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SMhasher

Linux Build status Windows Build status FreeBSD Build status

Hash function MiB/sec cycl./hash cycl./map size Quality problems
donothing32 11149460.06 4.00 - 13 bad seed 0, test NOP
donothing64 11787676.42 4.00 - 13 bad seed 0, test NOP
donothing128 11745060.76 4.06 - 13 bad seed 0, test NOP
NOP_OAAT_read64 11372846.37 14.00 - 47 test NOP
BadHash 769.94 73.97 - 47 bad seed 0, test FAIL
sumhash 10699.57 29.53 - 363 bad seed 0, test FAIL
sumhash32 42877.79 23.12 - 863 UB, test FAIL
multiply_shift 8026.77 26.05 226.80 (8) 345 bad seeds & 0xfffffff0, fails most tests
pair_multiply_shift 3716.95 40.22 186.34 (3) 609 fails most tests
--------------------------
crc32 383.12 134.21 257.50 (11) 422 insecure, 8590x collisions, distrib, PerlinNoise
md5_32 350.53 644.31 894.12 (10) 4419
md5_64 351.01 656.67 897.43 (12) 4419
md5-128 350.89 681.88 894.03 (13) 4419
sha1_32 353.03 1385.80 1759.94 (5) 5126 Sanity, Cyclic low32, 36.6% distrib
sha1_64 353.03 1385.80 1759.94 (5) 5126 Sanity, Cyclic low32, 36.6% distrib
sha1-160 364.95 1470.55 1794.16 (13) 5126 Comb/Cyclic low32
sha2-224 147.13 1354.81 1589.92 (12) Comb low32
sha2-224_64 147.60 1360.10 1620.93 (13) Cyclic low32
sha2-256 147.80 1374.90 1606.06 (16)
sha2-256_64 148.01 1376.34 1624.71 (16)
sha1ni 1601.21 174.16 397.28 (6) 989 insecure,sanity, Permutation, Zeroes, machine-specific
sha1ni_32 1576.17 174.04 405.56 (6) 989 machine-specific
sha2ni-256 1527.38 184.35 404.40 (4) 4241 insecure,sanity, Permutation, Zeroes, machine-specific
sha2ni-256_64 1501.85 186.20 407.96 (5) 4241 Zeroes, machine-specific
blake3_c 1288.84 357.69 582.89 (6) no 32bit portability
rmd128 290.90 710.49 965.55 (6)
rmd160 202.16 1045.79 1287.74 (16) Cyclic hi32
rmd256 364.81 584.86 835.02 (11)
edonr224 864.69 303.42 526.94 (6)
edonr256 847.85 305.79 510.01 (4)
blake2s-128 295.30 698.09 1059.24 (51)
blake2s-160 215.01 1026.74 1239.54 (11)
blake2s-224 207.06 1063.86 1236.50 (20)
blake2s-256 215.28 1014.88 1230.38 (28)
blake2s-256_64 211.52 1044.22 1228.43 (8)
blake2b-160 356.08 1236.84 1458.15 (12)
blake2b-224 356.59 1228.50 1425.87 (16)
blake2b-256 355.97 1232.22 1443.31 (19)
blake2b-256_64 356.97 1222.76 1435.03 (9)
asconhashv12 144.98 885.02 1324.23 (38) 4341
asconhashv12_64 159.68 386.90 480.86 (4) 6490
sha3-256 100.58 3877.18 4159.79 (37) PerlinNoise
sha3-256_64 100.57 3909.00 4174.63 (16) PerlinNoise
hasshe2 2773.89 64.35 282.30 (3) 445 Permutation,TwoBytes,Zeroes,Seed
poly_1_mersenne 1369.21 61.59 248.86 (4) 479 fails most tests
poly_2_mersenne 1364.03 70.30 261.00 (6) 479
poly_3_mersenne 1342.82 80.22 268.79 (2) 479
poly_4_mersenne 1343.19 89.13 277.52 (3) 479
