lattigo

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 Go to latest Published: Oct 14, 2024 License: Apache-2.0 Imports: 0 Imported by: 0

README

Lattigo: lattice-based multiparty homomorphic encryption library in Go

Go tests

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-hierarchy

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.

Documentation

Overview

Package lattigo is the open-source community-version of Tune Insight's Homomorphic Encryption library. It provides a pure Go implementation of state-of-the-art Homomorphic Encryption (HE) and Multiparty Homomorphic Encryption (MHE) schemes, enabling code-simplicity, cross-platform compatibility and easy builds, while retaining the same performance as C++ libraries.

Source Files

View all Source files

Directories

Path Synopsis
circuits
bgv/lintrans
Package lintrans implements homomorphic linear transformations for the BFV/BGV schemes.
 Package lintrans implements homomorphic linear transformations for the BFV/BGV schemes.
bgv/polynomial
Package polynomial implements a homomorphic polynomial evaluator for the BFV/BGV schemes.
 Package polynomial implements a homomorphic polynomial evaluator for the BFV/BGV schemes.
ckks/bootstrapping
Package bootstrapping implements bootstrapping for fixed-point encrypted approximate homomorphic encryption over the complex/real numbers (CKKS scheme).
 Package bootstrapping implements bootstrapping for fixed-point encrypted approximate homomorphic encryption over the complex/real numbers (CKKS scheme).
ckks/comparison
Package comparison implements homomorphic comparisons for the CKKS scheme.
 Package comparison implements homomorphic comparisons for the CKKS scheme.
ckks/dft
Package dft implements a homomorphic DFT circuit for the CKKS scheme.
 Package dft implements a homomorphic DFT circuit for the CKKS scheme.
ckks/inverse
Package inverse implements a homomorphic inversion circuit for the CKKS scheme.
 Package inverse implements a homomorphic inversion circuit for the CKKS scheme.
ckks/lintrans
Package lintrans implements homomorphic linear transformations for the CKKS scheme.
 Package lintrans implements homomorphic linear transformations for the CKKS scheme.
ckks/minimax
Package minimax implements a homomorphic minimax circuit for the CKKS scheme.
 Package minimax implements a homomorphic minimax circuit for the CKKS scheme.
ckks/mod1
Package mod1 implements a homomorphic mod1 circuit for the CKKS scheme.
 Package mod1 implements a homomorphic mod1 circuit for the CKKS scheme.
ckks/polynomial
Package polynomial implements a homomorphic polynomial evaluator for the CKKS scheme.
 Package polynomial implements a homomorphic polynomial evaluator for the CKKS scheme.
common/lintrans
Package lintrans bundles generic parts of the homomorphic linear transformation circuit.
 Package lintrans bundles generic parts of the homomorphic linear transformation circuit.
common/polynomial
Package polynomial bundles generic parts of the homomorphic polynomial evaluation circuit.
 Package polynomial bundles generic parts of the homomorphic polynomial evaluation circuit.
core
rgsw
Package rgsw implements an RLWE-based GSW encryption and external product RLWE x RGSW -> RLWE.
 Package rgsw implements an RLWE-based GSW encryption and external product RLWE x RGSW -> RLWE.
rgsw/blindrot
Package blindrot implements blind rotations evaluation for RLWE schemes.
 Package blindrot implements blind rotations evaluation for RLWE schemes.
rlwe
Package rlwe implements the generic cryptographic functionalities and operations that are common to R-LWE schemes.
 Package rlwe implements the generic cryptographic functionalities and operations that are common to R-LWE schemes.
Package examples contains several example Go applications that use Lattigo in both the single- and multiparty settings, as well as several example parameter sets.
 Package examples contains several example Go applications that use Lattigo in both the single- and multiparty settings, as well as several example parameter sets.
multiparty/int_pir
multiparty/int_psi
multiparty/thresh_eval_key_gen
singleparty/bgv_ride_hailing
singleparty/bgv_vectorized_ole
singleparty/ckks_bootstrapping/basics
Package main implements an example showcasing the basics of the bootstrapping for fixed-point approximate arithmetic over the reals/complexes.
 Package main implements an example showcasing the basics of the bootstrapping for fixed-point approximate arithmetic over the reals/complexes.
singleparty/ckks_bootstrapping/high_precision
Package main implements an example showcasing high-precision bootstrapping for high-precision fixed- point approximate arithmetic over the reals/complexes.
 Package main implements an example showcasing high-precision bootstrapping for high-precision fixed- point approximate arithmetic over the reals/complexes.
singleparty/ckks_bootstrapping/slim
Package main implements an example showcasing slim for bootstrapping for fixed-point approximate arithmetic over the reals/complexes numbers.
 Package main implements an example showcasing slim for bootstrapping for fixed-point approximate arithmetic over the reals/complexes numbers.
singleparty/ckks_scheme_switching
Package main showcases how lookup tables can complement fixed-point approximate homomorphic encryption to compute non-linear functions such as sign.
 Package main showcases how lookup tables can complement fixed-point approximate homomorphic encryption to compute non-linear functions such as sign.
singleparty/ckks_sigmoid_chebyshev
Package main implements an example of smooth function approximation using Chebyshev polynomial interpolation.
