Pro7ech's Lattigo: Lattice-Based Multiparty Homomorphic Encryption Library in Go

This is a fork of Tune Insight's Lattigo v5.0.2, that includes a refactored backend, many additional features and new protocols.

See CHANGELOG for additional information.

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:

• 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 offers support for blind rotations (a.k.a Lookup Tables) over packed RLWE ciphertexts.

  • hefloat: Homomorphic Encryption for fixed-point approximate arithmetic over the complex or real numbers. The backed is based on 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).

    • bootstrapping: 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. The backed is base on 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.

• 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.

• 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 supporting RLWExRGSW and RGSWxRGSW products.

• 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.

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

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

  • concurrency: Basic helpers for adding concurrency.
  • 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.

---
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}
HE --> HEBin
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

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Versions and Roadmap

The current version of the library 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 users to always update to the latest version.

See CHANGELOG for the current and past versions.

Stability

Branches with the prefix dev_ are branches in active development and will be frequently rebased. Hence, we don't recommend depending on them.

Contributing to the Library

See CONTRIBUTING

Security

See SECURITY

License

Apache 2.0. See LICENSE

Contact

You can mail me at jeanphilippe.bossuat@gmail.com

Citing

Please use the following BibTex entry for citing Lattigo:

@misc{lattigo,
    title = {Pro7ech's Lattigo},
    howpublished = {Online: \url{https://github.com/Pro7ech/lattigo}},
    month = Nov,
    year = 2024,
    note = {EPFL-LDS, Tune Insight SA, Jean-Philippe Bossuat}
}

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