tabulation32 5781.16 40.00 241.79 (10) 848 collisions
tabulation 7875.01 39.95 249.49 (3) 554
crc32_hw 6244.38 41.23 226.80 (2) 653 insecure, 100% bias, collisions, distrib, BIC, machine-specific (SSE4.2/NEON)
crc32_hw1 7569.29 49.07 233.75 (3) 671 insecure, 100% bias, collisions, distrib, BIC, machine-specific (x86 SSE4.2)
crc64_hw 6143.62 40.48 223.13 (2) 652 insecure, 100% bias, collisions, distrib, BIC, machine-specific (SSE4.2/NEON)
crc32_pclmul - - - insecure, 100% bias, collisions, distrib, BIC, machine-specific (x86 SSE4.2+PCLMUL)
o1hash 11629440.57 18.15 199.35 (2) 101 insecure, no seed, zeros, fails all tests
fibonacci 16878.32 22.94 803.18 (15) 1692 UB, zeros, fails all tests
FNV1a 760.52 73.83 254.29 (5) 204 bad seed, zeros, fails all tests
FNV1A_Totenschiff 6274.78 26.23 251.13 (2) 270 UB, zeros, fails all tests
FNV1A_Pippip_Yurii 6172.14 27.55 244.80 (2) 147 UB, sanity, fails all tests
FNV1a_YT 13486.49 30.50 237.43 (4) 321 bad seed, UB, fails all tests
FNV2 6171.60 32.20 208.59 (4) 278 fails all tests
FNV64 774.37 72.43 201.15 (2) 79 fails all tests
FNV128 390.14 136.42 289.00 (3) 171 fails all tests
k-hash32 2230.42 53.05 264.64 (3) 808 insecure, zeros, UB, bad seeds, fails all tests
k-hash64 2451.88 48.66 249.44 (2) 609 insecure, zeros, UB, bad seeds, fails all tests
fletcher2 15552.61 20.61 335.31 (3) 248 bad seed 0, UB, fails all tests
fletcher4 15556.93 20.60 358.60 (3) 371 bad seed 0, UB, fails all tests
bernstein 1045.97 58.31 225.78 (3) 41 bad seed 0, fails all tests
sdbm 784.83 68.57 222.68 (5) 41 bad seed 0, fails all tests
x17 748.75 74.13 236.00 (10) 79 99.98% bias, fails all tests
libiberty 628.66 84.95 225.07 (4) 37 insecure, 100% bias, fails all tests, bad seed
gcc 611.69 86.47 231.51 (5) 39 insecure, 100% bias, fails all tests, bad seed
JenkinsOOAT 627.64 107.04 252.79 (3) 153 bad seed 0, 53.5% bias, fails all tests
JenkinsOOAT_perl 608.10 94.17 254.09 (4) 65 bad seed 0, 1.5-11.5% bias, 7.2x collisions, BIC, LongNeighbors
MicroOAAT 701.35 76.68 251.01 (3) 68 100% bias, distrib, BIC
pearsonhash64 434.17 124.14 230.79 (4) Avalanche, Seed, SSSE3 only. broken MSVC
pearsonhash128 434.23 121.34 221.03 (7) Avalanche, Seed, SSSE3 only. broken MSVC
pearsonhash256 444.08 119.11 229.75 (4) Avalanche, Seed, SSSE3 only. broken MSVC
VHASH_32 13053.40 65.84 289.86 (3) 1231 sanity, Seed, MomentChi2
VHASH_64 13465.50 63.88 286.38 (5) 1231 sanity, Seed, Sparse
farsh32 27038.23 66.88 278.89 (5) 944 insecure: AppendedZeroes, collisions+bias, MomentChi2, LongNeighbors
farsh64 13829.32 112.46 332.59 (3) 944 insecure: AppendedZeroes, collisions+bias, MomentChi2, LongNeighbors
