This library implements the fully homomorphic encryption algorithm from TFHE using CUDA and OpenCL. Unlike TFHE, where FFT is used internally to speed up polynomial multiplication, nuFHE can use either FFT or purely integer NTT (DFT-like transform on a finite field). The latter is based on the arithmetic operations and NTT scheme from cuFHE.
| Platform | Library | Performance (ms/bit) | |
| Binary Gate | MUX Gate | ||
| Single Core/Single GPU - FFT | TFHE (CPU) | 13 | 26 |
| nuFHE | 0.13 | 0.22 | |
| Speedup | 100.9 | 117.7 | |
| Single Core/Single GPU - NTT | cuFHE | 0.35 | N/A |
| nuFHE | 0.35 | 0.67 | |
| Speedup | 1.0 | - | |
The code from this example can be found in examples/gate_nand.py.
nufhe uses reikna as a backend for GPU operations, and all the nufhe calls require a reikna Thread object, encapsulating a GPU context and a serialization queue for GPU kernel calls. It can be created interactively:
from reikna.cluda import cuda_api
thr = cuda_api().Thread.create(interactive=True)
where the user will be offered to choose between available platforms and videocards. Alternatively, one can pick an arbitrary available platform/device:
thr = cuda_api().Thread.create()
It is also possible to create a Thread using a known device, or existing PyCUDA or PyOpenCL context. This is advanced usage, for those who plan to integrate nuFHE into a larger GPU-based program. See the documentation for Thread and Thread.create() for details.
If one wants to use OpenCL instead of CUDA, cuda_api should be replaced with ocl_api. Alternatively, one can use any_api to select an arbitrary available one.
The next step is the creation of a private and a public key. The former is used to encrypt plaintexts or decrypt cyphertexts; the latter is required to apply gates to encrypted data. Note that the public key can be rather large (on the order of 100Mb).
import numpy
import nufhe
rng = numpy.random.RandomState()
private_key, public_key = nufhe.make_key_pair(thr, rng)
make_key_pair takes some keyword parameters that affect the security of the algorithm; the default values correspond to about 110 bits of security.
Using the private key we can encrypt some data. nuFHE gates operate on bit arrays:
size = 32
bits1 = rng.randint(0, 2, size=size).astype(numpy.bool)
bits2 = rng.randint(0, 2, size=size).astype(numpy.bool)
ciphertext1 = nufhe.encrypt(thr, rng, private_key, bits1)
ciphertext2 = nufhe.encrypt(thr, rng, private_key, bits2)
In this example we will test the NAND gate, so the reference result would be
reference = ~(bits1 * bits2)
On the server side, where only the public key is known, one can use it to apply a gate:
result = nufhe.empty_ciphertext(thr, public_key.params, ciphertext1.shape)
nufhe.gate_nand(thr, public_key, result, ciphertext1, ciphertext2)
After the processing, the person in possession of the private key can decrypt the result and verify that the gate was applied correctly:
result_bits = nufhe.decrypt(thr, private_key, result)
assert (result_bits == reference).all()