Release Overview

The sixth major release of Lattigo marks a departure from some of the abstractions
introduced in version five by refocusing the library onto the scheme level meaning the
implemented RLWE- and RGSW-based cryptosystems. This pivot comes at the expense of the
he package introduced in the previous version. In short, he provided abstractions of
the CKKS and BGV schemes from the schemes package with the intended goal of offering
a quick access to homomorphic encryption functionalities without requiring an extensive
amount of background knowledge of RLWE/RGSW-based cryptography and its accompanying
literature. Under the hood the he package was merely a thin wrapper around important
objects from schemes/ckks and schemes/bgv, which effectively constituted an elaborate
renaming/aliasing of structures such a parameters, encoders and evaluators. However,
the core focus of Lattigo has always been the implementation of common homomorphic
cryptosystems. Writing as well as utilizing circuits without at least a surface
knowledge of the underlying schemes is not a realistic goal at this stage in the life
cycle of homomorphic encryption. Unlike other cryptographic fields such a symmetric
cryptographic whose primitives can be safely utilized without domain knowledge, the
lacking maturity of homomorphic encryption does not permit a similar level of
abstraction. Moreover, the abstraction in he was leaky, e.g., schemes had to be
instantiated using the parameters objects from schemes/*, which basically voided the
raison d'être of the package.

The circuits Package

The removal of the he package has consequences for the homomorphic circuits such as CKKS
bootstrapping that were also part of he. All of them have been moved to a newly created
package termed circuits organized by scheme resulting in the following directory
structure.

circuits
├── bgv
│   ├── lintrans
│   └── polynomial
├── ckks
│   ├── bootstrapping
│   ├── comparison
│   ├── dft
│   ├── inverse
│   ├── lintrans
│   ├── minimax
│   ├── mod1
│   └── polynomial
└── common
    ├── lintrans
    └── polynomial

Note that both linear transformations and the polynomial evaluator support both the BGV
and CKKS schemes and thus scheme-generic structures are found in the circuits/common
sub-directory.

Removal of Circuit-Specific Evaluator Interfaces

All supported circuits in the new circuits package are instantiated with an
evaluator. In Lattigo-v5, such an evaluator had to conform to a circuit-specific interface
that for certain circuits appeared dauntingly complex (see e.g.,
EvaluatorForLinearTransformation). It is not clear how a user (layman and expert) was
supposed to make use of such interfaces without total knowledge of the entire Lattigo code
base down to the ring level. It is more likely, if a custom evaluator was required for a
particular circuit, then a user would simply adapt an existing scheme evaluator from
schemes to his needs. With the refocus of the sixth version of Lattigo onto the scheme
level, we tend to this use case by removing all EvaluatorFor[*] interfaces in the
circuit package and replacing them with a scheme-agnostic evaluator interface in
schemes/scheme.go. This design choice should streamline the creation of custom
evaluators based on existing ones making the hacking of new and existing circuits simpler.

HERMES-Inspired Ring Packing

Aa fresh ring packing routine based on the
HERMES work by Bae et al. (https://eprint.iacr.org/2023/1244) has been added which improves the time and
memory by a significant margin compared to the existing baseline packing implementation.
This operation adds to new operations to the packing facilities:

• Extraction. Recursively split the ciphertexts into left and right part of half
  the ring degree until the minimum ring degree defined by the user is reached before
  applying the extraction procedure.

• Repacking. Apply the sample repacking procedure in the small ring over multiple
  ciphertexts before merging them recursively back to the larger ring.

The new ring packing implementation has been moved from the removed he package into the
existing core/rlwe package and can be invoked through an updated API:

• New Evaluator rlwe.RingPackingEvaluator:
  • NewRingPackingEvaluator(evk *RingPackingEvaluationKey)
  • Extract(ct *rlwe.Ciphertext, idx []int, naive bool) (cts map[int]*rlwe.Ciphertext, err error)
  • Repack(cts map[int]*rlwe.Ciphertext, naive bool) (ct *rlwe.Ciphertext, err error)
  • Split(ctN, ctEvenNHalf, ctOddNHalf *rlwe.Ciphertext) (err error)
  • Merge(ctEvenNHalf, ctOddNHalf, ctN *rlwe.Ciphertext) (err error)
  • ShallowCopy() *RingPackingEvaluator
• New Evaluation Key rlwe.RingPackingEvaluationKey

Permutations

A second new feature are slot-wise permutations to
the linear transformation circuits in circuits/*/lintrans. Permutations provide the
ability to arbitrarily reorder ciphertext slots through a linear transformation. The exact
nature of the permutation is determined via the new lintrans.PermtuationMapping and
lintrans.Permutation objects:

type PermutationMapping[T bgv.Integer | ckks.Float] struct {
	From    int
	To      int
	Scaling T
}

type Permutation[T bgv.Integer | ckks.Float] []PermutationMapping[T]

func (p Permutation[T]) GetDiagonals(logSlots int) Diagonals[T] {}

Here, PermutationMapping specify the origin and destination index of a single ciphertext
slot. A slice of permutations mapping then yields a Permutation from which the diagonals
can be extracted to be passed to the initializer of the linear transformation.