 Package main implements an example of smooth function approximation using Chebyshev polynomial interpolation.
singleparty/ckks_sigmoid_minimax
Package main implements an example of smooth function approximation using minimax polynomial interpolation.
 Package main implements an example of smooth function approximation using minimax polynomial interpolation.
singleparty/ckks_vectorized_polynomial_evaluation
Package main implements an example of vectorized polynomial evaluation.
 Package main implements an example of vectorized polynomial evaluation.
singleparty/rgsw_blind_rotations
Package main implements an example of Blind Rotation (a.k.a.
 Package main implements an example of Blind Rotation (a.k.a.
singleparty/templates/bgv
Package main is a template encrypted modular arithmetic integers, with a set of example parameters, key generation, encoding, encryption, decryption and decoding.
 Package main is a template encrypted modular arithmetic integers, with a set of example parameters, key generation, encoding, encryption, decryption and decoding.
singleparty/templates/ckks
Package main is a template encrypted arithmetic with floating point values, with a set of example parameters, key generation, encoding, encryption, decryption and decoding.
 Package main is a template encrypted arithmetic with floating point values, with a set of example parameters, key generation, encoding, encryption, decryption and decoding.
singleparty/tutorials/ckks
Package multiparty implements RLWE-based scheme agnostic multiparty key-generation and proxy re-rencryption.
 Package multiparty implements RLWE-based scheme agnostic multiparty key-generation and proxy re-rencryption.
mpbgv
Package mpbgv implements homomorphic decryption to Linear-Secret-Shared-Shares (LSSS) and homomorphic re-encryption from LSSS, as well as interactive bootstrapping for the package `schemes/bgv` See `multiparty/README.md` for additional information on multiparty schemes.
 Package mpbgv implements homomorphic decryption to Linear-Secret-Shared-Shares (LSSS) and homomorphic re-encryption from LSSS, as well as interactive bootstrapping for the package `schemes/bgv` See `multiparty/README.md` for additional information on multiparty schemes.
mpckks
Package mpckks implements homomorphic decryption to Linear-Secret-Shared-Shares (LSSS) and homomorphic re-encryption from LSSS, as well as interactive bootstrapping for the package `circuits/bootstrapping` See `multiparty/README.md` for additional information on multiparty schemes.
 Package mpckks implements homomorphic decryption to Linear-Secret-Shared-Shares (LSSS) and homomorphic re-encryption from LSSS, as well as interactive bootstrapping for the package `circuits/bootstrapping` See `multiparty/README.md` for additional information on multiparty schemes.
Package ring implements RNS-accelerated modular arithmetic operations for polynomials, including: RNS basis extension; RNS rescaling; number theoretic transform (NTT); uniform, Gaussian and ternary sampling.
 Package ring implements RNS-accelerated modular arithmetic operations for polynomials, including: RNS basis extension; RNS rescaling; number theoretic transform (NTT); uniform, Gaussian and ternary sampling.
ringqp
Package ringqp is implements a wrapper for both the ringQ and ringP.
 Package ringqp is implements a wrapper for both the ringQ and ringP.
Package schemes contains the implemented cryptosystems.
 Package schemes contains the implemented cryptosystems.
bgv
Package bgv implements a unified RNS-accelerated version of the Fan-Vercauteren version of the Brakerski's scale invariant homomorphic encryption scheme (BFV) and Brakerski-Gentry-Vaikuntanathan (BGV) homomorphic encryption scheme.
 Package bgv implements a unified RNS-accelerated version of the Fan-Vercauteren version of the Brakerski's scale invariant homomorphic encryption scheme (BFV) and Brakerski-Gentry-Vaikuntanathan (BGV) homomorphic encryption scheme.
ckks
Package ckks implements a RNS-accelerated version of the Homomorphic Encryption for Arithmetic for Approximate Numbers (HEAAN, a.k.a.
 Package ckks implements a RNS-accelerated version of the Homomorphic Encryption for Arithmetic for Approximate Numbers (HEAAN, a.k.a.
Package utils implements various helper functions.
 Package utils implements various helper functions.
bignum
Package bignum implements arbitrary precision arithmetic for integers, reals and complex numbers.
 Package bignum implements arbitrary precision arithmetic for integers, reals and complex numbers.
buffer
Package buffer implement methods for efficiently writing and reading values to and from io.Writer and io.Reader that also expose their internal buffers.
 Package buffer implement methods for efficiently writing and reading values to and from io.Writer and io.Reader that also expose their internal buffers.
cosine
Package cosine method is the Go implementation of the polynomial-approximation algorithm by Han and Ki in
 Package cosine method is the Go implementation of the polynomial-approximation algorithm by Han and Ki in
factorization
Package factorization implements various algorithms for efficient factoring integers of small to medium size.
 Package factorization implements various algorithms for efficient factoring integers of small to medium size.
sampling
Package sampling implements secure sampling of bytes and integers.
 Package sampling implements secure sampling of bytes and integers.
structs
Package structs implements helpers to generalize vectors and matrices of structs, as well as their serialization.
 Package structs implements helpers to generalize vectors and matrices of structs, as well as their serialization.

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