SMhasher

Hash function	MiB/sec	cycl./hash	cycl./map	size	Quality problems
donothing32	11536809.55	4.00	-	13	bad seed 0, test NOP
donothing64	12269832.97	4.00	-	13	bad seed 0, test NOP
donothing128	11961841.48	4.08	-	13	bad seed 0, test NOP
NOP_OAAT_read64	11652662.97	14.00	-	47	test NOP
BadHash	794.68	72.80	-	47	bad seed 0, test FAIL
sumhash	10184.67	29.40	-	363	bad seed 0, test FAIL
sumhash32	44755.87	23.46	-	863	UB, test FAIL
multiply_shift	8286.63	25.39	209.06 (2)	345	bad seeds & 0xfffffff0, fails most tests
pair_multiply_shift	5728.05	39.67	218.48 (12)	609	fails most tests
--------------------------
crc32	369.88	142.33	396.81 (101)	422	insecure, 8590x collisions, distrib, PerlinNoise
md5_32	359.43	638.92	865.21 (6)	4419
md5_64	360.20	640.38	869.55 (6)	4419
md5-128	344.63	669.59	856.34 (5)	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	1632.88	170.77	379.84 (5)	989	insecure,sanity, Permutation, Zeroes, machine-specific
sha1ni_32	1583.50	172.17	387.70 (4)	989	machine-specific
sha2ni-256	1556.66	180.75	393.79 (5)	4241	insecure,sanity, Permutation, Zeroes, machine-specific
sha2ni-256_64	1508.82	184.89	393.07 (6)	4241	Zeroes, machine-specific
blake3_c	1298.04	354.25	563.63 (4)		no 32bit portability
rmd128	294.42	712.67	930.65 (4)
rmd160	202.16	1045.79	1287.74 (16)		Cyclic hi32
rmd256	366.21	615.39	830.04 (7)
edonr224	863.77	304.76	496.66 (3)
edonr256	870.97	296.40	517.82 (6)
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	159.33	402.54	473.15 (4)	6490
sha3-256	100.58	3877.18	4159.79 (37)		PerlinNoise
sha3-256_64	100.57	3909.00	4174.63 (16)		PerlinNoise
hasshe2	2879.93	62.47	272.34 (2)	445	Permutation,TwoBytes,Zeroes,Seed
poly_1_mersenne	1278.37	63.42	244.41 (1)	479	fails most tests
poly_2_mersenne	1391.90	69.97	255.44 (3)	479
poly_3_mersenne	1320.15	80.81	263.12 (2)	479
poly_4_mersenne	1393.93	89.07	262.97 (2)	479
tabulation32	5819.40	40.16	233.00 (3)	848	collisions
tabulation	7407.94	39.83	240.25 (4)	554
crc32_hw	5537.79	40.80	225.65 (3)	653	insecure, 100% bias, collisions, distrib, BIC, machine-specific (SSE4.2/NEON)
crc32_hw1	7626.17	50.21	228.50 (2)	671	insecure, 100% bias, collisions, distrib, BIC, machine-specific (x86 SSE4.2)
crc64_hw	5579.17	40.87	202.19 (1)	652	insecure, 100% bias, collisions, distrib, BIC, machine-specific (SSE4.2/NEON)
crc32_pclmul	7963.20	106.02	567.70 (3)		insecure, 100% bias, collisions, distrib, BIC, machine-specific (x86 SSE4.2+PCLMUL)
crc64_jones1	1673.67	83.00	249.16 (2)		insecure, 100% bias, collisions, distrib, BIC, machine-specific
crc64_jones2	2968.07	314.60	253.01 (3)		insecure, 100% bias, collisions, distrib, BIC, machine-specific
crc64_jones3	3398.80	302.59	258.16 (8)		insecure, 100% bias, collisions, distrib, BIC, machine-specific
