avaneev/smhasher

Hash function quality and speed tests

SMhasher

Hash function	MiB/sec	cycl./hash	cycl./map	size	Quality problems
donothing32	15316474.36	6.00	-	13	bad seed 0, test NOP
donothing64	15330019.19	6.00	-	13	bad seed 0, test NOP
donothing128	15278983.09	6.00	-	13	bad seed 0, test NOP
NOP_OAAT_read64	28467.50	18.48	-	47	test NOP
BadHash	524.81	96.20	-	47	bad seed 0, test FAIL
sumhash	7169.08	27.12	-	363	bad seed 0, test FAIL
sumhash32	22556.18	22.98	-	863	UB, test FAIL
multiply_shift	5418.36	28.69	157.11 (3)	345	bad seeds & 0xfffffff0, fails most tests
pair_multiply_shift	3716.95	40.22	186.34 (3)	609	fails most tests
--------------------------
crc32	392.10	131.62	204.58 (4)	422	insecure, 8590x collisions, distrib, PerlinNoise
md5_32	353.64	629.85	799.56 (9)	4419
md5_64	353.64	629.85	799.56 (9)	4419
md5-128	353.76	638.29	803.39 (9)	4419
sha1_32a	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	2019.96	135.84	564.40 (6)	989	insecure,sanity, Permutation, Zeroes, machine-specific
sha1ni_32	2019.94	136.82	589.46 (1)	989	machine-specific
sha2ni-256	1906.77	145.47	603.08 (22)	4241	insecure,sanity, Permutation, Zeroes, machine-specific
sha2ni-256_64	1910.34	146.06	595.16 (6)	4241	Zeroes, machine-specific
blake3_c	1285.91	340.01	552.63 (3)		no 32bit portability
rmd128	334.36	659.03	838.32 (9)
rmd160	202.16	1045.79	1287.74 (16)		Cyclic hi32
rmd256	362.49	617.02	815.44 (8)
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	86.73	684.02	606.93 (6)	6490
sha3-256	100.58	3877.18	4159.79 (37)		PerlinNoise
sha3-256_64	100.57	3909.00	4174.63 (16)		PerlinNoise
hasshe2	2372.52	68.64	216.74 (5)	445	Permutation,TwoBytes,Zeroes,Seed
poly_1_mersenne	1431.65	54.49	189.52 (3)	479	fails most tests
poly_2_mersenne	1323.69	66.93	190.88 (2)	479
poly_3_mersenne	1323.59	74.86	206.77 (2)	479
poly_4_mersenne	1323.57	82.67	200.36 (4)	479
tabulation32	4317.34	35.45	197.20 (2)	848	collisions
tabulation	7621.75	42.19	179.93 (2)	554
crc32_hw	6330.42	35.55	170.16 (1)	653	insecure, 100% bias, collisions, distrib, BIC, machine-specific (SSE4.2/NEON)
crc32_hw1	23208.73	46.74	179.70 (2)	671	insecure, 100% bias, collisions, distrib, BIC, machine-specific (x86 SSE4.2)
crc64_hw	8440.13	34.94	141.15 (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	12439661.09	16.77	166.13 (1)	101	insecure, no seed, zeros, fails all tests
fibonacci	11339.87	26.33	705.64 (2)	1692	UB, zeros, fails all tests
FNV1a	791.84	69.69	177.84 (2)	204	bad seed, zeros, fails all tests
FNV1A_Totenschiff	6258.23	27.99	198.20 (1)	270	UB, zeros, fails all tests
FNV1A_Pippip_Yurii	6258.46	28.19	184.41 (2)	147	UB, sanity, fails all tests
FNV1a_YT	9643.42	32.06	175.19 (2)	321	bad seed, UB, fails all tests
FNV2	6258.84	33.25	142.89 (1)	278	fails all tests
FNV64	791.82	70.24	159.29 (1)	79	fails all tests
k-hash32	2686.33	42.99	504.48 (17)	808	insecure, zeros, UB, bad seeds, fails all tests
k-hash64	2808.54	39.19	434.43 (15)	609	insecure, zeros, UB, bad seeds, fails all tests
fletcher2	12011.15	25.29	298.60 (1)	248	bad seed 0, UB, fails all tests
fletcher4	11928.55	25.27	293.49 (2)	371	bad seed 0, UB, fails all tests
bernstein	791.82	68.63	180.71 (2)	41	bad seed 0, fails all tests
