FHElium: FHE, built from the tensor up

Pronounced “philium” /ˈfɪliəm/ or “F-helium” /ˌɛf ˈhiːliəm/.

Documentation: fhelium.550w.host

FHElium is a full-stack CKKS framework for Python and PyTorch. It provides native CPU and NVIDIA CUDA execution, tensor-backed encrypted values, immediate Eager evaluation, inspectable Compile Programs, runtime resource management, and rank-local distributed execution.

Install

FHElium supports CPython 3.12 and 3.13 on Linux x86-64, Windows x86-64, and macOS Apple Silicon. It builds against the PyTorch installation selected by the user. CUDA builds require a compatible CUDA toolkit and C++17 compiler; macOS uses the CPU implementation rather than PyTorch MPS.

Use the installation selector to choose the operating system, Python version, PyTorch version, and CPU or CUDA configuration. The selector provides a prebuilt-wheel command when that exact combination is published and a source-build command otherwise.

For a source installation, install the intended PyTorch package first, then build FHElium in the same environment:

python -m pip install "scikit-build-core==1.0.3" "cmake>=3.18" ninja
python -m pip install \
  --no-binary=fhelium \
  --no-build-isolation --no-cache-dir --verbose \
  fhelium

--no-build-isolation keeps the selected Torch build available to CMake, and --no-cache-dir prevents reuse of a wheel compiled for another Torch or CUDA environment. Set CMAKE_ARGS="-DFHELIUM_NATIVE_BACKENDS=CPU" for a CPU-only build, CUDA for CUDA-only, or CPU+CUDA for both implementations.

See the installation guide for compiler requirements, CUDA architecture selection, and troubleshooting.

Programming models

FHElium provides two first-class ways to execute CKKS computations:

• fhelium.eager.Engine executes each requested operation immediately;
• fhelium.compile constructs and transforms source-independent fhelium.ir.Program objects.

Both use the same fhelium.backend operation implementations and arithmetic resources. Eager follows the public state transition of each called operation and dispatches from operand placement. Compile callers select the passes that assign CKKS state, preserve or lower operations, bind materials and keys, and construct a ProgramExecutable.

Eager execution

import torch
import fhelium as fh
from fhelium.eager import Engine

# Change this to "cuda:0" to create inputs and keys on CUDA.
torch.set_default_device("cpu")
engine = Engine(fh.Preset.slots8192_scale40_depth7_int64)

x = torch.linspace(-0.05, 0.05, 32, dtype=torch.float64)
y = torch.linspace(0.02, -0.02, 32, dtype=torch.float64)

ct_x = engine.encrypt_message(x)
ct_y = engine.encrypt_message(y)

ct_sum = engine.add(ct_x, ct_y)

x_ntt = engine.coefficient_domain_to_ntt_domain(ct_x)
y_ntt = engine.coefficient_domain_to_ntt_domain(ct_y)
product_triplet = engine.multiply(x_ntt, y_ntt)
ct_product = engine.rescale_to_next_depth(
    engine.relinearize(product_triplet)
)

rotation_key = engine.rotation_key(1)
ct_rotated = engine.rotate_with_key(ct_x, rotation_key)

sum_clear = engine.decrypt_message(ct_sum, is_real=True)[: x.numel()]
product_clear = engine.decrypt_message(ct_product, is_real=True)[: x.numel()]

torch.testing.assert_close(sum_clear, x + y, atol=2e-5, rtol=0)
torch.testing.assert_close(product_clear, x * y, atol=2e-5, rtol=0)

Each encrypted value records its CKKS level, actual scale, active primes, polynomial domain, modulus basis, residue representation, and component count. Multiplication does not implicitly relinearize or rescale, and operations do not silently move Tensor payloads between devices.