crc64_jones	3512.66	80.70	251.40 (2)		insecure, 100% bias, collisions, distrib, BIC, machine-specific
o1hash	11530366.92	18.40	206.94 (1)	101	insecure, no seed, zeros, fails all tests
fibonacci	15409.62	22.67	872.83 (3)	1692	UB, zeros, fails all tests
FNV1a	754.70	75.28	226.30 (2)	204	bad seed, zeros, fails all tests
FNV1A_Totenschiff	6166.85	26.60	235.71 (2)	270	UB, zeros, fails all tests
FNV1A_Pippip_Yurii	6115.29	28.03	233.52 (2)	147	UB, sanity, fails all tests
FNV1a_YT	13481.70	30.67	233.71 (7)	321	bad seed, UB, fails all tests
FNV2	5630.87	32.09	207.08 (1)	278	fails all tests
FNV64	747.70	74.18	189.18 (1)	79	fails all tests
FNV128	408.59	130.82	299.47 (20)	171	fails all tests
k-hash32	2227.90	53.85	255.78 (2)	808	insecure, zeros, UB, bad seeds, fails all tests
k-hash64	2492.66	48.18	242.58 (2)	609	insecure, zeros, UB, bad seeds, fails all tests
fletcher2	15410.12	20.72	345.55 (5)	248	bad seed 0, UB, fails all tests
fletcher4	15603.68	21.24	320.09 (2)	371	bad seed 0, UB, fails all tests
bernstein	1032.00	59.04	225.09 (3)	41	bad seed 0, fails all tests
sdbm	772.01	71.67	220.09 (2)	41	bad seed 0, fails all tests
x17	765.01	75.61	225.81 (2)	79	99.98% bias, fails all tests
libiberty	618.39	86.58	220.95 (2)	37	insecure, 100% bias, fails all tests, bad seed
gcc	612.10	88.44	224.62 (2)	39	insecure, 100% bias, fails all tests, bad seed
JenkinsOOAT	615.60	111.23	251.08 (2)	153	bad seed 0, 53.5% bias, fails all tests
JenkinsOOAT_perl	631.79	93.13	232.44 (1)	65	bad seed 0, 1.5-11.5% bias, 7.2x collisions, BIC, LongNeighbors
MicroOAAT	730.89	78.25	236.07 (3)	68	100% bias, distrib, BIC
pearsonhash64	439.85	123.07	213.68 (1)		Avalanche, Seed, SSSE3 only. broken MSVC
pearsonhash128	438.49	123.81	212.89 (2)		Avalanche, Seed, SSSE3 only. broken MSVC
pearsonhash256	440.63	120.72	224.63 (2)		Avalanche, Seed, SSSE3 only. broken MSVC
VHASH_32	13084.37	65.45	280.14 (2)	1231	sanity, Seed, MomentChi2
VHASH_64	13217.64	64.90	270.04 (2)	1231	sanity, Seed, Sparse
farsh32	27583.89	65.65	266.64 (2)	944	insecure: AppendedZeroes, collisions+bias, MomentChi2, LongNeighbors
farsh64	13558.69	113.74	327.26 (3)	944	insecure: AppendedZeroes, collisions+bias, MomentChi2, LongNeighbors
farsh128	7055.39	229.42	375.57 (4)	944	insecure: AppendedZeroes, collisions+bias, permut,combin,2bytes,zeroes,PerlinNoise
farsh256	3466.26	444.74	610.23 (4)	944	insecure: AppendedZeroes, collisions+bias, permut,combin,2bytes,zeroes,PerlinNoise
jodyhash32	1762.46	42.66	236.09 (2)	102	bias, collisions, distr, BIC LongNeighbors
jodyhash64	4861.84	44.05	234.35 (2)	118	bias, collisions, distr, BIC, LongNeighbors
lookup3	2474.09	40.19	238.22 (3)	341	UB, 28% bias, collisions, 30% distr, BIC
