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https://github.com/tuneinsight/lattigo

A library for lattice-based multiparty homomorphic encryption in Go
https://github.com/tuneinsight/lattigo

homomorphic-encryption lattice-based-crypto secure-multi-party-computation

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A library for lattice-based multiparty homomorphic encryption in Go

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# Lattigo: lattice-based multiparty homomorphic encryption library in Go





	




![Go tests](https://github.com/tuneinsight/lattigo/actions/workflows/ci.yml/badge.svg)



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 for different plaintext domains.



  - `hebin`: Homomorphic Encryption for binary arithmetic. It comprises 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`: Bootstrapping for fixed-point approximate arithmetic over the real

      and complex 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.



```mermaid

---

title: Packages Dependency & Organization

---

flowchart LR

RING(RING) --> RLWE(RLWE)

RLWE --> RGSW(RGSW)

RLWE --> HE([HE])

RLWE --> CKKS{{CKKS}}

RGSW --> HEBin{HEBin}

HE --> HEFloat{HEFloat}

HE --> HEInt{HEInt}

BFV/BGV --> HEInt

CKKS --> HEFloat

RLWE --> BFV/BGV{{BFV/BGV}}

MHE --> MHEFloat

HEFloat --> MHEFloat((MHEFloat))

HEFloat --> Bootstrapping

HEInt --> MHEInt((MHEInt))

RLWE --> MHE([MHE])

MHE --> MHEInt

```



## 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](https://tuneinsight.com).



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](https://github.com/tuneinsight/lattigo/blob/master/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: [[email protected]](mailto:[email protected]).



## Citing



Please use the following BibTex entry for citing Lattigo:



    @misc{lattigo,

	    title = {Lattigo v5},

	    howpublished = {Online: \url{https://github.com/tuneinsight/lattigo}},

	    month = Nov,

	    year = 2023,

	    note = {EPFL-LDS, Tune Insight SA}

    }

    



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

French](http://reneefrench.blogspot.com/).