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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: March 31, 2013 October 1, 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 Code.............................................9 58 5.1.1 FNV32 C Code.........................................9 59 5.1.2 FNV64 C Code.........................................9 60 5.1.3 FNV128 C Code........................................9 61 5.2 FNV Test Code..........................................9 63 6. Security Considerations................................10 64 6.1 Why is FNV Non-Cryptographic?.........................10 66 7. IANA Considerations....................................11 67 8. Acknowledgements.......................................11 69 9. References.............................................12 70 9.1 Normative References..................................12 71 9.2 Informative References................................12 73 Appendix A: Work Comparison with SHA-1....................13 74 Appendix B: Previous IETF Reference to FNV................14 75 Appendix C: A Few Test Vectors............................15 76 Appendix Z: Change Summary................................16 78 Author's Address..........................................18 80 1. Introduction 82 The FNV hash algorithm is based on an idea sent as reviewer comments 83 to the [IEEE] POSIX P1003.2 committee by Glenn Fowler and Phong Vo in 84 1991. In a subsequent ballot round Landon Curt Noll suggested an 85 improvement on their algorithm. Some people tried this hash and found 86 that it worked rather well. In an EMail message to Landon, they named 87 it the "Fowler/Noll/Vo" or FNV hash. [FNV] 89 FNV hashes are designed to be fast while maintaining a low collision 90 rate. The high dispersion of the FNV hashes makes them well suited 91 for hashing nearly identical strings such as URLs, hostnames, 92 filenames, text, IP addresses, etc. Their speed allows one to quickly 93 hash lots of data while maintaining a reasonably low collision rate. 94 However, they are generally not suitable for cryptographic use. (See 95 Section 6.1.) 97 The FNV hash is widely used, for example in DNS servers, the Twitter 98 service, database indexing hashes, major web search / indexing 99 engines, netnews history file Message-ID lookup functions, anti-spam 100 filters, a spellchecker programmed in Ada 95, flatassembler's open 101 source x86 assembler - user-defined symbol hashtree, non- 102 cryptographic file fingerprints, computing Unique IDs in DASM (DTN 103 Applications for Symbian Mobile-phones), Microsoft's hash_map 104 implementation for VC++ 2005, the realpath cache in PHP 5.x 105 (php-5.2.3/TSRM/tsrm_virtual_cwd.c), and many other uses. 107 A study has recommended FNV in connetion with the IPv6 Flow Label 108 field [IPv6flow]. 110 FNV hash algorithms and source code have been released into the 111 public domain. The authors of the FNV algorithm took deliberate steps 112 to disclose the algorithm in a public forum soon after it was 113 invented. More than a year passed after this public disclosure and 114 the authors deliberately took no steps to patent the FNV algorithm. 115 Therefore, it is safe to say that the FNV authors have no patent 116 claims on the FNV algorithm as published. 118 If you use an FNV function in an application, you are kindly 119 requested to send an EMail about it to: fnv-mail@asthe.com 121 2. FNV Basics 123 This document focuses on the FNV-1a function whose pseudo-code is as 124 follows: 126 hash = offset_basis 127 for each octet_of_data to be hashed 128 hash = hash xor octet_of_data 129 hash = hash * FNV_Prime 130 return hash 132 In the pseudo-code above, hash is a power-of-two number of bits (32, 133 64, ... 1024) and offset_basis and FNV_Prime depend on the size of 134 hash. 136 The FNV-1 algorithm is the same, including the values of offset_basis 137 and FNV_Prime, except that the order of the two lines with the "xor" 138 and multiply operations are reversed. Operational experience 139 indicates better hash dispersion for small amounts of data with 140 FNV-1a. FNV-0 is the same as FNV-1 but with offset_basis set to zero. 141 FNV-1a is suggested for general use. 143 2.1 FNV Primes 145 The theory behind FNV_Prime's is beyond the scope of this document 146 but the basic property to look for is how an FNV_Prime would impact 147 dispersion. Now, consider any n-bit FNV hash where n is >= 32 and 148 also a power of 2. For each such an n-bit FNV hash, an FNV_Prime p is 149 defined as: 151 When s is an integer and 4 < s < 11, then FNV_Prime is the 152 smallest prime p of the form: 154 256**int((5 + 2^s)/12) + 2**8 + b 156 where b is an integer such that: 158 0 < b < 2**8 159 The number of one-bits in b is 4 or 5 161 and where p mod (2**40 - 2**24 - 1) > (2**24 + 2**8 + 2**7). 