Benchmark results for FHE Matrix Multiplication using the TenSEAL FHE library

Overview

The following tables present timing results for Encrypted Matrix Multiplication (A \times B) using the TenSEAL Fully-Homomorphic Encryption (FHE) library. The results represent a first order analysis of the timing complexity considering Key Generation, Matrix Encryption, Matrix Multiplication, and Matrix Decryption. Two FHE algorithms assessed are: the Brakerski/Fan-Vercauteren (BFV, 2012); and the Cheon/Kim/Kim/Song (CKKS, 2017).

The results represent the median of 10 executions of the same functions for exactly the same matrix values on a AMD Ryzen 7 3800XT 8-Core Processor with 128GB of RAM running Ubuntu 18.04 LTS.

Cheon/Kim/Kim/Song (CKKS, 2017)

It considers values distributed in the interval [-1, 1].

Square Matrix Size	Poly Degree	Key Generation	Matrix Encryption	Matrix Multiplication	Matrix Decryption	Total
2	4096	0.0373685	0.00558531	0.00353527	0.000678956	0.047348
4	4096	0.0415051	0.00971408	0.0108032	0.00253088	0.065991
6	4096	0.0384495	0.0151066	0.0321764	0.00567592	0.0976619
8	4096	0.0378664	0.0249162	0.0531681	0.00990422	0.126971
10	4096	0.037962	0.0432207	0.109004	0.0154365	0.207592
12	4096	0.0390311	0.0509846	0.169315	0.02288	0.282631
14	4096	0.0390451	0.0726871	0.283288	0.0310608	0.427466
16	4096	0.0381212	0.08773	0.399686	0.0403261	0.565632
18	4096	0.0386489	0.105945	0.58683	0.0505936	0.782588
20	4096	0.0379708	0.126649	0.77721	0.0619784	1.00465

2	8192	0.351809	0.018675	0.0229037	0.0052375	0.399295
4	8192	0.314432	0.0265851	0.0611404	0.0202107	0.425485
6	8192	0.313806	0.0599225	0.182204	0.0451886	0.603148
8	8192	0.315484	0.0785349	0.361297	0.0809502	0.840385
10	8192	0.315917	0.13319	0.713796	0.125733	1.2869
12	8192	0.325244	0.160896	1.1832	0.188304	1.85589
14	8192	0.325775	0.232407	1.91734	0.255411	2.72282
16	8192	0.325226	0.2642	2.80793	0.334424	3.72532
18	8192	0.32283	0.329212	3.99955	0.42196	5.08879
20	8192	0.320731	0.397718	5.38735	0.518657	6.62535

2	16384	3.30117	0.0765723	0.153542	0.0343709	3.56885
4	16384	3.26297	0.104264	0.384418	0.137865	3.88944
6	16384	3.33185	0.251622	1.28806	0.314782	5.20725
8	16384	3.77817	0.339053	2.86381	0.643181	7.59356
10	16384	3.36282	0.535207	5.63527	1.01315	10.5234
12	16384	3.58629	0.723618	9.44421	1.4474	15.1965
14	16384	3.30264	0.990225	15.0997	1.95204	21.3634
16	16384	3.3449	1.24563	22.3121	2.57096	29.4396
18	16384	3.37075	1.5931	31.9139	3.28238	40.16
20	16384	3.40239	1.92663	43.2923	3.98654	52.6965

2	32768	22.2062	0.237622	0.498116	0.205471	23.1674
4	32768	22.2687	0.358636	1.91777	0.630358	25.1722
6	32768	22.5224	0.770142	6.3481	1.93495	31.5635
8	32768	21.944	1.21687	15.7835	3.47359	42.2752
10	32768	22.5665	1.89781	29.8854	5.45901	59.8807
12	32768	22.7846	2.63184	55.1396	7.89782	88.5128
14	32768	22.7331	3.64222	84.8491	10.7527	121.482
16	32768	22.5677	4.59591	131.853	13.785	172.652
18	32768	22.2236	5.84971	183.95	17.6166	229.475
20	32768	22.7574	7.21072	259.041	21.538	310.432

Brakerski/Fan-Vercauteren (BFV, 2012)

For values encoded in a 8-bits words, i.e., [-128, 127].

Square Matrix Size	Poly Degree	Key Generation	Matrix Encryption	Matrix Multiplication	Matrix Decryption	Total
2	4096	0.0377995	0.0079144	0.0119991	0.001757	0.059412
4	4096	0.0385401	0.0310754	0.04857	0.0101067	0.128903
6	4096	0.0388934	0.0711818	0.116208	0.0141443	0.240435
8	4096	0.0381538	0.125155	0.224531	0.0247384	0.411264
10	4096	0.0392515	0.202174	0.428509	0.0396459	0.70993
12	4096	0.038788	0.289526	0.699746	0.0572524	1.08411
14	4096	0.0393694	0.395334	1.15041	0.0777138	1.66316
16	4096	0.0380453	0.498316	1.63302	0.0991596	2.26808
18	4096	0.039335	0.648478	2.3776	0.12829	3.1923
20	4096	0.0386491	0.787167	3.16908	0.156403	4.14982

2	8192	0.31991	0.0245685	0.0622934	0.00594231	0.416783
4	8192	0.323777	0.100165	0.148528	0.0239333	0.596174
6	8192	0.325106	0.227095	0.535228	0.0537211	1.13977
8	8192	0.320736	0.398389	1.08796	0.0944704	1.90198
10	8192	0.327888	0.635885	2.19645	0.15062	3.30938
12	8192	0.317587	0.885985	3.60398	0.210393	5.01883
14	8192	0.325236	1.23842	5.87361	0.295459	7.72569
16	8192	0.323558	1.60148	8.53057	0.382403	10.8397
18	8192	0.324627	2.04541	12.3053	0.486117	15.1466
20	8192	0.321264	2.48859	16.6187	0.59123	20.0204

2	16384	3.34215	0.106466	0.299036	0.0276478	3.78774
4	16384	3.34082	0.572084	0.962007	0.11198	4.99987
6	16384	3.64353	1.26835	3.30309	0.247418	8.32709
8	16384	3.65239	1.95942	7.4746	0.435587	13.4169
10	16384	3.35543	3.56769	14.4802	0.692605	22.1931
12	16384	3.33258	5.11146	25.168	0.992516	34.4741
14	16384	3.30843	7.03182	39.4612	1.35115	51.1695
16	16384	3.50898	8.47907	59.7193	1.76845	73.6794
18	16384	3.35361	11.5886	84.2869	2.22871	101.457
20	16384	3.3764	14.309	116.513	2.77341	137.316

2	32768	19.5607	0.461412	1.09035	0.0958294	21.1562
4	32768	22.6645	2.05374	7.07852	0.390171	31.9644
6	32768	21.5771	3.58952	17.5453	0.85866	43.6383
8	32768	21.5342	6.75882	54.9134	1.52116	83.9918
10	32768	22.5634	12.4821	94.0993	2.43751	130.537
12	32768	22.5477	17.7262	185.33	3.49048	227.191
14	32768	22.9315	24.19	272.474	4.72813	322.338
16	32768	23.1699	30.9058	438.097	6.172	497.845
18	32768	23.2238	35.8982	595.899	7.80789	662.042
20	32768	23.0588	49.6902	851.113	9.5594	933.631

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Benchmark results for FHE Matrix Multiplication using the TenSEAL FHE library