Benchmarks
This document details the performance benchmarks of homomorphic operations using TFHE-rs.
By their nature, homomorphic operations run slower than their cleartext equivalents. The following are the timings for basic operations, including benchmarks from other libraries for comparison.
All CPU benchmarks were launched on an AWS hpc7a.96xlarge instance equipped with an AMD EPYC 9R14 CPU @ 2.60GHz and 740GB of RAM.
Integer operations
The following tables benchmark the execution time of some operation sets using FheUint (unsigned integers). The FheInt (signed integers) performs similarly.
The next table shows the operation timings on CPU when all inputs are encrypted:
Operation \ Size
FheUint8
FheUint16
FheUint32
FheUint64
FheUint128
FheUint256
Negation (-)
55.2 ms
80.4 ms
104 ms
130 ms
161 ms
202 ms
Add / Sub (+,-)
57.7 ms
82.1 ms
105 ms
128 ms
155 ms
195 ms
Mul (x)
80.8 ms
149 ms
211 ms
366 ms
961 ms
3.2 s
Equal / Not Equal (eq, ne)
31.9 ms
31.3 ms
48.7 ms
50.9 ms
51.4 ms
52.8 ms
Comparisons (ge, gt, le, lt)
48.1 ms
68.4 ms
83.2 ms
102 ms
121 ms
145 ms
Max / Min (max,min)
81.1 ms
96.4 ms
114 ms
133 ms
154 ms
198 ms
Bitwise operations (&, |, ^)
15.9 ms
16.1 ms
16.7 ms
17.8 ms
19.1 ms
21.9 ms
Div / Rem (/, %)
613 ms
1.56 s
3.73 s
8.83 s
20.6 s
53.8 s
Left / Right Shifts (<<, >>)
88.1 ms
108 ms
133 ms
160 ms
199 ms
403 ms
Left / Right Rotations (left_rotate, right_rotate)
83.6 ms
101 ms
127 ms
158 ms
198 ms
402 ms
Leading / Trailing zeros/ones
85.7 ms
135 ms
151 ms
206 ms
250 ms
308 ms
Log2
98.0 ms
151 ms
173 ms
231 ms
279 ms
333 ms
The next table shows the operation timings on CPU when the left input is encrypted and the right is a clear scalar of the same size:
Operation \ Size
FheUint8
FheUint16
FheUint32
FheUint64
FheUint128
FheUint256
Add / Sub (+,-)
61.7 ms
81.0 ms
99.3 ms
117 ms
144 ms
189 ms
Mul (x)
62.7 ms
133 ms
173 ms
227 ms
371 ms
917 ms
Equal / Not Equal (eq, ne)
33.2 ms
32.2 ms
31.4 ms
49.1 ms
49.8 ms
51.6 ms
Comparisons (ge, gt, le, lt)
32.1 ms
51.9 ms
70.8 ms
89.2 ms
110 ms
130 ms
Max / Min (max,min)
69.9 ms
88.8 ms
107 ms
130 ms
153 ms
188 ms
Bitwise operations (&, |, ^)
16.1 ms
16.3 ms
17.2 ms
18.2 ms
19.6 ms
22.1 ms
Div (/)
160 ms
194 ms
275 ms
391 ms
749 ms
2.02 s
Rem (%)
281 ms
404 ms
533 ms
719 ms
1.18 s
2.76 s
Left / Right Shifts (<<, >>)
16.0 ms
16.2 ms
16.7 ms
17.9 ms
19.2 ms
21.8 ms
Left / Right Rotations (left_rotate, right_rotate)
16.4 ms
16.6 ms
17.2 ms
18.4 ms
19.7 ms
22.2 ms
All timings are based on parallelized Radix-based integer operations where each block is encrypted using the default parameters PARAM_MESSAGE_2_CARRY_2_KS_PBS. To ensure predictable timings, we perform operations in the default mode, which propagates the carry bit as needed. You can minimize operational costs by selecting from 'unchecked', 'checked', or 'smart' modes, each balancing performance and security differently.
For more details about parameters, see here. You can find the benchmark results on GPU for all these operations here.
Shortint operations
The next table shows the execution time of some operations using various parameter sets of tfhe-rs::shortint. Except for unchecked_add, we perform all the operations in the default mode. This mode ensures predictable timings along the entire circuit by clearing the carry space after each operation. The configuration is Concrete FFT + AVX-512.
unchecked_add
341 ns
555 ns
2.47 µs
9.77 µs
add
5.96 ms
12.6 ms
102 ms
508 ms
mul_lsb
5.99 ms
12.3 ms
101 ms
500 ms
keyswitch_programmable_bootstrap
6.40 ms
12.9 ms
104 ms
489 ms
Boolean operations
The next table shows the execution time of a single binary Boolean gate.
tfhe-rs::boolean
DEFAULT_PARAMETERS_KS_PBS
8.49 ms
PARAMETERS_ERROR_PROB_2_POW_MINUS_165_KS_PBS
13.7 ms
TFHE_LIB_PARAMETERS
9.90 ms
tfhe-lib
Using the same hpc7a.96xlarge machine as the one for tfhe-rs, the timings are as follows:
default_128bit_gate_bootstrapping_parameters
13.5 ms
OpenFHE (v1.1.2)
Following the official instructions from OpenFHE, we use clang14 and the following command to setup the project: cmake -DNATIVE_SIZE=32 -DWITH_NATIVEOPT=ON -DCMAKE_C_COMPILER=clang -DCMAKE_CXX_COMPILER=clang++ -DWITH_OPENMP=OFF ..
The following example shows how to initialize the configuration to use the HEXL library:
Using the same hpc7a.96xlarge machine as the one for tfhe-rs, the timings are as follows:
FHEW_BINGATE/STD128_OR
25.5 ms
21,6 ms
FHEW_BINGATE/STD128_LMKCDEY_OR
25.4 ms
19.9 ms
Reproducing TFHE-rs benchmarks
TFHE-rs benchmarks can be easily reproduced from the source.
AVX512 is now enabled by default for benchmarks when available
The following example shows how to reproduce TFHE-rs benchmarks:
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