163 Experimentally, FNV_Primes matching the above constraints tend to 164 have better dispersion properties. They improve the polynomial 165 feedback characteristic when an FNV_Prime multiplies an intermediate 166 hash value. As such, the hash values produced are more scattered 167 throughout the n-bit hash space. 169 The case where s < 5 is not considered because the resulting hash 170 quality is too low. Such small hashes can, if desired, be derived 171 from a 32 bit FNV hash by XOR folding (see Section 3). The case where 172 s > 10 is not considered because of the doubtful utility of such 173 large FNV hashes and because the criteria for such large FNV_Primes 174 is more complex, due to the sparsity of such large primes, and would 175 needlessly clutter the criteria given above. 177 Per the above constraints, an FNV_Prime should have only 6 or 7 one- 178 bits in it. Therefore, some compilers may seek to improve the 179 performance of a multiplication with an FNV_Prime by replacing the 180 multiplication with shifts and adds. However, note that the 181 performance of this substitution is highly hardware-dependent and 182 should be done with care. FNV_Primes were selected primarily for the 183 quality of resulting hash function, not for compiler optimization. 185 2.2 FNV offset_basis 187 The offset_basis values for the n-bit FNV-1a algorithms are computed 188 by applying the n-bit FNV-0 algorithm to the 32 octets representing 189 the following character string in [ASCII]: 191 chongo /\../\ 193 The \'s in the above string are not C-style escape characters. In C- 194 string notation, these 32 octets are: 196 "chongo /\\../\\" 198 2.3 FNV Endianism 200 For persistent storage or interoperability between different hardware 201 platforms, an FNV hash shall be represented in the little endian 202 format. That is, the FNV hash will be stored in an array hash[N] with 203 N bytes such that its integer value can be retrieved as follows: 205 unsigned char hash[N]; 206 for ( i = N-1, value = 0; i >= 0; --i ) 207 value = value << 8 + hash[i]; 209 Of course, when FNV hashes are used in a single process or a group of 210 processes sharing memory on processors with compatible endian-ness, 211 the natural endianness of those processors can be used regardless of 212 its type, little, big, or some other exotic form. 214 3. Other Hash Sizes and XOR Folding 216 Many hash uses require a hash that is not one of the FNV sizes for 217 which constants are provided in Section 4. If a larger hash size is 218 needed, please contact the authors of this document. 220 Most hash applications make use of a hash that is a fixed size binary 221 field. Assume that k bits of hash are desired and k is less than 1024 222 but not one of the sizes for which constants are provided in Section 223 4. The recommended technique is to take the smallest FNV hash of size 224 S, where S is larger than k, and calculate the desired hash using xor 225 folding as shown below. The final bit masking operation is logically 226 unnecessarily if the size of hash is exactly the number of desired 227 bits. 229 temp = FNV_S ( data-to-be-hashed ) 230 hash = ( temp xor temp>>k ) bitwise-and ( 2**k - 1 ) 232 Hash functions are a trade-off between speed and strength. For 233 example, a somewhat stronger hash may be obtained for exact FNV sizes 234 by calculating an FNV twice as long as the desired output ( S = 2*k ) 235 and performing such data folding using a k equal to the size of the 236 desired output. However, if a much stronger hash, for example one 237 suitable for cryptographic applications, is wanted, algorithms 238 designed for that purpose, such as those in [RFC6234], should be 239 used. 241 If it is desired to obtain a hash result that is a value between 0 242 and max, where max is a not a power of two, simply choose an FNV hash 243 size S such that 2**S > max. Then calculate the following: 245 FNV_S mod ( max+1 ) 247 The resulting remainder will be in the range desired but will suffer 248 from a bias against large values with the bias being larger if 2**S 