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Run idnits with the --verbose option for more detailed information about the items above. -------------------------------------------------------------------------------- 1 Network Working Group Glenn Fowler 2 INTERNET-DRAFT AT&T Labs Research 3 Intended Status: Informational Landon Curt Noll 4 Cisco Systems 5 Kiem-Phong Vo 6 AT&T Labs Research 7 Donald Eastlake 8 Huawei Technologies 9 Expires: October 5, 2013 April 6, 2013 11 The FNV Non-Cryptographic Hash Algorithm 12 14 Abstract 16 FNV (Fowler/Noll/Vo) is a fast, non-cryptographic hash algorithm with 17 good dispersion. The purpose of this document is to make information 18 on FNV and open source code performing FNV conveniently available to 19 the Internet community. 21 Status of This Memo 23 This Internet-Draft is submitted to IETF in full conformance with the 24 provisions of BCP 78 and BCP 79. 26 Distribution of this document is unlimited. Comments should be sent 27 to the authors. 29 Internet-Drafts are working documents of the Internet Engineering 30 Task Force (IETF), its areas, and its working groups. Note that 31 other groups may also distribute working documents as Internet- 32 Drafts. 34 Internet-Drafts are draft documents valid for a maximum of six months 35 and may be updated, replaced, or obsoleted by other documents at any 36 time. It is inappropriate to use Internet-Drafts as reference 37 material or to cite them other than as "work in progress." 39 The list of current Internet-Drafts can be accessed at 40 http://www.ietf.org/1id-abstracts.html. The list of Internet-Draft 41 Shadow Directories can be accessed at 42 http://www.ietf.org/shadow.html. 44 Table of Contents 46 1. Introduction............................................3 48 2. FNV Basics..............................................4 49 2.1 FNV Primes.............................................4 50 2.2 FNV offset_basis.......................................5 51 2.3 FNV Endianism..........................................5 53 3. Other Hash Sizes and XOR Folding........................6 54 4. FNV Constants...........................................7 56 5. The Source Code.........................................9 57 5.1 FNV C Headers..........................................9 58 5.2 FNV C Code.............................................9 59 5.3 FNV Test Code..........................................9 61 6. Security Considerations................................10 62 6.1 Why is FNV Non-Cryptographic?.........................10 64 7. IANA Considerations....................................11 65 8. Acknowledgements.......................................11 67 9. References.............................................12 68 9.1 Normative References..................................12 69 9.2 Informative References................................12 71 Appendix A: Work Comparison with SHA-1....................13 72 Appendix B: Previous IETF Reference to FNV................14 73 Appendix C: A Few Test Vectors............................15 75 Appendix Z: Change Summary................................16 77 Author's Address..........................................18 79 1. Introduction 81 The FNV hash algorithm is based on an idea sent as reviewer comments 82 to the [IEEE] POSIX P1003.2 committee by Glenn Fowler and Phong Vo in 83 1991. In a subsequent ballot round Landon Curt Noll suggested an 84 improvement on their algorithm. Some people tried this hash and found 85 that it worked rather well. In an EMail message to Landon, they named 86 it the "Fowler/Noll/Vo" or FNV hash. [FNV] 88 FNV hashes are designed to be fast while maintaining a low collision 89 rate. The high dispersion of the FNV hashes makes them well suited 90 for hashing nearly identical strings such as URLs, hostnames, 91 filenames, text, IP addresses, etc. Their speed allows one to quickly 92 hash lots of data while maintaining a reasonably low collision rate. 93 However, they are generally not suitable for cryptographic use. (See 94 Section 6.1.) 