paillier

Additively homomorphic Paillier encryption: a Rust implementation on top of GMP, bound to Python through pyo3.

Add encrypted numbers without decrypting them:

import paillier

pub, sec = paillier.generate_keypair(2048)

blobs = [bytes(b) for b in paillier.encrypt_many(pub, [1.5, 2.25, -0.75])]
total = paillier.add_many(pub, blobs)      # adding CIPHERTEXTS

paillier.decrypt(sec, total)               # 3.0

Whoever does the adding never sees the terms. Whoever holds the private key sees only the sum.

pip install pypaillier

Wheels for CPython 3.10, 3.11, 3.12 and 3.13. No compiler and no system GMP required.

The distribution is pypaillier; the import name is paillier. PyPI would not take paillier as a project name, and there was no reason to carry that into the API.

📖 Documentation

Read this before using it

This is not textbook Paillier. The scheme is the Damgård–Jurik variant with a short exponent: c = (1 + m·n) · hs^r mod n², where the base is fixed and the exponent — |n|/2 bits — is what varies. Almost all of the speed comes from that, and so does the consequence: ciphertext indistinguishability rests on more than DCRA alone. It needs an additional short-exponent assumption. That assumption is standard and published, but it exists, and "secure under DCRA" is not a sentence you can say here unconditionally.

There is NO constant time. Two timing side channels are closed, one stays open — about 0.118 bits out of 1024. It is named, measured, and guarded by a test that watches it does not grow.

Both statements are worked through in full, with measurements and with what the scheme does not give: documentation.

Numbers

2048-bit key, one machine, medians over five repeats:

operation cost
encryption, all cores 6500+ ops/s
encryption, one core 980 ops/s
addition 7.3 µs per term
decryption 3.75 ms
key generation 1.4–2.8 s (spread 1.0–10.3)
ciphertext 512–513 B

Encryption is 98 % modular multiplications inside the window table; encoding, serialisation and the rest come to under half a percent together. Key generation has an enormous spread because it is a search: safe primes are rare and the time to a hit is random.

Everything here is reproducible from the repository: python benches/measure.py.

Accuracy is configurable

blobs = paillier.encrypt_many(pub, values, scale_pow10=12)

The scale travels inside the ciphertext: decryption reads it from there, and addition refuses a batch that mixes scales. The two sides have nothing to agree on.

At scale_pow10 = 12 the sum error over a million sign-constant terms drops below the resolution of f64 itself — at the cost of narrowing the input range from |v| ≲ 9e7 to ≲ 9e3.

Checks

cargo test --release
python -m pytest

Performance and accuracy benchmarks live in benches/, each answering one question: reference.

Building from source

pip install maturin
maturin build --release

Needs stable Rust. GMP is built and linked statically; you do not need to install it separately.

Licences

The sources are MIT OR Apache-2.0, at your option.

The built wheels additionally contain GMP, statically linked through rug, and therefore fall under LGPL-3.0+ as a whole. Installing a wheel from PyPI gets you a combined work, not only our code.

If you need a binary with no LGPL code inside, build it from the source distribution against your own GMP: pip install --no-binary pypaillier pypaillier.

Full breakdown, including how the LGPL §4 conditions are met and where the techniques came from: NOTICE.md.

Project links

Data verified by PyPI on Aug 27, 2026
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Key dates

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  • Released:
Newer release available (0.7.0)

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Avatar for veryviolet from gravatar.com veryviolet

Credits

Author: Kirill Groshenkov

GitHub Statistics

Data verified by PyPI on Aug 27, 2026
The GitHub source repository was provided by the project maintainers and verified by PyPI at the time of upload. Stars, forks, and open issues/PRs are derived from that repository and have not been independently verified.

License expression

(MIT OR Apache-2.0) AND LGPL-3.0-or-later
View SPDX License List

Requires

Python >=3.10

Tags

paillier homomorphic-encryption cryptography federated-learning privacy

Classifiers

Report project as malware

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