farsh128 6878.88 233.35 384.85 (3) 944 insecure: AppendedZeroes, collisions+bias, permut,combin,2bytes,zeroes,PerlinNoise
farsh256 3467.37 440.40 593.57 (5) 944 insecure: AppendedZeroes, collisions+bias, permut,combin,2bytes,zeroes,PerlinNoise
jodyhash32 1794.34 41.12 235.12 (4) 102 bias, collisions, distr, BIC LongNeighbors
jodyhash64 4813.10 40.72 239.22 (6) 118 bias, collisions, distr, BIC, LongNeighbors
lookup3 2475.35 39.65 240.10 (3) 341 UB, 28% bias, collisions, 30% distr, BIC
superfast 2058.22 49.56 254.12 (3) 210 UB, bad seed 0, 91% bias, 5273.01x collisions, 37% distr, BIC
MurmurOAAT 506.66 103.33 236.89 (3) 47 bad seed 0, collisions, 99.998% distr., BIC, LongNeighbors
Crap8 3041.14 37.25 247.87 (4) 342 UB, 2.42% bias, collisions, 2% distrib
Murmur1 2027.85 48.51 253.34 (3) 358 UB, 1 bad seed, 511x collisions, Diff, BIC
Murmur2 3089.18 41.22 238.42 (4) 358 UB, 1 bad seed, 1.7% bias, 81x coll, 1.7% distrib, BIC
Murmur2A 3087.98 45.90 238.54 (4) 407 UB, 1 bad seed, 12.7% bias, LongNeighbors
Murmur2B 5919.38 38.18 215.96 (3) 433 UB, 1.8% bias, collisions, 3.4% distrib, BIC
Murmur2C 3810.98 49.09 218.51 (3) 444 UB, 2^32 bad seeds, 91% bias, collisions, distr, BIC, LongNeighbors
Murmur3A 2982.67 49.08 245.78 (4) 351 UB, 1 bad seed, Moment Chi2 69
PMurHash32 3005.85 48.88 242.38 (3) 1862 1 bad seed, Moment Chi2 69
Murmur3C 4833.18 56.87 250.47 (6) 859 UB, LongNeighbors, Text, DiffDist
mirhash32low 6145.39 36.95 235.09 (4) 1112 UB, 4 bad seeds, Cyclic, LongNeighbors, machine-specific (32/64 differs)
PMPML_32 6639.68 45.33 257.45 (3) 1084 Avalanche >512, unseeded: Seed, BIC, MomentChi2, PerlinNoise
PMPML_64 9833.77 50.00 251.64 (6) 1305 unseeded: Seed, MomentChi2, BIC
xxHash32 5865.17 49.20 242.74 (3) 738 LongNeighbors, collisions with 4bit diff, MomentChi2 220
metrohash64 14741.56 39.44 215.76 (2) 624 UB, LongNeighbors, BIC
metrohash64_1 14298.77 40.31 223.25 (4) 624 UB, LongNeighbors, BIC, MomentChi2
metrohash64crc_1 6929.69 44.65 223.68 (3) 632 UB, Cyclic 8/8 byte, DiffDist, BIC, MomentChi2, machine-specific (SSE4.2/NEON)
metrohash64crc_2 8150.65 43.72 219.45 (5) 632 UB, Cyclic 8/8 byte, DiffDist, BIC, machine-specific (SSE4.2/NEON)
cmetrohash64_1o 14921.73 38.95 213.25 (2) 3506 UB, LongNeighbors, BIC, MomentChi2
cmetrohash64_1 14151.73 40.90 211.89 (2) 652 UB, LongNeighbors, BIC, MomentChi2
City64noSeed 14209.19 31.80 225.90 (5) 1038 Avalanche, Sparse, TwoBytes, MomentChi2, Seed
City64 13887.84 46.32 239.77 (3) 1120 Sparse, TwoBytes
t1ha1_64le 13442.64 31.41 219.58 (3) 517 Avalanche
t1ha1_64be 11586.02 32.74 232.55 (3) 555 Avalanche
t1ha0_32le 7401.21 48.27 238.99 (3) 509 Sparse, LongNeighbors
t1ha0_32be 6217.37 50.66 244.51 (3) 533 Sparse, LongNeighbors
