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.

Parameter set	PARAM_MESSAGE_1_CARRY_1	PARAM_MESSAGE_2_CARRY_2	PARAM_MESSAGE_3_CARRY_3	PARAM_MESSAGE_4_CARRY_4
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

Parameter set	Concrete FFT + AVX-512
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:

Parameter set	spqlios-fma
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:

export CXX=clang++
export CC=clang

scripts/configure.sh
Release -> y
hexl -> y

scripts/build-openfhe-development-hexl.sh

Using the same hpc7a.96xlarge machine as the one for tfhe-rs, the timings are as follows:

Parameter set	GINX	GINX w/ Intel HEXL
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:

#Boolean benchmarks:
make bench_boolean

#Integer benchmarks:
make bench_integer

#Shortint benchmarks:
make bench_shortint