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

Lattigo is a strictly hierarchical library whose packages form a linear dependency chain ranging from low-level arithmetic functionalities to high-level homomorphic circuits. A graphical depiction of the Lattigo package organization is given in the Figure above.

• lattigo/ring: At the lowest level resides the ring package providing 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/core: This package implements the core cryptographic functionalities of the library and builds directly upon the arithmetic functionalities provided by the ring package:

    • 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/schemes: The implementation of RLWE-based homomorphic encryption schemes are found in the schemes package:

  • 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/circuits: The circuits package provides implementation of a select set of homomorphic circuits for the bgv and ckks cryptosystems:

  • bgv/lintrans, ckks/lintrans: Arbitrary linear transformations and slot permutations for both bgv and ckks. Scheme-generic objects and functions are part of common/lintrans.

  • bgv/polynomial, ckks/polynomial: Polynomial evaluation circuits for bgv and ckks. Scheme-generic objects and functions are part of common/polynomial.

  • ckks/minimax: Minimax composite polynomial evaluator for ckks.

  • ckks/comparison: Homomorphic comparison-based circuits such as sign, max and step for the ckks scheme.

  • ckks/inverse: Homomorphic inverse circuit for ckks.

  • ckks/mod1: Homomorphic circuit for the mod1 function using the ckks cryptosystem.

  • ckks/dft: Homomorphic Discrete Fourier Transform circuits for the ckks scheme.

  • ckks/bootstrapping: Bootstrapping for fixed-point approximate arithmetic over the real and complex numbers, i.e., the ckks scheme, 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.

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

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

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

• 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.

Documentation

The full documentation of the individual packages can be browsed as a web page using official Golang documentation rendering tool pkgsite or browsing the Go doc.

$ go install golang.org/x/pkgsite/cmd/pkgsite@latest
$ cd lattigo
$ pkgsite -open .

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, (v6.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.

External contributions will require the signature of a Contributor License Agreement (CLA). You can contact us using the following email to request a copy of the CLA: lattigo@tuneinsight.com.

Bug Reports

Lattigo welcomes bug/regression reports of any kind that conform to the preset template, which is automatically generated upon creation of a new empty issue. Nonconformity will result in the issue being closed without acknowledgement.

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 or report a security issue, you have a feature proposal or request, or you 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 v6},
    howpublished = {Online: \url{https://github.com/tuneinsight/lattigo}},
    month = Aug,
    year = 2024,
    note = {EPFL-LDS, Tune Insight SA}
}

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