Absorption of BFV

The implementation of the BFV cryptosystem simply wraps the BGV scheme by redefining
the multiplication methods of the evaluator. This introduced a significant amount of code
duplication. The new way of instantiating BFV is through the BGV evaluator by setting the
scaleInvariant flag. See the READMEs of schemes/bfv and schemes/bgv for more information.

bfvEvaluator := bgv.NewEvaluator(params, evaluationKeys, true)

Refactored Unit Test Context

Lattigo-v6 provides an improved unit test context generations skeleton that reduces the amount of
boilerplate code duplication for the creation of Lattigo objects such as parameters and
evaluators for the usage in unit tests. The files schemes/*/test_utils.go now contain
scheme-specific functions to be reused in unit tests of all packages that depend on
schemes.

Miscellaneous

• The lintrans.Parameters struct now allows for a fine-grained instantiation of the both
  the $Q$ and $P$ levels with the new lintrans.Parameters.LevelQ and
  lintrans.Parameters.LevelP fields.
• Moving the masking operation in rlwe.Evaluator.gadgetProductSinglePAndBitDecompLazy
  to an earlier point in the computation reduces the number of required masking
  invocations and thus accelerates the gadget product.
• A small refactor of the linearization key generation in the multi-party protocol
  reduces the degree of the ciphertext. This change reduces the size of some of the keys
  that need to passed over the channel.
• Docstrings at various points in the code base have been fixed and amended with godoc
  references using the [*] operator. This allows for a quick navigation of the
  documentation when viewed in a browser.
• The mhe package has been renamed to multiparty containing packages
  multiparty/mpbgv and multiparty/mpckks to better reflect the removal of the
  he package.
• RGSW blind rotations have been moved to core/rlwe leading the complete deletion of
  the he/bin package.
• Several bugfixes have been included since version five.
• A large set of linter warnings have been fixed.

Switching to Lattigo-v6

Lattigo-v6 now requires a minimum Golang version of 1.21. The support for earlier
versions has been deprecate. The principal reason for this change is the usage of the
newly introduces slices package in the standard library whose functions replace some of
the procedures in utils/slices.go.

The removal of the he package necessitate some changes in projects that relied
on Lattigo-v5. However, since he was only renaming key structures from schemes/* the
required changes are straightforward.

• hefloat. Any code that used the he/hefloat package needs to rename the imports to
  schemes/ckks with the exception of code that made us of circuits that formerly were
  also part of he/hefloat. This circuits now have to be imported separately, for
  example circuits/ckks/lintrans.
• heint. Any code that used the he/heint package needs to rename the imports to
  schemes/ckks with the exception of code that made us of circuits that formerly were
  also part of he/heint. This circuits now have to be imported separately, for
  example circuits/bgv/polynomial.

Acknowledgements

The Lattigo team would like to thank Christian Mouchet @ChristianMct for his insightful reviews
and comments during the development phase.

Relevant PRs and Commits

• Bugfixes #427 by @Pro7ech in https://github.com/tuneinsight/lattigo/pull/428
• Bugfixes #437 by @Pro7ech in https://github.com/tuneinsight/lattigo/pull/438
• Update README with CLA for contributions by @romainbou in https://github.com/tuneinsight/lattigo/pull/442
• Bugfixes April 2024 by @qantik in https://github.com/tuneinsight/lattigo/pull/456
• Add Go v1.22 to the CI tests and update staticcheck by @romainbou in https://github.com/tuneinsight/lattigo/pull/462
• Bugfixes May 2024 Part 1 by @qantik in https://github.com/tuneinsight/lattigo/pull/474
• Bugfixes #457 by @romainbou in https://github.com/tuneinsight/lattigo/pull/473
• Bugfixes May 2024 Part 2 by @qantik in https://github.com/tuneinsight/lattigo/pull/482
• Godoc Formatting Cleanup by @qantik in https://github.com/tuneinsight/lattigo/pull/486
• Bugfixes June 2024 Part 1 by @qantik in https://github.com/tuneinsight/lattigo/pull/483
• Bugfixes June 2024 Part 2 by @qantik in https://github.com/tuneinsight/lattigo/pull/484
• Permutations & Packing #485 by @Pro7ech in https://github.com/tuneinsight/lattigo/pull/485
• Removal of the he package by @qantik (c2c6f716 to e2e37218)
• Absorption of the bfv package by @qantik (1487afa1)

• Fixed bfv.Evaluator.ShallowCopy() that wasn't shallowcopying the basis extender, which would result in correctness error when using multiple shallowcopied evaluators concurrently and the scale invariant tensoring (BFV-style multiplication).