96 The FNV hash is widely used, for example in DNS servers, the Twitter 97 service, database indexing hashes, major web search / indexing 98 engines, netnews history file Message-ID lookup functions, anti-spam 99 filters, a spellchecker programmed in Ada 95, flatassembler's open 100 source x86 assembler - user-defined symbol hashtree, non- 101 cryptographic file fingerprints, computing Unique IDs in DASM (DTN 102 Applications for Symbian Mobile-phones), Microsoft's hash_map 103 implementation for VC++ 2005, the realpath cache in PHP 5.x 104 (php-5.2.3/TSRM/tsrm_virtual_cwd.c), and many other uses. 106 A study has recommended FNV in connetion with the IPv6 Flow Label 107 field [IPv6flow]. 109 FNV hash algorithms and source code have been released into the 110 public domain. The authors of the FNV algorithm took deliberate steps 111 to disclose the algorithm in a public forum soon after it was 112 invented. More than a year passed after this public disclosure and 113 the authors deliberately took no steps to patent the FNV algorithm. 114 Therefore, it is safe to say that the FNV authors have no patent 115 claims on the FNV algorithm as published. 117 If you use an FNV function in an application, you are kindly 118 requested to send an EMail about it to: fnv-mail@asthe.com 120 2. FNV Basics 122 This document focuses on the FNV-1a function whose pseudo-code is as 123 follows: 125 hash = offset_basis 126 for each octet_of_data to be hashed 127 hash = hash xor octet_of_data 128 hash = hash * FNV_Prime 129 return hash 131 In the pseudo-code above, hash is a power-of-two number of bits (32, 132 64, ... 1024) and offset_basis and FNV_Prime depend on the size of 133 hash. 135 The FNV-1 algorithm is the same, including the values of offset_basis 136 and FNV_Prime, except that the order of the two lines with the "xor" 137 and multiply operations are reversed. Operational experience 138 indicates better hash dispersion for small amounts of data with 139 FNV-1a. FNV-0 is the same as FNV-1 but with offset_basis set to zero. 140 FNV-1a is suggested for general use. 142 2.1 FNV Primes 144 The theory behind FNV_Prime's is beyond the scope of this document 145 but the basic property to look for is how an FNV_Prime would impact 146 dispersion. Now, consider any n-bit FNV hash where n is >= 32 and 147 also a power of 2. For each such an n-bit FNV hash, an FNV_Prime p is 148 defined as: 150 When s is an integer and 4 < s < 11, then FNV_Prime is the 151 smallest prime p of the form: 153 256**int((5 + 2^s)/12) + 2**8 + b 155 where b is an integer such that: 157 0 < b < 2**8 158 The number of one-bits in b is 4 or 5 160 and where p mod (2**40 - 2**24 - 1) > (2**24 + 2**8 + 2**7). 162 Experimentally, FNV_Primes matching the above constraints tend to 163 have better dispersion properties. They improve the polynomial 164 feedback characteristic when an FNV_Prime multiplies an intermediate 165 hash value. As such, the hash values produced are more scattered 166 throughout the n-bit hash space. 168 The case where s < 5 is not considered because the resulting hash 169 quality is too low. Such small hashes can, if desired, be derived 170 from a 32 bit FNV hash by XOR folding (see Section 3). The case where 171 s > 10 is not considered because of the doubtful utility of such 172 large FNV hashes and because the criteria for such large FNV_Primes 173 is more complex, due to the sparsity of such large primes, and would 174 needlessly clutter the criteria given above. 176 Per the above constraints, an FNV_Prime should have only 6 or 7 one- 177 bits in it. Therefore, some compilers may seek to improve the 178 performance of a multiplication with an FNV_Prime by replacing the 179 multiplication with shifts and adds. However, note that the 180 performance of this substitution is highly hardware-dependent and 181 should be done with care. FNV_Primes were selected primarily for the 182 quality of resulting hash function, not for compiler optimization. 