249 is only a little bigger than max. If this bias is acceptable, no 250 further processing is needed. If this bias is unacceptable, it can be 251 avoided by retrying for certain high values of hash, as follows, 252 before applying the mod operation above: 254 X = ( int( ( 2**S - 1 ) / ( max+1 ) ) ) * ( max+1 ) 255 while ( hash >= X ) 256 hash = ( hash * FNV_Prime ) + offset_basis 258 4. FNV Constants 260 The FNV Primes are as follows: 262 32 bit FNV_Prime = 2**24 + 2**8 + 0x93 = 16,777,619 263 = 0x01000193 265 64 bit FNV_Prime = 2**40 + 2**8 + 0xB3 = 1,099,511,628,211 266 = 0x00000100 000001B3 268 128 bit FNV_Prime = 2**88 + 2**8 + 0x3B = 269 309,485,009,821,345,068,724,781,371 270 = 0x00000000 01000000 00000000 0000013B 272 256 bit FNV_Prime = 2**168 + 2**8 + 0x63 = 273 374,144,419,156,711,147,060,143,317,175,368,453,031,918,731,002,211 = 274 0x0000000000000000 0000010000000000 0000000000000000 0000000000000163 276 512 bit FNV_Prime = 2**344 + 2**8 + 0x57 = 35, 277 835,915,874,844,867,368,919,076,489,095,108,449,946,327,955,754,392, 278 558,399,825,615,420,669,938,882,575,126,094,039,892,345,713,852,759 = 279 0x0000000000000000 0000000000000000 0000000001000000 0000000000000000 280 0000000000000000 0000000000000000 0000000000000000 0000000000000157 282 1024 bit FNV_Prime = 2**680 + 2**8 + 0x8D = 5, 283 016,456,510,113,118,655,434,598,811,035,278,955,030,765,345,404,790, 284 744,303,017,523,831,112,055,108,147,451,509,157,692,220,295,382,716, 285 162,651,878,526,895,249,385,292,291,816,524,375,083,746,691,371,804, 286 094,271,873,160,484,737,966,720,260,389,217,684,476,157,468,082,573 = 287 0x0000000000000000 0000000000000000 0000000000000000 0000000000000000 288 0000000000000000 0000010000000000 0000000000000000 0000000000000000 289 0000000000000000 0000000000000000 0000000000000000 0000000000000000 290 0000000000000000 0000000000000000 0000000000000000 000000000000018D 292 The FNV offset_basis values are as follows: 294 32 bit offset_basis = 2,166,136,261 = 0x811C9DC5 296 64 bit offset_basis = 14695981039346656037 = 0xCBF29CE4 84222325 298 128 bit offset_basis = 144066263297769815596495629667062367629 = 299 0x6C62272E 07BB0142 62B82175 6295C58D 301 256 bit offset_basis = 100,029,257,958,052,580,907,070,968, 302 620,625,704,837,092,796,014,241,193,945,225,284,501,741,471,925,557 = 303 0xDD268DBCAAC55036 2D98C384C4E576CC C8B1536847B6BBB3 1023B4C8CAEE0535 304 512 bit offset_basis = 9, 305 659,303,129,496,669,498,009,435,400,716,310,466,090,418,745,672,637, 306 896,108,374,329,434,462,657,994,582,932,197,716,438,449,813,051,892, 307 206,539,805,784,495,328,239,340,083,876,191,928,701,583,869,517,785 = 308 0xB86DB0B1171F4416 DCA1E50F309990AC AC87D059C9000000 0000000000000D21 309 E948F68A34C192F6 2EA79BC942DBE7CE 182036415F56E34B AC982AAC4AFE9FD9 311 1024 bit offset_basis = 14,197,795,064,947,621,068,722,070,641,403, 312 218,320,880,622,795,441,933,960,878,474,914,617,582,723,252,296,732, 313 303,717,722,150,864,096,521,202,355,549,365,628,174,669,108,571,814, 314 760,471,015,076,148,029,755,969,804,077,320,157,692,458,563,003,215, 315 304,957,150,157,403,644,460,363,550,505,412,711,285,966,361,610,267, 316 868,082,893,823,963,790,439,336,411,086,884,584,107,735,010,676,915 = 317 0x0000000000000000 005F7A76758ECC4D 32E56D5A591028B7 4B29FC4223FDADA1 318 6C3BF34EDA3674DA 9A21D90000000000 0000000000000000 0000000000000000 319 0000000000000000 0000000000000000 0000000000000000 000000000004C6D7 320 EB6E73802734510A 555F256CC005AE55 6BDE8CC9C6A93B21 AFF4B16C71EE90B3 322 5. The Source Code 324 The following sub-sections are intended, in later versions, to 325 include reference C source code and a test driver for FNV-1a. 327 5.1 FNV C Code 329 5.1.1 FNV32 C Code 331 TBD 333 5.1.2 FNV64 C Code 335 TBD 337 5.1.3 FNV128 C Code 339 TBD 341 5.2 FNV Test Code 343 TBD 345 6. Security Considerations 347 This document is intended to provide convenient open source access by 348 the Internet community to the FNV non-cryptographic hash. No 349 assertion of suitability for cryptographic applications is made for 350 the FNV hash algorithms. 352 6.1 Why is FNV Non-Cryptographic? 