• Fixed panics in lattigo/ring benchmarks
• Uniformized benchmarks in lattigo/schemes
• Added benchmarks in lattigo/he/hebin, lattigo/he/heint and lattigo/he/hefloat

Release Overview

The following sections give an overview of the main changes brought by the v5. This list is not exhaustive and we recommend taking a look at the CHANGELOG.md for the full list of changes.

Reorganization of the Library

The library has been fully reorganized to provide a better user experience tailored around plaintext spaces and functionalities rather than schemes. The new organization of the packages is as follows, from highest to lowest level:

• he: The highest level package, intended to be the user-facing part of the library for most applications. It contains three sub-packages which provide homomorphic encryption functionalities based on the plaintext domain:
  • hefloat: Homomorphic encryption with fixed-point approximate encrypted arithmetic over the real or complex numbers. This package is intended to be used for encrypted arithmetic with floating point numbers and is implemented as a wrapper over the schemes/ckks package, with additional functionalities.
    • bootstrapping: Bootstrapping for fixed-point approximate arithmetic over the real and complex numbers.
  • heint: Homomorphic encryption for modular encrypted arithmetic over the integers. This package is intended to be used for encrypted arithmetic over integers and is implemented as wrapper of the schemes/bgv package, with additional functionalities.
  • hebin: Homomorphic encryption for binary arithmetic. It currently implements blind rotations (a.k.a Lookup Tables) (previously rgsw/lut).
• mhe: This package implements scheme-agnostic RLWE-based multiparty key-generation and proxy re-encryption (previously drlwe).
  • mhefloat: Homomorphic decryption from RLWE to Linear-Secret-Sharing-Shares (LSSS) and homomorphic re-encryption from LSSS to RLWE, as well as interactive bootstrapping for he/hefloat (previously dckks).
  • mheint: Homomorphic decryption from RLWE to Linear-Secret-Sharing-Shares (LSSS) and homomorphic re-encryption from LSSS to RLWE, as well as interactive bootstrapping for he/heint (previously dbfv and dbgv).
• schemes: This package regroups all the homomorphic encryption schemes implemented in the library, which are the backend of the he package. It currently contains the following schemes:
  • bgv: A Full-RNS generalization of the Brakerski-Fan-Vercauteren scale-invariant (BFV) and Brakerski-Gentry-Vaikuntanathan (BGV) 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.
  • ckks: A Full-RNS variant of the Homomorphic Encryption for Arithmetic for Approximate Numbers (HEAAN, a.k.a. CKKS) scheme.
• core : This package implements the core homomorphic cryptographic functionalities of the library which are common to all the RLWE and LWE schemes.
  • rlwe: A package that implements the generic cryptographic functionalities and operations that are common to all RLWE-based homomorphic encryption schemes.
  • rgsw: A package that provides support for Ring-GSW encryption and the external product.
• ring: A package implementing arithmetic for power-of-two cyclotomic rings.
• utils: A package implementing various utility functions, secure sampling, serialization, and linear algebra.

Modular Implementation of High Level Functionalities

The package lattigo/he provides scheme agnostic interfaces for basic encoding, homomorphic operations and generic implementations for higher level operations such as polynomial evaluation and linear transformations. These are used to implement scheme specific functionalities in he/hebin, he/heint and he/hefloat in a way that enables user to easily provide custom implementations of sub-routines (e.g. adding concurrency).

API Reduction & Uniformization

The bfv, bgv and ckks encoders and evaluators have had their API reduced, simplified and uniformized across schemes. This enables the definition of scheme-agnostic interfaces in the he package. The API reduction mostly consolidates redundant methods into a single one. For example, the ckks.Evaluator used to have the methods

• MultByConst(ctIn *rlwe.Ciphertext, constant interface{}, ctOut *rlwe.Ciphertext)
• MultByGaussianInteger(ctIn *rlwe.Ciphertext, cReal, cImag interface{}, ctOut *rlwe.Ciphertext)
• MultByi(ctIn *rlwe.Ciphertext, ctOut *rlwe.Ciphertext)
• DivByi(ctIn *rlwe.Ciphertext, ctOut *rlwe.Ciphertext)
• Mul/MulRelin(ctIn *rlwe.Ciphertext, op1 rlwe.Operand, ctOut *rlwe.Ciphertext).

