........................................9 5.1.3 FNV128 Code..........................................9 5.1.4 FNV256 C Code........................................9 5.1.5 FNV512 C Code........................................9 5.1.6 FNV1024 C Code......................................10 5.2 FNV Test Code.........................................10 6. Security Considerations................................11 6.1 Why is FNV Non-Cryptographic?.........................11 7. IANA Considerations....................................12 Acknowledgements..........................................12 Normative References......................................13 Informative References....................................13 Appendix A: Work Comparison with SHA-1....................14 Appendix B: Previous IETF Reference to FNV................15 Appendix C: A Few Test Vectors............................16 Appendix Z: Change Summary................................17 Author's Address..........................................19 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. 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] 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: 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] INTERNET-DRAFT FNV 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 <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 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] 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 provide reference C source code and a test driver for FNV-1a. Section 5.1 provides the direct FNV-1a function for each of the lengths for which it is specified in this document. Note that for applications of FNV-32 where 32-bit integers are supported and FNV-64 where 64-bit integers are supported, the code is sufficiently simple that use of open coding or macros may be more appropriate to maximize performance. Section 5.2 provides a test driver. 5.1 FNV-1a Code TBD 5.1.1 FNV32 Code TBD 5.1.2 FNV64 C Code TBD 5.1.3 FNV128 Code TBD 5.1.4 FNV256 C Code TBD 5.1.5 FNV512 C Code TBD G. Fowler, L. Noll, K. Vo & D. Eastlake [Page 9] INTERNET-DRAFT FNV 5.1.6 FNV1024 C Code TBD 5.2 FNV Test Code TBD G. Fowler, L. Noll, K. Vo & D. Eastlake [Page 10] 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. 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 through seventh least significant bits of an FNV hash have a similar weakness; only the top bit of the bottom byte of output, and higher order bits, depend on all input bits. 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. G. Fowler, L. Noll, K. Vo & D. Eastlake [Page 11] INTERNET-DRAFT FNV 7. IANA Considerations This document requires no IANA Actions. RFC Editor Note: please delete this section before publication. Acknowledgements The contributions of the following are gratefully acknowledged: Frank Ellermann, Bob Moskowitz, and Stefan Santesson. G. Fowler, L. Noll, K. Vo & D. Eastlake [Page 12] INTERNET-DRAFT FNV 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. 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 13] INTERNET-DRAFT FNV 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. G. Fowler, L. Noll, K. Vo & D. Eastlake [Page 14] INTERNET-DRAFT FNV 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: <CODE BEGINS> /** * 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; } } <CODE ENDS> G. Fowler, L. Noll, K. Vo & D. Eastlake [Page 15] INTERNET-DRAFT FNV 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 G. Fowler, L. Noll, K. Vo & D. Eastlake [Page 16] INTERNET-DRAFT FNV 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 17] INTERNET-DRAFT FNV 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. From -05 to -06 1. Add code subsections. 2. Update dates and version number. From -06 to -07 to -08 1. Update Author info. 2. Minor edits. G. Fowler, L. Noll, K. Vo & D. Eastlake [Page 18] INTERNET-DRAFT FNV Author's Address Glenn Fowler Google Email: glenn.s.fowler@gmail.com Landon Curt Noll Cisco Systems 170 West Tasman Drive San Jose, CA 95134 USA Telephone: +1-408-424-1102 Email: fnv-ietf2-mail@asthe.com URL: http://www.isthe.com/chongo/index.html Kiem-Phong Vo Google Email: phongvo@gmail.com Donald Eastlake Huawei Technologies 155 Beaver Street Milford, MA 01757 USA Telephone: +1-508-333-2270 EMail: d3e3e3@gmail.com G. Fowler, L. Noll, K. Vo & D. Eastlake [Page 19] INTERNET-DRAFT FNV Copyright, Disclaimer, and Additional IPR Provisions Copyright (c) 2014 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 20]