sdbm	791.84	67.69	177.06 (2)	41	bad seed 0, fails all tests
x17	527.90	98.78	184.09 (2)	79	99.98% bias, fails all tests
libiberty	556.16	87.56	273.09 (15)	37	insecure, 100% bias, fails all tests, bad seed
gcc	619.25	85.10	245.78 (17)	39	insecure, 100% bias, fails all tests, bad seed
JenkinsOOAT	452.48	142.85	213.93 (2)	153	bad seed 0, 53.5% bias, fails all tests
JenkinsOOAT_perl	452.49	118.78	194.78 (1)	65	bad seed 0, 1.5-11.5% bias, 7.2x collisions, BIC, LongNeighbors
MicroOAAT	977.60	59.61	185.06 (2)	68	100% bias, distrib, BIC
pearsonhash64	287.95	174.11	196.50 (1)		Avalanche, Seed, SSSE3 only. broken MSVC
pearsonhash128	287.95	171.72	194.61 (1)		Avalanche, Seed, SSSE3 only. broken MSVC
pearsonhash256	264.51	184.87	218.79 (0)		Avalanche, Seed, SSSE3 only. broken MSVC
VHASH_32	9404.99	77.01	250.57 (2)	1231	sanity, Seed, MomentChi2
VHASH_64	9392.39	74.72	227.92 (2)	1231	sanity, Seed, Sparse
farsh32	14053.09	74.29	245.33 (3)	944	insecure: AppendedZeroes, collisions+bias, MomentChi2, LongNeighbors
farsh64	7216.29	130.30	302.44 (3)	944	insecure: AppendedZeroes, collisions+bias, MomentChi2, LongNeighbors
farsh128	3776.92	232.48	398.67 (6)	944	insecure: AppendedZeroes, collisions+bias, permut,combin,2bytes,zeroes,PerlinNoise
farsh256	1895.77	459.86	575.95 (3)	944	insecure: AppendedZeroes, collisions+bias, permut,combin,2bytes,zeroes,PerlinNoise
jodyhash32	1428.37	44.36	185.85 (3)	102	bias, collisions, distr, BIC LongNeighbors
jodyhash64	2848.42	29.99	164.36 (1)	118	bias, collisions, distr, BIC, LongNeighbors
lookup3	1658.31	48.84	194.15 (2)	341	UB, 28% bias, collisions, 30% distr, BIC
superfast	1956.25	53.61	180.10 (3)	210	UB, bad seed 0, 91% bias, 5273.01x collisions, 37% distr, BIC
MurmurOAAT	452.49	113.07	197.83 (2)	47	bad seed 0, collisions, 99.998% distr., BIC, LongNeighbors
Crap8	3149.63	36.23	195.11 (1)	342	UB, 2.42% bias, collisions, 2% distrib
Murmur1	1804.67	51.51	188.41 (1)	358	UB, 1 bad seed, 511x collisions, Diff, BIC
Murmur2	3146.91	41.87	187.89 (2)	358	UB, 1 bad seed, 1.7% bias, 81x coll, 1.7% distrib, BIC
Murmur2A	3146.79	46.87	191.96 (4)	407	UB, 1 bad seed, 12.7% bias, LongNeighbors
Murmur2B	4882.95	39.72	149.43 (2)	433	UB, 1.8% bias, collisions, 3.4% distrib, BIC
Murmur2C	4092.99	51.84	164.65 (2)	444	UB, 2^32 bad seeds, 91% bias, collisions, distr, BIC, LongNeighbors
Murmur3A	2413.88	53.36	182.37 (3)	351	UB, 1 bad seed, Moment Chi2 69
PMurHash32	2344.78	58.48	196.43 (4)	1862	1 bad seed, Moment Chi2 69
Murmur3C	3197.63	67.90	198.00 (2)	859	UB, LongNeighbors, Text, DiffDist
mirhash32low	5412.76	39.79	182.13 (3)	1112	UB, 4 bad seeds, Cyclic, LongNeighbors, machine-specific (32/64 differs)
PMPML_32	6704.53	53.50	197.43 (4)	1084	Avalanche >512, unseeded: Seed, BIC, MomentChi2, PerlinNoise
PMPML_64	8161.19	53.20	179.16 (2)	1305	unseeded: Seed, MomentChi2, BIC
xxHash32	6040.87	51.77	177.91 (4)	738	LongNeighbors, collisions with 4bit diff, MomentChi2 220
metrohash64	9664.61	44.59	150.74 (2)	624	UB, LongNeighbors, BIC
metrohash64_1	9664.57	45.37	152.31 (2)	624	UB, LongNeighbors, BIC, MomentChi2
metrohash64crc_1	14000.50	49.08	150.54 (2)	632	UB, Cyclic 8/8 byte, DiffDist, BIC, MomentChi2, machine-specific (SSE4.2/NEON)