184 2.2 FNV offset_basis 186 The offset_basis values for the n-bit FNV-1a algorithms are computed 187 by applying the n-bit FNV-0 algorithm to the 32 octets representing 188 the following character string in [ASCII]: 190 chongo /\../\ 192 The \'s in the above string are not C-style escape characters. In C- 193 string notation, these 32 octets are: 195 "chongo /\\../\\" 197 2.3 FNV Endianism 199 For persistent storage or interoperability between different hardware 200 platforms, an FNV hash shall be represented in the little endian 201 format. That is, the FNV hash will be stored in an array hash[N] with 202 N bytes such that its integer value can be retrieved as follows: 204 unsigned char hash[N]; 205 for ( i = N-1, value = 0; i >= 0; --i ) 206 value = value << 8 + hash[i]; 208 Of course, when FNV hashes are used in a single process or a group of 209 processes sharing memory on processors with compatible endian-ness, 210 the natural endianness of those processors can be used regardless of 211 its type, little, big, or some other exotic form. 213 3. Other Hash Sizes and XOR Folding 215 Many hash uses require a hash that is not one of the FNV sizes for 216 which constants are provided in Section 4. If a larger hash size is 217 needed, please contact the authors of this document. 219 Most hash applications make use of a hash that is a fixed size binary 220 field. Assume that k bits of hash are desired and k is less than 1024 221 but not one of the sizes for which constants are provided in Section 222 4. The recommended technique is to take the smallest FNV hash of size 223 S, where S is larger than k, and calculate the desired hash using xor 224 folding as shown below. The final bit masking operation is logically 225 unnecessarily if the size of hash is exactly the number of desired 226 bits. 228 temp = FNV_S ( data-to-be-hashed ) 229 hash = ( temp xor temp>>k ) bitwise-and ( 2**k - 1 ) 231 Hash functions are a trade-off between speed and strength. For 232 example, a somewhat stronger hash may be obtained for exact FNV sizes 233 by calculating an FNV twice as long as the desired output ( S = 2*k ) 234 and performing such data folding using a k equal to the size of the 235 desired output. However, if a much stronger hash, for example one 236 suitable for cryptographic applications, is wanted, algorithms 237 designed for that purpose, such as those in [RFC6234], should be 238 used. 240 If it is desired to obtain a hash result that is a value between 0 241 and max, where max is a not a power of two, simply choose an FNV hash 242 size S such that 2**S > max. Then calculate the following: 244 FNV_S mod ( max+1 ) 246 The resulting remainder will be in the range desired but will suffer 247 from a bias against large values with the bias being larger if 2**S 248 is only a little bigger than max. If this bias is acceptable, no 249 further processing is needed. If this bias is unacceptable, it can be 250 avoided by retrying for certain high values of hash, as follows, 251 before applying the mod operation above: 253 X = ( int( ( 2**S - 1 ) / ( max+1 ) ) ) * ( max+1 ) 254 while ( hash >= X ) 255 hash = ( hash * FNV_Prime ) + offset_basis 257 4. FNV Constants 259 The FNV Primes are as follows: 261 32 bit FNV_Prime = 2**24 + 2**8 + 0x93 = 16,777,619 262 = 0x01000193 264 64 bit FNV_Prime = 2**40 + 2**8 + 0xB3 = 1,099,511,628,211 265 = 0x00000100 000001B3 267 128 bit FNV_Prime = 2**88 + 2**8 + 0x3B = 268 309,485,009,821,345,068,724,781,371 269 = 0x00000000 01000000 00000000 0000013B 271 256 bit FNV_Prime = 2**168 + 2**8 + 0x63 = 272 374,144,419,156,711,147,060,143,317,175,368,453,031,918,731,002,211 = 273 0x0000000000000000 0000010000000000 0000000000000000 0000000000000163 275 512 bit FNV_Prime = 2**344 + 2**8 + 0x57 = 35, 276 835,915,874,844,867,368,919,076,489,095,108,449,946,327,955,754,392, 277 558,399,825,615,420,669,938,882,575,126,094,039,892,345,713,852,759 = 278 0x0000000000000000 0000000000000000 0000000001000000 0000000000000000 