t1ha2_stream 14011.63 80.72 275.17 (3) 1665 Sparse, Permutation, LongNeighbors
t1ha2_stream128 13136.06 97.80 306.11 (7) 1665 Sparse, Permutation, LongNeighbors
aesnihash 5579.32 56.83 258.71 (5) 1209 fails many tests, machine-specific (x64 AES-NI)
falkhash 50631.69 123.02 322.14 (7) 264 Sparse, LongNeighbors, machine-specific (x64 AES-NI)
MeowHash 29969.40 64.96 274.29 (4) 1764 Sparse, invertible, machine-specific (x64 AES-NI)
MeowHash64low 29485.59 65.98 278.05 (3) 1764 Sparse, invertible, machine-specific (x64 AES-NI)
MeowHash32low 26944.58 65.95 292.79 (9) 1764 Sparse, invertible, machine-specific (x64 AES-NI)
--------------------------------------
tifuhash_64 35.60 1679.52 1212.75 (15) 276 Cyclic low32
floppsyhash 35.72 1868.92 1411.07 (7) 623
beamsplitter 789.22 682.45 1150.33 (26) 4203 UB
discohash1 4131.12 199.00 398.35 (5) 1294
discohash1-128 4072.95 234.17 438.43 (5) 1294
discohash2 3986.52 207.52 421.99 (2) 1294
discohash2-128 4094.73 236.61 433.35 (4) 1294
discoNONG 3698.45 399.67 597.78 (9) bad seeds
chaskey 1143.05 113.70 294.43 (4) 1609 PerlinNoise
SipHash 943.53 147.15 338.74 (4) 1071
HalfSipHash 1141.57 79.65 263.96 (3) 700 zeroes
GoodOAAT 743.81 85.62 231.22 (3) 237
pearsonbhash64 1794.83 97.80 268.90 (8) 683
pearsonbhash128 1691.62 104.57 272.38 (4) 1134
pearsonbhash256 1442.59 126.04 309.34 (4) 844
prvhash64_64m 3077.18 47.31 241.92 (3) 349
prvhash64_64 3015.08 48.03 240.64 (3) 384
prvhash64_128 3353.81 67.64 266.32 (2) 718
prvhash64s_64 6591.34 273.50 464.65 (3) 2640
prvhash64s_128 6581.40 333.83 528.07 (5) 2799
SipHash13 1812.75 106.56 310.76 (5) 778 0.9% bias
TSip 4233.17 53.31 249.19 (3) 519 !msvc
seahash 8261.80 58.94 256.08 (4) 871 PerlinNoise, !msvc
seahash32low 8266.17 58.90 290.21 (16) 871 PerlinNoise 32, !msvc
clhash 18703.04 70.19 282.12 (6) 1809 PerlinNoise, machine-specific (x64 SSE4.2)
HighwayHash64 6242.58 99.55 248.41 (3) 2546
Murmur3F 7623.44 52.69 221.87 (3) 699 UB
MUM 9563.99 34.99 228.55 (5) 1912 UB, too many bad seeds, machine-specific (32/64 differs)
MUMlow 9261.89 36.17 247.66 (4) 1912 UB, 5 bad seeds
xmsx32 2039.10 46.39 249.30 (7) 192 2 bad seeds
mirhash 6139.07 37.02 209.47 (3) 1112 UB, 2^36 bad seeds, LongNeighbors, machine-specific (32/64 differs)
mirhashstrict 3549.01 49.99 224.91 (2) 1112
mirhashstrict32low 3441.35 50.60 247.19 (3) 1112 1 bad seed, MomentChi2 9
fasthash32 6128.28 40.30 241.64 (4) 566 UB
fasthash64 5818.92 38.70 220.74 (2) 509 UB
aesni 31232.34 29.21 230.14 (4) 519 machine-specific (x64 AES-NI)
aesni-low 31221.14 29.64 226.18 (3) 519 machine-specific (x64 AES-NI)
mx3 9034.90 48.71 227.89 (2) 734 UB
pengyhash 13428.80 74.24 275.42 (5) 421
City32 5551.28 54.40 261.64 (2) 1319