metrohash64crc_2	14034.84	48.94	162.54 (2)	632	UB, Cyclic 8/8 byte, DiffDist, BIC, machine-specific (SSE4.2/NEON)
cmetrohash64_1o	9658.31	42.84	163.45 (1)	3506	UB, LongNeighbors, BIC, MomentChi2
cmetrohash64_1	9683.33	45.20	161.01 (2)	652	UB, LongNeighbors, BIC, MomentChi2
City64noSeed	9090.42	32.23	171.53 (3)	1038	Avalanche, Sparse, TwoBytes, MomentChi2, Seed
City64	9066.90	47.81	197.78 (1)	1120	Sparse, TwoBytes
t1ha1_64le	9723.86	34.39	176.91 (1)	517	Avalanche
t1ha1_64be	7481.37	38.16	193.22 (2)	555	Avalanche
t1ha0_32le	5132.18	54.83	193.53 (2)	509	Sparse, LongNeighbors
t1ha0_32be	4585.59	55.98	183.45 (2)	533	Sparse, LongNeighbors
t1ha2_stream	9068.55	74.56	219.85 (6)	1665	Sparse, Permutation, LongNeighbors
t1ha2_stream128	9065.50	93.19	236.50 (3)	1665	Sparse, Permutation, LongNeighbors
aesnihash	2963.39	71.24	217.73 (3)	1209	fails many tests, machine-specific (x64 AES-NI)
falkhash	20202.42	173.63	321.52 (2)	264	Sparse, LongNeighbors, machine-specific (x64 AES-NI)
MeowHash	17371.91	85.48	247.96 (2)	1764	Sparse, invertible, machine-specific (x64 AES-NI)
MeowHash64low	17378.06	85.48	237.60 (2)	1764	Sparse, invertible, machine-specific (x64 AES-NI)
MeowHash32low	17374.64	85.48	258.53 (2)	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
BEBB4185	2951.62	222.03	343.63 (4)	1294	UB, msvc-specific
chaskey	753.23	153.42	288.26 (2)	1609	PerlinNoise
SipHash	980.88	127.77	246.19 (4)	1071
HalfSipHash	755.78	114.47	243.72 (4)	700	zeroes
GoodOAAT	1052.00	71.62	192.19 (1)	237
pearsonbhash64	1486.34	104.32	185.03 (2)	683
pearsonbhash128	1347.03	121.75	214.84 (2)	1134
pearsonbhash256	998.90	167.05	261.29 (3)	844
prvhash64_64m	2200.79	54.38	172.82 (1)	349
prvhash64_64	2159.17	55.20	182.99 (1)	384
prvhash64_128	2568.27	98.05	234.43 (2)	718
prvhash64s_64	4697.82	343.49	491.84 (2)	2640
prvhash64s_128	4241.02	442.13	586.42 (2)	2799
SipHash13	1889.10	89.00	199.95 (4)	778	0.9% bias
TSip	3228.14	57.96	211.71 (3)	519	!msvc
seahash	4796.97	58.55	201.58 (2)	871	PerlinNoise, !msvc
seahash32low	4801.33	58.54	227.31 (4)	871	PerlinNoise 32, !msvc
clhash	4472.31	82.72	229.73 (3)	1809	PerlinNoise, machine-specific (x64 SSE4.2)
HighwayHash64	6242.58	99.55	248.41 (3)	2546
Murmur3F	5226.40	52.18	175.85 (1)	699	UB
MUM	7134.56	37.85	172.34 (1)	1912	UB, too many bad seeds, machine-specific (32/64 differs)
MUMlow	7225.18	37.85	197.92 (3)	1912	UB, 5 bad seeds
mirhash	5413.73	39.68	154.47 (3)	1112	UB, 2^36 bad seeds, LongNeighbors, machine-specific (32/64 differs)
mirhashstrict	2217.32	65.53	182.07 (2)	1112
mirhashstrict32low	2218.87	65.48	190.59 (4)	1112	1 bad seed, MomentChi2 9
fasthash32	4737.61	45.32	181.86 (2)	566	UB
fasthash64	4737.21	42.79	164.87 (2)	509	UB
mx3	6146.02	52.48	173.09 (3)	734	UB
pengyhash	8744.48	85.31	222.45 (4)	421
City32	3675.04	57.73	212.04 (3)	1319
City64low	9089.45	47.75	201.73 (1)	1120
City128	9640.19	88.45	225.38 (3)	1841
CityCrc128	12343.43	74.50	209.75 (2)	295
FarmHash32	17112.05	47.70	214.71 (2)	11489	machine-specific (x64 SSE4/AVX)
FarmHash64	8684.76	48.13	200.51 (4)	3758
FarmHash128	9409.63	74.52	210.25 (3)	163
farmhash32_c	16299.81	47.79	219.19 (4)	762	machine-specific (x64 SSE4/AVX)
