Lattigo: lattice-based multiparty homomorphic encryption library in Go

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

• Optimized arithmetic for power-of-two cyclotomic rings.
• Advanced and scheme agnostic implementation of RLWE-based primitives, key-generation, and their multiparty version.
• Implementation of the BFV/BGV and CKKS schemes and their multiparty version.
• Support for RGSW, external product and LMKCDEY blind rotations.
• A pure Go implementation, enabling cross-platform builds, including WASM compilation for browser clients, with comparable performance to state-of-the-art C++ libraries.

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/he: The main package of the library which provides scheme-agnostic interfaces and Homomorphic Encryption based on the plaintext domain.

  • hebin: Blind rotations (a.k.a Lookup Tables) over RLWE ciphertexts.

  • hefloat: Homomorphic Encryption for fixed-point approximate arithmetic over the complex or real numbers.

    • bootstrapper: State-of-the-Art bootstrapping for fixed-point approximate arithmetic over the real and comples numbers, with support for the Conjugate Invariant ring, batch bootstrapping with automatic packing/unpacking of sparsely packed/smaller ring degree ciphertexts, arbitrary precision bootstrapping and advanced circuit customization/parameterization.

  • heint: Homomorphic Encryption for modular arithmetic over the integers.

• lattigo/mhe: Package for multiparty (a.k.a. distributed or threshold) key-generation and interactive ciphertext bootstrapping with secret-shared secret keys.

  • mhefloat: Homomorphic decryption and re-encryption from and to Linear-Secret-Sharing-Shares, as well as interactive ciphertext bootstrapping for the package he/hefloat.

  • mheint: Homomorphic decryption and re-encryption from and to Linear-Secret-Sharing-Shares, as well as interactive ciphertext bootstrapping for the package he/heint.

• lattigo/schemes: A package implementing RLWE-based homomorphic encryption schemes.

  • bfv: A Full-RNS variant of the Brakerski-Fan-Vercauteren scale-invariant homomorphic encryption scheme. This scheme is instantiated via a wrapper of the bgv scheme. It provides modular arithmetic over the integers.

  • bgv: A Full-RNS generalization of the Brakerski-Fan-Vercauteren scale-invariant (BFV) and Brakerski-Gentry-Vaikuntanathan (BGV) homomorphic encryption schemes. It provides modular arithmetic over the integers.

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

• lattigo/core: A package implementing the core cryptographic functionalities of the library.

  • rlwe: Common base for generic RLWE-based homomorphic encryption. It provides all homomorphic functionalities and defines all structs that are not scheme specific. This includes plaintext, ciphertext, key-generation, encryption, decryption and key-switching, as well as other more advanced primitives such as RLWE-repacking.

  • rgsw: A Full-RNS variant of Ring-GSW ciphertexts and the external product.

• 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/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: Generic utility methods. This package also contains the following sub-pacakges:

  • bignum: Arbitrary precision linear algebra and polynomial approximation.
  • buffer: Efficient methods to write/read on io.Writer and io.Reader.
  • factorization: Various factorization algorithms for medium-sized integers.
  • sampling: Secure bytes sampling.
  • structs: Generic structs for maps, vectors and matrices, including serialization.

Versions and Roadmap

The Lattigo library was originally exclusively developed by the EPFL Laboratory for Data Security until its version 2.4.0.

Starting with the release of version 3.0.0, Lattigo is maintained and supported by Tune Insight SA.

Also starting with from version 3.0.0, the module name has changed to github.com/tuneinsight/lattigo/v[X], and the official repository has been moved to https://github.com/tuneinsight/lattigo. This has the following implications for modules that depend on Lattigo:

• Modules that require github.com/ldsec/lattigo/v2 will still build correctly.
• To upgrade to a version X.y.z >= 3.0.0, depending modules must require github.com/tuneinsight/lattigo/v[X]/, for example by changing the imports to github.com/tuneinsight/lattigo/v[X]/[package] and by running go mod tidy.

The current version of Lattigo, (v4.x.x) is fast-evolving and in constant development. Consequently, there will still be backward-incompatible changes within this major version, in addition to many bug fixes and new features. Hence, we encourage all Lattigo users to update to the latest Lattigo version.

See CHANGELOG.md for the current and past versions.

Stability

To keep a comprehensive history, we prioritize rebases over merges for branches other than main. Branches with the prefix dev_ are branches in active development and will be frequently rebased. Hence, we don't recommend depending on them.

Pull Requests

External pull requests should only be used to propose new functionalities that are substantial and would require a fair amount of work if done on our side. If you plan to open such a pull request, please contact us before doing so to make sure that the proposed changes are aligned with our development roadmap.

External pull requests only proposing small or trivial changes will be converted to an issue and closed.

License

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

Contact

Before contacting us directly, please make sure that your request cannot be handled through an issue.

If you want to contribute to Lattigo, have a feature proposal or request, to report a security issue or simply want to contact us directly, please do so using the following email: lattigo@tuneinsight.com.

Citing

Please use the following BibTex entry for citing Lattigo:

@misc{lattigo,
    title = {Lattigo v4},
    howpublished = {Online: \url{https://github.com/tuneinsight/lattigo}},
    month = Aug,
    year = 2022,
    note = {EPFL-LDS, Tune Insight SA}
}

References

1. Efficient Bootstrapping for Approximate Homomorphic Encryption with Non-Sparse Keys (https://eprint.iacr.org/2020/1203)
2. Bootstrapping for Approximate Homomorphic Encryption with Negligible Failure-Probability by Using Sparse-Secret Encapsulation (https://eprint.iacr.org/2022/024)
3. Somewhat Practical Fully Homomorphic Encryption (https://eprint.iacr.org/2012/144)
4. Multiparty Homomorphic Encryption from Ring-Learning-With-Errors (https://eprint.iacr.org/2020/304)
5. An Efficient Threshold Access-Structure for RLWE-Based Multiparty Homomorphic Encryption (https://eprint.iacr.org/2022/780)
6. A Full RNS Variant of FV Like Somewhat Homomorphic Encryption Schemes (https://eprint.iacr.org/2016/510)
7. An Improved RNS Variant of the BFV Homomorphic Encryption Scheme (https://eprint.iacr.org/2018/117)
8. Homomorphic Encryption for Arithmetic of Approximate Numbers (https://eprint.iacr.org/2016/421)
9. A Full RNS Variant of Approximate Homomorphic Encryption (https://eprint.iacr.org/2018/931)
10. Improved Bootstrapping for Approximate Homomorphic Encryption
11. Fully Homomorphic Encryption without Bootstrapping (https://eprint.iacr.org/2011/277)
12. Homomorphic Encryption for Arithmetic of Approximate Numbers (https://eprint.iacr.org/2016/421)
13. A Full RNS Variant of Approximate Homomorphic Encryption (https://eprint.iacr.org/2018/931)
14. Improved Bootstrapping for Approximate Homomorphic Encryption (https://eprint.iacr.org/2018/1043)
15. Better Bootstrapping for Approximate Homomorphic Encryption (https://eprint.iacr.org/2019/688)
16. Post-quantum key exchange - a new hope (https://eprint.iacr.org/2015/1092)
17. Faster arithmetic for number-theoretic transforms (https://arxiv.org/abs/1205.2926)
18. Speeding up the Number Theoretic Transform for Faster Ideal Lattice-Based Cryptography (https://eprint.iacr.org/2016/504)
19. 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.