Lattigo: lattice-based multiparty homomorphic encryption library in Go

Lattigo is a Go module that implements Ring-Learning-With-Errors-based homomorphic-encryption primitives and Multiparty-Homomorphic-Encryption-based secure protocols. The library features:

• An implementation of the full-RNS BFV and CKKS schemes and their respective multiparty versions.
• Comparable performance to state-of-the-art C++ libraries.
• Dense-key and sparse-key efficient and high-precision bootstrapping procedures for full-RNS CKKS.
• A pure Go implementation that enables cross-platform builds, including WASM compilation for browser clients.

Lattigo is meant to support HE in distributed systems and microservices architectures, for which Go is a common choice thanks to its natural concurrency model and portability.

Library overview

The library exposes the following packages:

• lattigo/ring: Modular arithmetic operations for polynomials in the RNS basis, including: RNS basis extension; RNS rescaling; number theoretic transform (NTT); uniform, Gaussian and ternary sampling.

• lattigo/bfv: The Full-RNS variant of the Brakerski-Fan-Vercauteren scale-invariant homomorphic encryption scheme. It provides modular arithmetic over the integers.

• lattigo/ckks: The Full-RNS Homomorphic Encryption for Arithmetic for Approximate Numbers (HEAAN, a.k.a. CKKS) scheme. It provides approximate arithmetic over the complex numbers (in its classic variant) and over the real numbers (in its conjugate-invariant variant).

• lattigo/dbfv and lattigo/dckks: Multiparty (a.k.a. distributed or threshold) versions of the BFV and CKKS schemes that enable secure multiparty computation solutions with secret-shared secret keys.

• lattigo/rlwe and lattigo/drlwe: common base for generic RLWE-based multiparty homomorphic encryption. It is imported by the lattigo/bfv and lattigo/ckks packages.

• lattigo/examples: Executable Go programs that demonstrate the use of the Lattigo library. Each subpackage includes test files that further demonstrate the use of Lattigo primitives.

• lattigo/utils: Supporting structures and functions.

Versions and Roadmap

This version of Lattigo, (v2.x.x) is meant to be a working prototype. Hence, there will be backward-incompatible changes within this version.

See CHANGELOG.md for the current and past versions.

Disclaimer

This library is still at an experimental stage and should be used for research purposes only.

License

Lattigo is licensed under the Apache 2.0 License. See LICENSE.

Contact

If you want to contribute to Lattigo or you have any suggestion, do not hesitate to contact us at [email protected].

Citing

Please use the following BibTex entry for citing Lattigo:

@misc{lattigo,
    title = {Lattigo v2.4.0},
    howpublished = {Online: \url{https://github.com/ldsec/lattigo}},
    month = Jan,
    year = 2022,
    note = {EPFL-LDS}
}

References

1. Efficient Bootstrapping for ApproximateHomomorphic Encryption with Non-Sparse Keys (https://eprint.iacr.org/2020/1203)
2. Somewhat Practical Fully Homomorphic Encryption (https://eprint.iacr.org/2012/144)
3. Multiparty Homomorphic Encryption: From Theory to Practice (https://eprint.iacr.org/2020/304)
4. A Full RNS Variant of FV Like Somewhat Homomorphic Encryption Schemes (https://eprint.iacr.org/2016/510)
5. An Improved RNS Variant of the BFV Homomorphic Encryption Scheme (https://eprint.iacr.org/2018/117)
6. Homomorphic Encryption for Arithmetic of Approximate Numbers (https://eprint.iacr.org/2016/421)
7. A Full RNS Variant of Approximate Homomorphic Encryption (https://eprint.iacr.org/2018/931)
8. Improved Bootstrapping for Approximate Homomorphic Encryption (https://eprint.iacr.org/2018/1043)
9. Better Bootstrapping for Approximate Homomorphic Encryption (https://epring.iacr.org/2019/688)
10. Post-quantum key exchange - a new hope (https://eprint.iacr.org/2015/1092)
11. Faster arithmetic for number-theoretic transforms (https://arxiv.org/abs/1205.2926)
12. Speeding up the Number Theoretic Transform for Faster Ideal Lattice-Based Cryptography (https://eprint.iacr.org/2016/504)
13. Gaussian sampling in lattice-based cryptography (https://tel.archives-ouvertes.fr/tel-01245066v2)

The Lattigo logo is a lattice-based version of the original Golang mascot by Renee French.