superfast	2085.79	49.89	230.76 (3)	210	UB, bad seed 0, 91% bias, 5273.01x collisions, 37% distr, BIC
MurmurOAAT	513.75	105.23	244.81 (4)	47	bad seed 0, collisions, 99.998% distr., BIC, LongNeighbors
Crap8	3081.04	37.15	234.94 (2)	342	UB, 2.42% bias, collisions, 2% distrib
Murmur1	1955.36	48.84	236.25 (2)	358	UB, 1 bad seed, 511x collisions, Diff, BIC
Murmur2	3082.03	41.62	250.72 (4)	358	UB, 1 bad seed, 1.7% bias, 81x coll, 1.7% distrib, BIC
Murmur2A	2850.40	46.60	284.58 (13)	407	UB, 1 bad seed, 12.7% bias, LongNeighbors
Murmur2B	6039.96	38.70	212.23 (1)	433	UB, 1.8% bias, collisions, 3.4% distrib, BIC
Murmur2C	3802.68	49.82	220.13 (2)	444	UB, 2^32 bad seeds, 91% bias, collisions, distr, BIC, LongNeighbors
Murmur3A	3027.30	48.99	234.49 (2)	351	UB, 1 bad seed, Moment Chi2 69
PMurHash32	3001.44	48.99	240.35 (3)	1862	1 bad seed, Moment Chi2 69
Murmur3C	4824.95	57.39	243.91 (2)	859	UB, LongNeighbors, Text, DiffDist
mirhash32low	6168.04	38.35	234.32 (2)	1112	UB, 4 bad seeds, Cyclic, LongNeighbors, machine-specific (32/64 differs)
PMPML_32	6904.30	44.25	233.59 (2)	1084	Avalanche >512, unseeded: Seed, BIC, MomentChi2, PerlinNoise
PMPML_64	10030.67	49.22	239.07 (5)	1305	unseeded: Seed, MomentChi2, BIC
xxHash32	6064.37	48.86	234.27 (3)	738	LongNeighbors, collisions with 4bit diff, MomentChi2 220
metrohash64	14209.14	40.85	225.16 (2)	624	UB, LongNeighbors, BIC
metrohash64_1	14495.30	40.83	213.00 (2)	624	UB, LongNeighbors, BIC, MomentChi2
metrohash64crc_1	8010.90	44.43	213.94 (2)	632	UB, Cyclic 8/8 byte, DiffDist, BIC, MomentChi2, machine-specific (SSE4.2/NEON)
metrohash64crc_2	7939.65	44.84	222.01 (2)	632	UB, Cyclic 8/8 byte, DiffDist, BIC, machine-specific (SSE4.2/NEON)
cmetrohash64_1o	14678.56	40.33	216.44 (2)	3506	UB, LongNeighbors, BIC, MomentChi2
cmetrohash64_1	14332.75	41.04	216.05 (2)	652	UB, LongNeighbors, BIC, MomentChi2
City64noSeed	14023.27	33.37	223.59 (2)	1038	Avalanche, Sparse, TwoBytes, MomentChi2, Seed
City64	14390.09	46.69	231.99 (2)	1120	Sparse, TwoBytes
t1ha1_64le	13425.03	31.37	221.97 (2)	517	Avalanche
t1ha1_64be	12002.50	31.57	226.52 (2)	555	Avalanche
t1ha0_32le	7276.16	49.11	236.39 (2)	509	Sparse, LongNeighbors
t1ha0_32be	6860.87	50.16	241.26 (2)	533	Sparse, LongNeighbors
t1ha0_aes_avx1	27881.52	36.78	227.13 (2)	533	Sparse, LongNeighbors
t1ha2_stream	13673.22	81.12	263.88 (3)	1665	Sparse, Permutation, LongNeighbors
t1ha2_stream128	13913.43	94.60	296.15 (4)	1665	Sparse, Permutation, LongNeighbors
aesnihash	5365.60	57.21	255.87 (3)	1209	fails many tests, machine-specific (x64 AES-NI)
aesni-hash-peterrk	29107.73	28.86	217.57 (1)		machine-specific (x64 AES-NI)
falkhash	52401.48	122.70	316.79 (4)	264	Sparse, LongNeighbors, machine-specific (x64 AES-NI)