279 0000000000000000 0000000000000000 0000000000000000 0000000000000157 281 1024 bit FNV_Prime = 2**680 + 2**8 + 0x8D = 5, 282 016,456,510,113,118,655,434,598,811,035,278,955,030,765,345,404,790, 283 744,303,017,523,831,112,055,108,147,451,509,157,692,220,295,382,716, 284 162,651,878,526,895,249,385,292,291,816,524,375,083,746,691,371,804, 285 094,271,873,160,484,737,966,720,260,389,217,684,476,157,468,082,573 = 286 0x0000000000000000 0000000000000000 0000000000000000 0000000000000000 287 0000000000000000 0000010000000000 0000000000000000 0000000000000000 288 0000000000000000 0000000000000000 0000000000000000 0000000000000000 289 0000000000000000 0000000000000000 0000000000000000 000000000000018D 291 The FNV offset_basis values are as follows: 293 32 bit offset_basis = 2,166,136,261 = 0x811C9DC5 295 64 bit offset_basis = 14695981039346656037 = 0xCBF29CE4 84222325 297 128 bit offset_basis = 144066263297769815596495629667062367629 = 298 0x6C62272E 07BB0142 62B82175 6295C58D 300 256 bit offset_basis = 100,029,257,958,052,580,907,070,968, 301 620,625,704,837,092,796,014,241,193,945,225,284,501,741,471,925,557 = 302 0xDD268DBCAAC55036 2D98C384C4E576CC C8B1536847B6BBB3 1023B4C8CAEE0535 303 512 bit offset_basis = 9, 304 659,303,129,496,669,498,009,435,400,716,310,466,090,418,745,672,637, 305 896,108,374,329,434,462,657,994,582,932,197,716,438,449,813,051,892, 306 206,539,805,784,495,328,239,340,083,876,191,928,701,583,869,517,785 = 307 0xB86DB0B1171F4416 DCA1E50F309990AC AC87D059C9000000 0000000000000D21 308 E948F68A34C192F6 2EA79BC942DBE7CE 182036415F56E34B AC982AAC4AFE9FD9 310 1024 bit offset_basis = 14,197,795,064,947,621,068,722,070,641,403, 311 218,320,880,622,795,441,933,960,878,474,914,617,582,723,252,296,732, 312 303,717,722,150,864,096,521,202,355,549,365,628,174,669,108,571,814, 313 760,471,015,076,148,029,755,969,804,077,320,157,692,458,563,003,215, 314 304,957,150,157,403,644,460,363,550,505,412,711,285,966,361,610,267, 315 868,082,893,823,963,790,439,336,411,086,884,584,107,735,010,676,915 = 316 0x0000000000000000 005F7A76758ECC4D 32E56D5A591028B7 4B29FC4223FDADA1 317 6C3BF34EDA3674DA 9A21D90000000000 0000000000000000 0000000000000000 318 0000000000000000 0000000000000000 0000000000000000 000000000004C6D7 319 EB6E73802734510A 555F256CC005AE55 6BDE8CC9C6A93B21 AFF4B16C71EE90B3 321 5. The Source Code 323 The following sub-sections are intended, in later versions, to 324 include reference C source code and a test driver for FNV-1a. 326 5.1 FNV C Headers 328 TBD 330 5.2 FNV C Code 332 TBD 334 5.3 FNV Test Code 336 TBD 338 6. Security Considerations 340 This document is intended to provide convenient open source access by 341 the Internet community to the FNV non-cryptographic hash. No 342 assertion of suitability for cryptographic applications is made for 343 the FNV hash algorithms. 345 6.1 Why is FNV Non-Cryptographic? 347 A full discussion of cryptographic hash requirements and strength is 348 beyond the scope of this document. However, here are three 349 characteristics of FNV that would generally be considered to make it 350 non-cryptographic: 352 1. Work Factor - To make brute force inversion hard, a cryptographic 353 hash should be computationally expensive, especially for a general 354 purpose processor. But FNV is designed to be very inexpensive on a 355 general-purpose processor. (See Appendix A.) 357 2. Sticky State - A cryptographic hash should not have a state in 358 which it can stick for a plausible input pattern. But, in the very 359 unlikely event that the FNV hash variable becomes zero and the 360 input is a sequence of zeros, the hash variable will remain at 361 zero until there is a non-zero input byte and the final hash value 362 will be unaffected by the length of that sequence of zero input 363 bytes. Of course, for the common case of fixed length input, this 364 would not be significant because the number of non-zero bytes 365 would vary inversely with the number of zero bytes and for some 366 types of input runs of zeros do not occur. Furthermore, the 367 inclusion of even a little unpredictable input may be sufficient 368 to stop an adversary from inducing a zero hash variable. 