City64low 13904.10 46.24 260.08 (3) 1120
City128 14031.96 89.09 290.05 (10) 1841
CityCrc128 7916.44 55.50 240.79 (2) 295
FarmHash32 21755.58 47.54 258.35 (3) 11489 machine-specific (x64 SSE4/AVX)
FarmHash64 12845.53 47.11 251.58 (3) 3758
FarmHash128 13913.65 70.25 263.06 (3) 163
farmhash32_c 21601.86 47.38 273.00 (3) 762 machine-specific (x64 SSE4/AVX)
farmhash64_c 12834.10 47.23 246.20 (2) 3688
farmhash128_c 13753.24 68.96 263.76 (3) 1890
metrohash64_2 14316.37 40.23 218.28 (3) 627 UB, LongNeighbors
cmetrohash64_2 14294.26 40.76 221.40 (4) 655 LongNeighbors
metrohash128 15634.66 73.28 261.23 (4) 773 UB, LongNeighbors
metrohash128_1 15806.97 72.30 260.90 (4) 773 UB, LongNeighbors
metrohash128_2 15822.60 72.30 255.34 (3) 773 UB, LongNeighbors
metrohash128crc_1 8009.23 78.72 281.55 (13) 723 UB, machine-specific (SSE4.2/NEON)
metrohash128crc_2 7878.22 79.90 275.22 (4) 723 UB, machine-specific (SSE4.2/NEON)
xxHash64 12108.87 49.78 228.83 (2) 1999
Spooky32 13108.95 56.27 255.36 (3) 2221 UB
Spooky64 13529.36 58.76 236.31 (3) 2221 UB
Spooky128 11781.35 58.91 242.91 (3) 2221 UB
SpookyV2_32 13529.16 55.55 248.37 (4) 2069
SpookyV2_64 12678.82 56.71 243.21 (4) 2069
SpookyV2_128 13512.82 58.33 244.56 (5) 2069
ahash64 9862.62 27.32 181.68 (1) 412 rust
xxh3 21033.55 29.48 226.77 (4) 744 DiffDist bit 7 w. 36 bits, BIC
xxh3low 17093.19 30.57 242.07 (7) 756
xxh128 18802.16 32.37 234.30 (4) 1012
xxh128low 18833.05 32.30 234.68 (3) 1012
t1ha2_atonce 13854.44 37.92 233.54 (2) 541 Zeroes low3
t1ha2_atonce128 14148.42 55.70 253.74 (6) 613 LongNeighbors
t1ha0_aes_noavx 27231.59 37.70 236.10 (3) 925 LongNeighbors, machine-specific (x86 AES-NI)
t1ha0_aes_avx1 22714.85 48.12 226.52 (16) 843 LongNeighbors, machine-specific (x64 AVX.txt)
t1ha0_aes_avx2 56919.46 36.70 233.14 (2) 792 LongNeighbors, machine-specific (x64 AVX2)
wyhash32 2532.89 48.40 484.57 (1) 426 4 bad and broken seeds, 32-bit
wyhash32low 22393.77 29.04 243.40 (3) 474 5 bad seeds
wyhash 22540.23 28.87 236.16 (8) 474
rapidhash 23789.79 22.80 138.71 (7) 574
rapidhash_unrolled 23892.88 23.41 139.47 (12) 782
umash32 21427.57 42.12 255.55 (5) 1530
umash32_hi 21483.12 42.65 251.09 (4) 1530
umash64 21690.08 41.67 238.01 (4) 1530
umash128 13211.88 43.37 237.40 (3) 1530
halftime_hash64 4735.63 99.90 315.34 (3) 2911
halftime_hash128 17534.53 97.97 311.10 (4) 2462
halftime_hash256 18003.39 99.46 315.09 (3) 2622
halftime_hash512 10890.15 118.05 333.45 (3) 3550
nmhash32 12969.62 55.88 265.69 (4) 2445
nmhash32x 12775.08 42.66 246.05 (3) 1494
k-hashv32 9181.87 52.76 245.14 (3) 1280
k-hashv64 7850.92 46.94 193.94 (1) 1279
komihash 12242.78 33.02 236.07 (2) 1323
polymur 9676.33 42.70 246.53 (3) 1128