MeowHash	29969.81	64.90	273.79 (8)	1764	Sparse, invertible, machine-specific (x64 AES-NI)
MeowHash64low	29438.45	63.76	269.41 (4)	1764	Sparse, invertible, machine-specific (x64 AES-NI)
MeowHash32low	30562.54	63.77	283.26 (3)	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	4152.62	202.14	414.34 (4)	1294
discohash1-128	4064.39	231.06	430.94 (6)	1294
discohash2	4026.84	204.37	408.13 (6)	1294
discohash2-128	4153.48	226.54	429.24 (4)	1294
discoNONG	3661.23	397.81	651.23 (54)		bad seeds
chaskey	1142.38	113.98	288.04 (1)	1609	PerlinNoise
SipHash	953.51	147.32	332.02 (5)	1071
HalfSipHash	1128.85	80.48	260.42 (2)	700	zeroes
GoodOAAT	744.67	87.23	243.36 (2)	237
pearsonbhash64	1749.98	99.84	257.11 (2)	683
pearsonbhash128	1656.68	106.78	276.92 (3)	1134
pearsonbhash256	1418.61	123.68	301.26 (3)	844
prvhash64_64m	3107.77	47.31	236.76 (2)	349
prvhash64_64	3057.79	47.83	244.16 (2)	384
prvhash64_128	3340.87	67.90	264.44 (2)	718
prvhash64s_64	6724.41	266.09	438.90 (3)	2640
prvhash64s_128	6703.66	326.46	508.67 (3)	2799
SipHash13	1803.96	107.93	304.05 (3)	778	0.9% bias
TSip	4330.87	52.43	245.31 (2)	519	!msvc
seahash	8240.58	58.61	260.35 (1)	871	PerlinNoise, !msvc
seahash32low	8245.91	58.61	264.07 (2)	871	PerlinNoise 32, !msvc
clhash	22932.36	67.22	262.78 (2)	1809	PerlinNoise, machine-specific (x64 SSE4.2)
HighwayHash64	6242.58	99.55	248.41 (3)	2546
Murmur3F	7104.08	52.69	216.34 (2)	699	UB
MUM	9631.26	34.78	219.14 (2)	1912	UB, too many bad seeds, machine-specific (32/64 differs)
MUMlow	8532.17	35.95	238.37 (2)	1912	UB, 5 bad seeds
xmsx32	2105.03	45.35	238.92 (3)	192	2 bad seeds
mirhash	5793.85	38.15	212.91 (2)	1112	UB, 2^36 bad seeds, LongNeighbors, machine-specific (32/64 differs)
mirhashstrict	3587.79	49.85	219.49 (2)	1112
mirhashstrict32low	3642.77	50.16	233.34 (3)	1112	1 bad seed, MomentChi2 9
fasthash32	6107.05	40.49	237.83 (2)	566	UB
fasthash64	5600.11	38.04	219.71 (2)	509	UB
aesni	31185.98	29.45	226.75 (2)	519	machine-specific (x64 AES-NI)
aesni-low	31027.39	29.47	232.54 (2)	519	machine-specific (x64 AES-NI)
mx3	9332.99	47.07	221.61 (2)	734	UB
pengyhash	13347.17	74.79	278.74 (3)	421
City32	5745.83	52.44	242.69 (2)	1319
City64low	13119.17	47.92	251.81 (2)	1120
City128	14472.20	88.71	285.61 (10)	1841
CityCrc128	12255.05	89.25	281.85 (2)	295
CityCrc256	12428.45	164.93	358.73 (2)
FarmHash32	22136.14	46.75	258.73 (2)	11489	machine-specific (x64 SSE4/AVX)
FarmHash64	12929.54	46.82	238.50 (2)	3758
FarmHash128	14454.12	68.09	254.04 (2)	163
farmhash32_c	22150.13	46.08	251.43 (3)	762	machine-specific (x64 SSE4/AVX)
farmhash64_c	12925.73	46.76	239.47 (2)	3688
farmhash128_c	14284.69	68.80	256.66 (3)	1890
metrohash64_2	14359.39	41.09	215.53 (2)	627	UB, LongNeighbors
cmetrohash64_2	14498.20	40.87	219.65 (2)	655	LongNeighbors