370 3. Diffusion - Every output bit of a cryptographic hash should be an 371 equally complex function of every input bit. But it is easy to see 372 that the least significant bit of a direct FNV hash is the XOR of 373 the least significant bits of every input byte and does not depend 374 on any other input bit. While more complex, the second least 375 significant bit of an FNV hash has a similar weakness. If these 376 properties are considered a problem, they can be easily fixed by 377 XOR folding (see Section 3). 379 Nevertheless, none of the above have proven to be a problem in actual 380 practice for the many applications of FNV. 382 7. IANA Considerations 384 This document requires no IANA Actions. RFC Editor Note: please 385 delete this section before publication. 387 8. Acknowledgements 389 The contributions of the following are gratefully acknowledged: 391 Frank Ellermann, Bob Moskowitz, and Stefan Santesson. 393 9. References 395 Below are the normative and informative references for this document. 397 9.1 Normative References 399 [ASCII] - American National Standards Institute (formerly United 400 States of America Standards Institute), "USA Code for 401 Information Interchange", ANSI X3.4-1968, 1968. ANSI X3.4-1968 402 has been replaced by newer versions with slight modifications, 403 but the 1968 version remains definitive for the Internet. 405 9.2 Informative References 407 [FNV] - FNV web site: 408 http://www.isthe.com/chongo/tech/comp/fnv/index.html 410 [IEEE] - http://www.ieee.org 412 [IPv6flow] - https://researchspace.auckland.ac.nz/bitstream/handle/ 413 2292/13240/flowhashRep.pdf 415 [RFC3174] - Eastlake 3rd, D. and P. Jones, "US Secure Hash Algorithm 416 1 (SHA1)", RFC 3174, September 2001. 418 [RFC6194] - Polk, T., Chen, L., Turner, S., and P. Hoffman, "Security 419 Considerations for the SHA-0 and SHA-1 Message-Digest 420 Algorithms", RFC 6194, March 2011. 422 [RFC6234] - Eastlake 3rd, D. and T. Hansen, "US Secure Hash 423 Algorithms (SHA and SHA-based HMAC and HKDF)", RFC 6234, May 424 2011. 426 Appendix A: Work Comparison with SHA-1 428 This section provides a simplistic rough comparison of the level of 429 effort required per input byte to compute FNV-1a and SHA-1 [RFC3174]. 431 Ignoring transfer of control and conditional tests and equating all 432 logical and arithmetic operations, FNV requires 2 operations per 433 byte, an XOR and a multiply. 435 SHA-1 is a relatively weak cryptographic hash producing a 160-bit 436 hash. It that has been partially broken [RFC6194]. It is actually 437 designed to accept a bit vector input although almost all computer 438 uses apply it to an integer number of bytes. It processes blocks of 439 512 bits (64 bytes) and we estimate the effort involved in SHA-1 440 processing a full block. Ignoring SHA-1 initial set up, transfer of 441 control, and conditional tests, but counting all logical and 442 arithmetic operations, including counting indexing as an addition, 443 SHA-1 requires 1,744 operations per 64 bytes block or 27.25 444 operations per byte. So by this rough measure, it is a little over 13 445 times the effort of FNV for large amounts of data. However, FNV is 446 commonly used for small inputs. Using the above method, for inputs of 447 N bytes, where N is <= 55 so SHA-1 will take one block (SHA-1 448 includes padding and an 8-byte length at the end of the data in the 449 last block), the ratio of the effort for SHA-1 to the effort for FNV 450 will be 872/N. For example, with an 8 byte input, SHA-1 will take 109 451 times as much effort as FNV. 453 Stronger cryptographic functions than SHA-1 generally have an even 454 high work factor. 456 Appendix B: Previous IETF Reference to FNV 458 FNV-1a was referenced in draft-ietf-tls-cached-info-08.txt that has 459 since expired. It was later decided that it would be better to use a 460 cryptographic hash for that application. 