The sortable table variants:

Summary

I added some SSE assisted hashes and fast intel/arm CRC32-C, AES and SHA HW variants. See also the old https://github.com/aappleby/smhasher/wiki, the improved, but unmaintained fork https://github.com/demerphq/smhasher, and the new improved version SMHasher3 https://gitlab.com/fwojcik/smhasher3.

So the fastest hash functions on x86_64 without quality problems are:

  • rapidhash (an improved wyhash)
  • xxh3low
  • wyhash
  • umash (even universal!)
  • ahash64
  • t1ha2_atonce
  • komihash
  • FarmHash (not portable, too machine specific: 64 vs 32bit, old gcc, ...)
  • halftime_hash128
  • Spooky32
  • pengyhash
  • nmhash32
  • mx3
  • MUM/mir (different results on 32/64-bit archs, lots of bad seeds to filter out)
  • fasthash32

Hash functions for symbol tables or hash tables typically use 32 bit hashes, for databases, file systems and file checksums typically 64 or 128bit, for crypto now starting with 256 bit.

Typical median key size in perl5 is 20, the most common 4. Similar for all other dynamic languages. See github.com/rurban/perl-hash-stats

When used in a hash table the instruction cache will usually beat the CPU and throughput measured here. In my tests the smallest FNV1A beats the fastest crc32_hw1 with Perl 5 hash tables. Even if those worse hash functions will lead to more collisions, the overall speed advantage and inline-ability beats the slightly worse quality. See e.g. A Seven-Dimensional Analysis of Hashing Methods and its Implications on Query Processing for a concise overview of the best hash table strategies, confirming that the simplest Mult hashing (bernstein, FNV*, x17, sdbm) always beat "better" hash functions (Tabulation, Murmur, Farm, ...) when used in a hash table.

The fast hash functions tested here are recommendable as fast for file digests and maybe bigger databases, but not for 32bit hash tables. The "Quality problems" lead to less uniform distribution, i.e. more collisions and worse performance, but are rarely related to real security attacks, just the 2nd sanity AppendZeroes test against \0 invariance is security relevant.

Columns

MiB/sec: The average of the Bulk key speed test for alignments 0-7 with 262144-byte keys. The higher the better.

cycl./hash: The average of the Small key speed test for 1-31 byte keys. The smaller the better.

cycl./map: The result of the Hashmap test for /usr/dict/words with fast C++ hashmap get queries, with the standard deviation in brackets. This tests the inlinability of the hash function in practise (see size). The smaller the better.

size: The object size in byte on AMD64. This affects the inlinability in e.g. hash tables. The smaller the better.

Quality problems: See the failures in the linked doc. The less the better.

Other

SECURITY

The hash table attacks described in SipHash against City, Murmur or Perl JenkinsOAAT or at Hash Function Lounge are not included here. We list some known attacks at GH #186.

Such an attack avoidance cannot be the problem of the hash function, but only the hash table collision resolution scheme. You can attack every single hash function, even the best and most secure if you detect the seed, e.g. from language (mis-)features, side-channel attacks, collision timings and independly the sort-order, so you need to protect your collision handling scheme from the worst-case O(n), i.e. separate chaining with linked lists. Linked lists chaining allows high load factors, but is very cache-unfriendly. The only recommendable linked list scheme is inlining the key or hash into the array. Nowadays everybody uses fast open addressing, even if the load factor needs to be ~50%, unless you use Cuckoo Hashing.

I.e. the usage of SipHash for their hash table in Python 3.4, ruby, rust, systemd, OpenDNS, Haskell and OpenBSD is pure security theatre. SipHash is not secure enough for security purposes and not fast enough for general usage. Brute-force generation of ~32k collisions need 2-4m for all these hashes. siphash being the slowest needs max 4m, other typically max 2m30s, with <10s for practical 16k collision attacks with all hash functions. Using Murmur is usually slower than a simple Mult, even in the worst case. Provable secure is only uniform hashing, i.e. 2-5 independent Mult or Tabulation, or using a guaranteed logarithmic collision scheme (a tree) or a linear collision scheme, such as swisstable/folly-F14, Robin Hood or Cuckoo hashing with collision counting.

One more note regarding security: Nowadays even SHA1 can be solved in a solver, like Z3 (or faster ones) for practical hash table collision attacks (i.e. 14-20 bits). All hash functions with less than 160 bits tested here cannot be considered "secure" at all.

The '\0' vulnerability attack with binary keys is tested in the 2nd Sanity Zero test.

CRYPTO

Our crypto hashes are hardened with an added size_t seed, mixed into the initial state, and the versions which require zero-padding are hardened by adding the len also, to prevent from collisions with AppendedZeroes for the padding. The libtomcrypt implementations already provide for that, but others might not. Without, such crypto hash functions are unsuitable for normal tasks, as it's trivial to create collisions by padding or bad seeds.