metrohash128	15847.63	72.33	266.54 (2)	773	UB, LongNeighbors
metrohash128_1	15556.40	73.49	259.05 (2)	773	UB, LongNeighbors
metrohash128_2	15408.56	74.36	259.57 (2)	773	UB, LongNeighbors
metrohash128crc_1	8182.02	77.38	256.80 (2)	723	UB, machine-specific (SSE4.2/NEON)
metrohash128crc_2	7996.33	78.81	262.53 (2)	723	UB, machine-specific (SSE4.2/NEON)
xxHash64	11176.72	49.67	230.24 (6)	1999
Spooky32	13623.84	55.45	248.11 (3)	2221	UB
Spooky64	13400.95	55.06	244.86 (3)	2221	UB
Spooky128	13621.00	59.05	235.42 (2)	2221	UB
SpookyV2_32	13626.51	56.19	256.57 (19)	2069
SpookyV2_64	13401.13	56.18	246.33 (11)	2069
SpookyV2_128	12252.64	58.94	235.46 (2)	2069
ahash64	9862.62	27.32	181.68 (1)	412	rust
xxh3	20853.74	29.46	220.07 (2)	744	DiffDist bit 7 w. 36 bits, BIC
xxh3low	20568.96	29.98	243.82 (5)	756
xxh128	19259.99	31.58	228.84 (2)	1012
xxh128low	19555.88	30.85	227.83 (2)	1012
t1ha2_atonce	14275.60	37.02	224.12 (2)	541	Zeroes low3
t1ha2_atonce128	14059.85	56.44	251.53 (3)	613	LongNeighbors
t1ha0_aes_noavx	27335.47	37.34	230.59 (2)	925	LongNeighbors, machine-specific (x86 AES-NI)
t1ha0_aes_avx1	27881.52	36.78	227.13 (2)	843	LongNeighbors, machine-specific (x64 AVX)
t1ha0_aes_avx2	56581.83	36.51	223.59 (1)	792	LongNeighbors, machine-specific (x64 AVX2)
wyhash32	2532.89	48.40	484.57 (1)	426	4 bad and broken seeds, 32-bit
wyhash32low	23104.85	28.56	239.71 (4)	474	5 bad seeds
wyhash	22640.53	28.91	229.00 (2)	474
w1hash	14208.56	26.85	221.76 (2)
rapidhash	22147.09	29.07	214.80 (2)	574
rapidhash_unrolled	21723.13	29.40	220.97 (3)	782
umash32	21999.19	41.14	239.07 (2)	1530
umash32_hi	22347.33	41.22	251.12 (4)	1530
umash64	21963.54	41.12	228.34 (1)	1530
umash128	13629.66	41.65	228.25 (1)	1530
halftime_hash64	4801.79	99.05	310.02 (2)	2911
halftime_hash128	18220.34	94.31	307.50 (1)	2462
halftime_hash256	18249.32	97.56	322.85 (2)	2622
halftime_hash512	10906.18	118.54	326.76 (3)	3550
nmhash32	12676.08	57.09	255.20 (2)	2445
nmhash32x	13072.64	42.09	288.12 (3)	1494
k-hashv32	8393.09	53.95	252.98 (3)	1280
k-hashv64	9251.05	51.72	251.83 (2)	1279
komihash	12179.74	33.23	224.80 (2)	1323
polymur	9913.53	41.68	232.56 (3)	1128
gxhash32	47943.08	37.71	251.38 (2)	736	AES only
gxhash64	48919.73	36.61	236.98 (3)	720	AES only

The sortable table variants:

• Default AMD Ryzen 5 3350G 3.6GHz
• Intel i7-6820HQ 3.5GHz (Lenovo P50 from 2024)
• fast AMD EPYC 9554P 64-Core Processor (Server from 2024)
• Intel i5-2300 2.8GHz
• AMD Ryzen 5 PRO 3350G 3.6GHz 32bit 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:

• 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

• 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. 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'