354 A full discussion of cryptographic hash requirements and strength is 355 beyond the scope of this document. However, here are three 356 characteristics of FNV that would generally be considered to make it 357 non-cryptographic: 359 1. Work Factor - To make brute force inversion hard, a cryptographic 360 hash should be computationally expensive, especially for a general 361 purpose processor. But FNV is designed to be very inexpensive on a 362 general-purpose processor. (See Appendix A.) 364 2. Sticky State - A cryptographic hash should not have a state in 365 which it can stick for a plausible input pattern. But, in the very 366 unlikely event that the FNV hash variable becomes zero and the 367 input is a sequence of zeros, the hash variable will remain at 368 zero until there is a non-zero input byte and the final hash value 369 will be unaffected by the length of that sequence of zero input 370 bytes. Of course, for the common case of fixed length input, this 371 would not be significant because the number of non-zero bytes 372 would vary inversely with the number of zero bytes and for some 373 types of input runs of zeros do not occur. Furthermore, the 374 inclusion of even a little unpredictable input may be sufficient 375 to stop an adversary from inducing a zero hash variable. 377 3. Diffusion - Every output bit of a cryptographic hash should be an 378 equally complex function of every input bit. But it is easy to see 379 that the least significant bit of a direct FNV hash is the XOR of 380 the least significant bits of every input byte and does not depend 381 on any other input bit. While more complex, the second least 382 significant bit of an FNV hash has a similar weakness. If these 383 properties are considered a problem, they can be easily fixed by 384 XOR folding (see Section 3). 386 Nevertheless, none of the above have proven to be a problem in actual 387 practice for the many applications of FNV. 389 7. IANA Considerations 391 This document requires no IANA Actions. RFC Editor Note: please 392 delete this section before publication. 394 8. Acknowledgements 396 The contributions of the following are gratefully acknowledged: 398 Frank Ellermann, Bob Moskowitz, and Stefan Santesson. 400 9. References 402 Below are the normative and informative references for this document. 404 9.1 Normative References 406 [ASCII] - American National Standards Institute (formerly United 407 States of America Standards Institute), "USA Code for 408 Information Interchange", ANSI X3.4-1968, 1968. ANSI X3.4-1968 409 has been replaced by newer versions with slight modifications, 410 but the 1968 version remains definitive for the Internet. 412 9.2 Informative References 414 [FNV] - FNV web site: 415 http://www.isthe.com/chongo/tech/comp/fnv/index.html 417 [IEEE] - http://www.ieee.org 419 [IPv6flow] - https://researchspace.auckland.ac.nz/bitstream/handle/ 420 2292/13240/flowhashRep.pdf 422 [RFC3174] - Eastlake 3rd, D. and P. Jones, "US Secure Hash Algorithm 423 1 (SHA1)", RFC 3174, September 2001. 425 [RFC6194] - Polk, T., Chen, L., Turner, S., and P. Hoffman, "Security 426 Considerations for the SHA-0 and SHA-1 Message-Digest 427 Algorithms", RFC 6194, March 2011. 429 [RFC6234] - Eastlake 3rd, D. and T. Hansen, "US Secure Hash 430 Algorithms (SHA and SHA-based HMAC and HKDF)", RFC 6234, May 431 2011. 433 Appendix A: Work Comparison with SHA-1 435 This section provides a simplistic rough comparison of the level of 436 effort required per input byte to compute FNV-1a and SHA-1 [RFC3174]. 438 Ignoring transfer of control and conditional tests and equating all 439 logical and arithmetic operations, FNV requires 2 operations per 440 byte, an XOR and a multiply. 442 SHA-1 is a relatively weak cryptographic hash producing a 160-bit 443 hash. It that has been partially broken [RFC6194]. It is actually 444 designed to accept a bit vector input although almost all computer 445 uses apply it to an integer number of bytes. It processes blocks of 446 512 bits (64 bytes) and we estimate the effort involved in SHA-1 447 processing a full block. Ignoring SHA-1 initial set up, transfer of 448 control, and conditional tests, but counting all logical and 449 arithmetic operations, including counting indexing as an addition, 450 SHA-1 requires 1,744 operations per 64 bytes block or 27.25 451 operations per byte. So by this rough measure, it is a little over 13 452 times the effort of FNV for large amounts of data. However, FNV is 453 commonly used for small inputs. Using the above method, for inputs of 454 N bytes, where N is <= 55 so SHA-1 will take one block (SHA-1 455 includes padding and an 8-byte length at the end of the data in the 456 last block), the ratio of the effort for SHA-1 to the effort for FNV 457 will be 872/N. For example, with an 8 byte input, SHA-1 will take 109 458 times as much effort as FNV. 460 Stronger cryptographic functions than SHA-1 generally have an even 461 high work factor. 