462 Below is the Jave code for FNV64 from that TLS draft include by the 463 kind permission of the author: 465 /** 466 * Java code sample, implementing 64 bit FNV-1a 467 * By Stefan Santesson 468 */ 470 import java.math.BigInteger; 472 public class FNV { 474 static public BigInteger getFNV1aToByte(byte[] inp) { 476 BigInteger m = new BigInteger("2").pow(64); 477 BigInteger fnvPrime = new BigInteger("1099511628211"); 478 BigInteger fnvOffsetBasis = 479 new BigInteger("14695981039346656037"); 481 BigInteger digest = fnvOffsetBasis; 483 for (byte b : inp) { 484 digest = digest.xor(BigInteger.valueOf((int) b & 255)); 485 digest = digest.multiply(fnvPrime).mod(m); 486 } 487 return digest; 489 } 490 } 492 Appendix C: A Few Test Vectors 494 Below are a few test vectors in the form of ASCII strings and their 495 FNV32 and FNV64 hashes using the FNV-1a algorithm. 497 Strings without null (zero byte) termination: 499 String FNV32 FNV64 500 "" 0x811c9dc5 0xcbf29ce484222325 501 "a" 0xe40c292c 0xaf63dc4c8601ec8c 502 "foobar" 0xbf9cf968 0x85944171f73967e8 504 Strings including null (zero byte) termination: 506 String FNV32 FNV64 507 "" 0x050c5d1f 0xaf63bd4c8601b7df 508 "a" 0x2b24d044 0x089be207b544f1e4 509 "foobar" 0x0c1c9eb8 0x34531ca7168b8f38 511 Appendix Z: Change Summary 513 RFC Editor Note: Please delete this appendix on publication. 515 From -00 to -01 517 1. Add Security Considerations section on why FNV is non- 518 cryptographic. 520 2. Add Appendix A on a work factor comparison with SHA-1. 522 3. Add Appendix B concerning previous IETF draft referenced to FNV. 524 4. Minor editorial changes. 526 From -01 to -02 528 1. Correct FNV_Prime determination criteria and add note as to why s 529 < 5 and s > 10 are not considered. 531 2. Add acknowledgements list. 533 3. Add a couple of references. 535 4. Minor editorial changes. 537 From -02 to -03 539 1. Replace direct reference to US-ASCII standard with reference to 540 RFC 20. 542 2. Update dates and verion number. 544 3. Minor editing changes. 546 From -03 to -04 548 1. Change reference to RFC 20 back to a reference to the ANSI 1968 549 ASCII standard. 551 2. Minor addition to Section 6, point 3. 553 3. Update dates and version number. 555 4. Minor editing changes. 557 From -04 to -05 559 1. Add Twitter as a use example and IPv6 flow hash study reference. 561 2. Update dates and version number. 563 Author's Address 565 Glenn Fowler 566 AT&T Labs Research 567 180 Park Avenue 568 Florham Park, NJ 07932 USA 570 Email: gsf@research.att.com 571 URL: http://www.research.att.com/~gsf/ 573 Landon Curt Noll 574 Cisco Systems 575 170 West Tasman Drive 576 San Jose, CA 95134 USA 578 Telephone: +1-408-424-1102 579 Email: fnv-rfc-mail@asthe.com 580 URL: http://www.isthe.com/chongo/index.html 582 Kiem-Phong Vo 583 AT&T Labs Research 584 180 Park Avenue 585 Florham Park, NJ 07932 USA 587 Email: kpv@research.att.com 588 URL: http://www.research.att.com/info/kpv/ 590 Donald Eastlake 591 Huawei Technologies 592 155 Beaver Street 593 Milford, MA 01757 USA 595 Telephone: +1-508-333-2270 596 EMail: d3e3e3@gmail.com 598 Copyright, Disclaimer, and Additional IPR Provisions 600 Copyright (c) 2013 IETF Trust and the persons identified as the 601 document authors. All rights reserved. 603 This document is subject to BCP 78 and the IETF Trust's Legal 604 Provisions Relating to IETF Documents 605 (http://trustee.ietf.org/license-info) in effect on the date of 606 publication of this document. Please review these documents 607 carefully, as they describe your rights and restrictions with respect 608 to this document. Code Components extracted from this document must 609 include Simplified BSD License text as described in Section 4.e of 610 the Trust Legal Provisions and are provided without warranty as 611 described in the Simplified BSD License. This Internet-Draft is 612 submitted to IETF in full conformance with the provisions of BCP 78 613 and BCP 79.