Lattigo: lattice-based cryptographic library in Go

The Lattigo library unleashes the potential of lattice-based cryptography in secure multiparty computation for modern software stacks.

Lattigo is a Go package implementing lattice-based cryptographic primitives. The library features:

• A pure Go implementation bringing code-simplicity and easy builds.
• A public interface for an efficient multiprecision polynomial arithmetic layer.
• Comparable performance to state-of-the-art C++ libraries.

Lattigo aims at enabling fast prototyping of secure-multiparty computation solutions based on distributed homomorphic cryptosystems, by harnessing Go's natural concurrency model.

Library overview

The library comprises the following sub-packages:

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

• lattigo/bfv: RNS-accelerated Fan-Vercauteren version of Brakerski's scale invariant homomorphic encryption scheme. It provides modular arithmetic over the integers.

• lattigo/ckks: RNS-accelerated version of the Homomorphic Encryption for Arithmetic for Approximate Numbers (HEAAN, a.k.a. CKKS) scheme. It provides approximate arithmetic over the complex numbers.

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

• lattigo/examples: Executable Go programs demonstrating the usage of the Lattigo library. Note that each subpackage includes test files that further demonstrate the usage of Lattigo primitives.

• lattigo/utils: Supporting structures and functions.

Versions and Roadmap

The first version of Lattigo, (v1.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.

Upcoming features

• Bootstrapping for CKKS.
• README for distributed schemes
• Network layer implementation of protocols supporting Secure Multiparty Computation (SMC).

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.

Contact

If you want to contribute to Lattigo or you have any suggestion, do not hesitate to contact us at lattigo@listes.epfl.ch.

Citing

Please use the following BibTex entry for citing Lattigo:

@misc{lattigo,
    title = {Lattigo 1.3.0},
    howpublished = {Online: \url{http://github.com/ldsec/lattigo}},
    month = dec,
    year = 2019,
    note = {EPFL-LDS}
}

References

1. Somewhat Practical Fully Homomorphic Encryption (https://eprint.iacr.org/2012/144)
2. Computing accross Trust Boundaries using Distributed Homomorphic Cryptography (https://eprint.iacr.org/2019/961)
3. A Full RNS Variant of FV Like Somewhat Homomorphic Encryption Schemes (https://eprint.iacr.org/2016/510)
4. An Improved RNS Variant of the BFV Homomorphic Encryption Scheme (https://eprint.iacr.org/2018/117)
5. Homomorphic Encryption for Arithmetic of Approximate Numbers (https://eprint.iacr.org/2016/421)
6. A Full RNS Variant of Approximate Homomorphic Encryption (https://eprint.iacr.org/2018/931)
7. Improved Bootstrapping for Approximate Homomorphic Encryption (https://eprint.iacr.org/2018/1043)
8. Post-quantum key exchange - a new hope (https://eprint.iacr.org/2015/1092)
9. Faster arithmetic for number-theoretic transforms (https://arxiv.org/abs/1205.2926)
10. Speeding up the Number Theoretic Transform for Faster Ideal Lattice-Based Cryptography (https://eprint.iacr.org/2016/504)
11. 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.