The official NIST hash function testsuite does not do such extensive statistical tests, to search for weak ranges in the bits. Also crypto does not change the initial state, which we do here for our random 32bit seed. Crypto mostly cares about unreversable key -> hash functions without changing the initial fixed state and timings/sidechannel attacks.

The NIST "Cryptographic Algorithm Validation Program" (CAVP) involves the testing of the implementations of FIPS-approved and NIST-recommended cryptographic algorithms. During the NIST SHA-3 competition, the testing methodology was borrowed from the "CAVP", as the KATs and MCTs of the SHA-3 Competition Test Suite were based on the CAVP tests for SHA-2. In addition to this, the “Extremely Long Message Test,” not present in the CAVP for SHA-2, required the submitters to generate the hash value corresponding to a message with a length of 1 GiB. “NIST - Cryptographic Algorithm Validation Program (CAVP),” June 2017. Available: http://csrc.nist.gov/groups/STM/cavp (No testing source code provided, just high-level descriptions)

Two other independent third party testsuites found an extensive number of bugs and weaknesses in the SHA3 candidates. "Finding Bugs in Cryptographic Hash Function Implementations", Nicky Mouha, Mohammad S Raunak, D. Richard Kuhn, and Raghu Kacker, 2017. https://eprint.iacr.org/2017/891.pdf

Maybe independent researchers should come together to do a better public SHA-4 round, based on better and more testing methods, open source code for the tests, and using standard industry practices, such as valgrind, address-sanitizer and ubsan to detect obvious bugs.

PROBLEMS

  • Bad Seeds

    Hash functions are typically initialized with a random seed. But some seed values may lead to bad hash functions, regardless of the key. In the regular case with random seeds the probablity of such bad seeds is very low, like 2^32 or 2^64. A practical application needs to know if bad seeds exist and choose another one. See e.g. mirhash_seed_init() and mirhash_bad_seeds() in Hashes.h. Note that a bad seed is not really a problem when you skip this seed during initialization. It can still be a GOOD or recommended hash function. But a bad seed of 0 leading to collisions is considered a bug, a bad hash function.

    We test for internal secrets, if they will be multiplied with 0. This is also called "blinding multiplication". main.cpp lists some secrets for each hash function we test against. The function <hash>_bad_seeds() lists the confirmed bad seeds.

    Special care needs to be taken for crc, most FNV1 variants, fletcher, Jenkins. And with GOOD hashes most MUM variants, like mirhash, MUM, wyhash.

    Independently from this, when the attacker knows the seed it will lead to DDOS attacks. Even with crypto hashes in power2 hashtables.

Typical undefined behaviour (UB) problems:

  • Misaligned

    Many word-wise hashes (in opposite to safe byte-wise processing) don't check the input buffer for proper word alignment, which will fail with ubsan or Sparc. word being int32_t or int64_t or even more. On some old RISC hardware this will be a BUS error, you can even let Intel HW generate such a bus error by setting some CPU flag. But generally using misaligned accesses is fine.

    These are: mx3, Spooky, mirhash (but not strict), MUM, fasthash, Murmur3*, Murmur2*, metrohash* (all but cmetro*), Crap8, beamsplitter, lookup3, fletcher4, fletcher2, all sanmayce FNV1a_ variants (FNV1a_YT, FNV1A_Pippip_Yurii, FNV1A_Totenschiff, ...), fibonacci.

    The usual mitigation is to check the buffer alignment either in the caller, provide a pre-processing loop for the misaligned prefix, or copy the whole buffer into a fresh aligned area. Put that extra code inside #ifdef HAVE_ALIGNED_ACCESS_REQUIRED.

  • oob - Out of bounds

    Some hash function assume a padded input buffer which can be accessed past its length up to the word size. This allows for faster loop processing, as no 2nd loop or switch table for the rest is needed, but it requires a cooperative calling enviroment and is as such considered cheating.

  • Signed integer overflow

    A simple type error, this hash needs to use unsigned integer types internally, to avoid undefined and inconsistent behaviour. i.e. SuperFastHash: signed integer overflow: -2147483641 + -113 cannot be represented in type 'int'

  • shift exponent overflow

    With: FNV1A_Pippip_Yurii, FNV1A_Totenschiff, pair_multiply_shift, sumhash32 shift exponent 64 is too large for 64-bit type 'long unsigned int'