463 Appendix B: Previous IETF Reference to FNV 465 FNV-1a was referenced in draft-ietf-tls-cached-info-08.txt that has 466 since expired. It was later decided that it would be better to use a 467 cryptographic hash for that application. 469 Below is the Jave code for FNV64 from that TLS draft include by the 470 kind permission of the author: 472 /** 473 * Java code sample, implementing 64 bit FNV-1a 474 * By Stefan Santesson 475 */ 477 import java.math.BigInteger; 479 public class FNV { 481 static public BigInteger getFNV1aToByte(byte[] inp) { 483 BigInteger m = new BigInteger("2").pow(64); 484 BigInteger fnvPrime = new BigInteger("1099511628211"); 485 BigInteger fnvOffsetBasis = 486 new BigInteger("14695981039346656037"); 488 BigInteger digest = fnvOffsetBasis; 490 for (byte b : inp) { 491 digest = digest.xor(BigInteger.valueOf((int) b & 255)); 492 digest = digest.multiply(fnvPrime).mod(m); 493 } 494 return digest; 496 } 497 } 499 Appendix C: A Few Test Vectors 501 Below are a few test vectors in the form of ASCII strings and their 502 FNV32 and FNV64 hashes using the FNV-1a algorithm. 504 Strings without null (zero byte) termination: 506 String FNV32 FNV64 507 "" 0x811c9dc5 0xcbf29ce484222325 508 "a" 0xe40c292c 0xaf63dc4c8601ec8c 509 "foobar" 0xbf9cf968 0x85944171f73967e8 511 Strings including null (zero byte) termination: 513 String FNV32 FNV64 514 "" 0x050c5d1f 0xaf63bd4c8601b7df 515 "a" 0x2b24d044 0x089be207b544f1e4 516 "foobar" 0x0c1c9eb8 0x34531ca7168b8f38 518 Appendix Z: Change Summary 520 RFC Editor Note: Please delete this appendix on publication. 522 From -00 to -01 524 1. Add Security Considerations section on why FNV is non- 525 cryptographic. 527 2. Add Appendix A on a work factor comparison with SHA-1. 529 3. Add Appendix B concerning previous IETF draft referenced to FNV. 531 4. Minor editorial changes. 533 From -01 to -02 535 1. Correct FNV_Prime determination criteria and add note as to why s 536 < 5 and s > 10 are not considered. 538 2. Add acknowledgements list. 540 3. Add a couple of references. 542 4. Minor editorial changes. 544 From -02 to -03 546 1. Replace direct reference to US-ASCII standard with reference to 547 RFC 20. 549 2. Update dates and verion number. 551 3. Minor editing changes. 553 From -03 to -04 555 1. Change reference to RFC 20 back to a reference to the ANSI 1968 556 ASCII standard. 558 2. Minor addition to Section 6, point 3. 560 3. Update dates and version number. 562 4. Minor editing changes. 564 From -04 to -05 566 1. Add Twitter as a use example and IPv6 flow hash study reference. 568 2. Update dates and version number. 570 From -05 to -06 572 1. Add code subsections. 574 2. Update dates and version number. 576 Author's Address 578 Glenn Fowler 579 AT&T Labs Research 580 180 Park Avenue 581 Florham Park, NJ 07932 USA 583 Email: gsf@research.att.com 584 URL: http://www.research.att.com/~gsf/ 586 Landon Curt Noll 587 Cisco Systems 588 170 West Tasman Drive 589 San Jose, CA 95134 USA 591 Telephone: +1-408-424-1102 592 Email: fnv-rfc-mail@asthe.com 593 URL: http://www.isthe.com/chongo/index.html 595 Kiem-Phong Vo 596 AT&T Labs Research 597 180 Park Avenue 598 Florham Park, NJ 07932 USA 600 Email: kpv@research.att.com 601 URL: http://www.research.att.com/info/kpv/ 603 Donald Eastlake 604 Huawei Technologies 605 155 Beaver Street 606 Milford, MA 01757 USA 608 Telephone: +1-508-333-2270 609 EMail: d3e3e3@gmail.com 611 Copyright, Disclaimer, and Additional IPR Provisions 613 Copyright (c) 2013 IETF Trust and the persons identified as the 614 document authors. All rights reserved. 616 This document is subject to BCP 78 and the IETF Trust's Legal 617 Provisions Relating to IETF Documents 618 (http://trustee.ietf.org/license-info) in effect on the date of 619 publication of this document. Please review these documents 620 carefully, as they describe your rights and restrictions with respect 621 to this document. Code Components extracted from this document must 622 include Simplified BSD License text as described in Section 4.e of 623 the Trust Legal Provisions and are provided without warranty as 624 described in the Simplified BSD License. This Internet-Draft is 625 submitted to IETF in full conformance with the provisions of BCP 78 626 and BCP 79.