farmhash64_c	8713.16	47.96	201.00 (2)	3688
farmhash128_c	9244.13	79.08	209.44 (2)	1890
metrohash64_2	9668.51	44.45	164.30 (2)	627	UB, LongNeighbors
cmetrohash64_2	9669.95	44.75	149.67 (2)	655	LongNeighbors
metrohash128	9569.16	58.68	167.53 (2)	773	UB, LongNeighbors
metrohash128_1	9558.17	59.04	175.94 (2)	773	UB, LongNeighbors
metrohash128_2	9584.94	59.10	167.43 (2)	773	UB, LongNeighbors
metrohash128crc_1	13948.67	65.20	168.08 (2)	723	UB, machine-specific (SSE4.2/NEON)
metrohash128crc_2	13920.19	65.12	176.70 (1)	723	UB, machine-specific (SSE4.2/NEON)
xxHash64	8936.63	51.31	174.34 (3)	1999
Spooky32	9747.13	62.24	196.96 (4)	2221	UB
Spooky64	9747.47	62.20	191.71 (2)	2221	UB
Spooky128	9751.14	63.84	192.47 (2)	2221	UB
SpookyV2_32	9529.38	64.36	194.47 (1)	2069
SpookyV2_64	9505.69	64.44	192.19 (1)	2069
SpookyV2_128	9524.31	65.81	187.24 (1)	2069
ahash64	9862.62	27.32	181.68 (1)	412	rust
xxh3	16538.52	32.81	184.86 (2)	744	DiffDist bit 7 w. 36 bits, BIC
xxh3low	16462.36	32.77	199.79 (2)	756
xxh128	15174.14	40.46	195.65 (2)	1012
xxh128low	15174.85	33.79	187.05 (2)	1012
t1ha2_atonce	9237.12	38.94	194.32 (2)	541	Zeroes low3
t1ha2_atonce128	8350.99	55.65	203.53 (4)	613	LongNeighbors
t1ha0_aes_noavx	22785.26	38.71	180.61 (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	22345.33	44.38	556.47 (89)	792	LongNeighbors, machine-specific (x64 AVX2)
wyhash32	2532.89	48.40	484.57 (1)	426	2 bad seeds, 32-bit
wyhash32low	12911.09	29.59	205.43 (2)	474	2 bad seeds, PerlinNoise AV
wyhash	12879.00	30.35	196.77 (2)	474	2^33 bad seeds, PerlinNoise AV
umash32	4633.19	53.42	216.33 (3)	1530
umash32_hi	4662.92	54.22	214.20 (2)	1530
umash64	4662.09	53.42	188.09 (1)	1530
umash128	2427.46	70.60	197.29 (2)	1530
halftime_hash64	4990.72	120.55	281.64 (3)	2911
halftime_hash128	13478.23	97.79	252.14 (2)	2462
halftime_hash256	11620.28	98.44	252.60 (2)	2622
halftime_hash512	7681.62	125.81	274.01 (3)	3550
nmhash32	7850.01	56.74	207.59 (1)	2445
nmhash32x	7850.92	46.94	193.94 (1)	1494
k-hashv32	7079.27	62.44	213.31 (1)	1280
k-hashv64	7850.92	46.94	193.94 (1)	1279
komihash	10444.53	39.55	176.50 (1)	728

The sortable table variants:

• Default Intel i5-2300 2.8GHz
• Intel i5-2300 2.8GHz 32bit
• AMD Ryzen 3 3200U 3.5GHz
• Mac Air i7-4650
• Cortex-A53 2GHz (Sony XPeria L4)

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:

• xxh3low
• wyhash
• 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

• https://github.com/martinus/better-faster-stronger-mixer Mixers. And in his blog the best C++ hashmap benchmarks.
• http://nohatcoder.dk/2019-05-19-1.html gives a new, useful hash level classification 1-5.
• http://www.strchr.com/hash_functions lists other benchmarks and quality of most simple and fast hash functions.
• http://bench.cr.yp.to/primitives-hash.html lists the benchmarks of all currently tested secure hashes.
• http://valerieaurora.org/hash.html Lifetimes of cryptographic hash functions

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. wyhash_seed_init() and wyhash_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 all 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, discohash, 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'