Compile Programs

Compile captures or imports a source-independent Program and applies the pass sequence selected by the caller:

from fhelium import compile as fh_compile


def workload(secret, public):
    return secret + public


captured = fh_compile.capture(
    workload,
    inputs={
        "secret": fh_compile.encrypted(),
        "public": fh_compile.message(),
    },
)

pipeline = fh_compile.Pipeline(
    (
        fh_compile.EliminateDeadValuesPass(),
        fh_compile.LowerSemanticToLogicalPass(),
    )
)
compiled = pipeline.run(captured)

print(compiled.program.to_text())
print(compiled.reports)

A caller can continue from the same Compilation with CKKS state assignment, transition placement, CKKS-to-RNS/NTT lowering, key analysis, Backend linking, or custom passes. See examples/17_compose_and_execute.py for an encrypted end-to-end execution and examples/19_customize_compile_pass.py for a caller-defined BSGS transformation.

Runtime and distributed execution

fhelium.runtime provides device observations, reusable value buffers, and CUDA Graph execution. fhelium.residency manages live value placement and lifetime accounting. fhelium.distributed provides rank-local value transport and CKKS-aware collectives. Bootstrapping, multiparty CKKS, and JIT interfaces are available under fhelium.experimental.

The runtime components can be used independently around an evaluator:

from fhelium.runtime import (
    CpuTopology,
    CudaGraphProgram,
    MemorySnapshot,
    ReusableValueBuffer,
)
from fhelium.residency import PAGEABLE_HOST, ResidencyManager

cpu = CpuTopology.probe()
memory = MemorySnapshot.read("cuda:0")
buffer = ReusableValueBuffer.like(prototype, device="cuda:0")
program = CudaGraphProgram.capture(evaluator, example_inputs=(prototype,))
result = program.replay(next_input, synchronize=True)

residency = ResidencyManager()
weight_handle = residency.adopt(weight, at=PAGEABLE_HOST)
snapshot = residency.snapshot()

FHElium uses a single-program, multiple-data (SPMD) model. Each process owns a local device and an Eager Engine; the application chooses its data partition, keys, process groups, and communication schedule.

import torch
import fhelium as fh
import fhelium.distributed as dist
from fhelium.eager import Engine


def main():
    dist.init()
    torch.set_default_device(dist.local_device())
    engine = Engine(fh.Preset.slots32768_scale40_depth34_int64)

    weight = (
        engine.encode(torch.ones(16, dtype=torch.float64))
        if dist.get_rank() == 0
        else None
    )
    weight = dist.broadcast_plaintext(weight, src=0)
    print(
        f"rank={dist.get_rank()} device={weight.device} depth={weight.depth}"
    )
    dist.shutdown()


if __name__ == "__main__":
    main()

Save the program as distributed_example.py and launch one process per local GPU:

torchrun --standalone --nproc-per-node=2 distributed_example.py

The distributed API supports transport of independent values, modular reduction of additive ciphertext partials, and partitioning/reconstruction of residue-number-system limbs.

Command-line tools

The fhelium command reports the installed version, inspects CUDA devices and peer topology, runs benchmarks, and evaluates NTT backend candidates:

fhelium version
fhelium cuda info
fhelium cuda topo --bandwidth
fhelium benchmark list
fhelium benchmark run --device cpu --output results/benchmark.json
fhelium benchmark recommend ntt --suite kernel --device cuda:0

Running fhelium benchmark without a subcommand opens the interactive benchmark interface. See Inspect runtime and CUDA and Benchmark methodology for the complete command options and output schemas.

Documentation and examples

• Tutorials
• Concepts
• How-to guides
• Architecture
• API reference
• Developer guide

Start with examples/01_basic_ckks_flow.py or browse examples/README.md for Eager, Compile, CUDA Graph, distributed, persistence, Residency, batching, Bootstrap, and multiparty examples.

Development

Create the locked development environment and run the project checks:

git clone https://github.com/VisualDust/fhelium.git
cd fhelium
uv sync --locked
source .venv/bin/activate
just check

The contributor guide documents custom Torch environments, native builds, editor configuration, and the validation workflow.

Citation

If you use FHElium in research or software, cite the project as:

@software{fhelium2026,
  author  = {Zhaoting Gong and Jiaming Liang and Ran Ran and Wujie Wen},
  title   = {FHElium: A Cross-Stack CKKS Research Framework for CPU and CUDA},
  year    = {2026},
  version = {0.25.0},
  url     = {https://github.com/VisualDust/fhelium}
}

The same metadata is available in CITATION.cff.

License

FHElium is licensed under the MIT License.