These have been consolidated into the single method Mul/MulRelin(ctIn *rlwe.Ciphertext, op1 rlwe.Operand, ctOut *rlwe.Ciphertext).

This change renders scheme-specific interfaces such as bgv.Encoder or ckks.Evaluator obsolete, so they have been removed. Their functionality is now covered by the scheme-agnostic interfaces he.Encoder and he.Evaluator.

Improved Cryptographic Parameterization

The previous implementation did only allow a ternary distribution for the secret, and a Gaussian distribution for the error. We have removed this restriction and it is now possible to use custom distributions for the secret and error, as long as they satisfy the ring.DistributionParameters interface. Available distributions are ring.DiscreteGaussian, ring.Ternary, and ring.Uniform.

Additionally, the sampling and related interfaces have been improved. Notably, the interface ring.Sampler has been added and it is possible to instantiate a sampler directly from a ring.DistributionParameters.

Finally, the ring.GaussianSampler has been extended to support large-norm Gaussian sampling, enabling proper smudging.

Improvements to the ring.Ring Object

The ring.Ring object was previously a single struct storing all the pre-computed constants (e.g. NTT Tables) as double slices, indexed by their respective prime. This required a large struct that was difficult to re-slice and didn't represent well the underlying mathematical object of an RNS decomposed large ring. The new ring.Ring object is now much closer to the mathematical definition and is composed of ring.SubRing, one per prime. These ring.SubRing define all the pre-computed constants for their respective prime and they operate on slices modulo this prime.

Improved Plaintext/Ciphertext Structs & Metadata

Plaintext and ciphertexts are now wrappers of the rlwe.Element generic type, which contains a pointer to the rlwe.MetaData struct. This struct comprises the fields rlwe.CiphertextMetaData and rlwe.PlaintextMetaData, which contain metadata about the state of the ciphertext and plaintext.

Hybrid BFV/BGV Scheme

The implementation of the BGV scheme has been entirely rewritten to provide a unified variant of the BFV and BGV schemes. The proposed implementation provides all the functionalities of the BFV and BGV schemes under a unified framework. This is enabled by the equivalence between the LSB and MSB encodings when the plaintext modulus $t$ is coprime with the ciphertext modulus $Q$. In other words, if $t$ is coprime with $Q$, then the BFV and BGV schemes are indistinguishable up to a factor of $t^{-1} \mod Q$.

In this hybrid implementation, the BGV plaintext is scaled by $t^{-1} \mod Q$ (MSB encoding) instead of the error being scaled by $t$ (LSB encoding). This approach enables an implementation that behaves exactly like both schemes in terms of noise growth and performance depending on which multiplication is used: the regular tensoring (BGV/CKKS) or the scale-invariant tensoring (BFV).

For backwards compatibility, the standalone implementation of the BFV scheme still exists, but it is now instantiated as a wrapper of the new hybrid BGV scheme which essentially restricts the multiplication to only the scale invariant tensoring. The functionalities and noise growth are identical to the original BFV implementation, except that the plaintext modulus must be coprime with the ciphertext modulus.

High-Precision Approximate Homomorphic Encryption & Advanced Arithmetic

The implementation of the CKKS scheme now supports a scaling factor of up to 120 bits, enabling high precision fixed-point approximate arithmetic. Additionally the following advanced arithmetic operations have been improved/added in the package he/hefloat:

• Polynomial Evaluation
• Linear Transformations
• Homomorphic Encoding/Decoding
• Homomorphic Modular Reduction
• Full domain division
• Composite Minimax Polynomial Evaluation
• Sign and Step piece-wise functions
• Min/Max

Improvements to the Bootstrapping for Approximate Homomorphic Encryption

The generic interface he.Bootstrapper[CiphertextType any] has been added to the package he, enabling easy plug-and-play black-box bootstrapping in any implementation defining the bootstrapping via this interface.

The usability and range of parameterization of the bootstrapping for fixed-point approximate homomorphic encryption over real and complex numbers has been substantially improved:

• Decorrelation between the bootstrapping parameters (parameters used during the bootstrapping) and the residual parameters (parameters outside of the bootstrapping). The user only needs to provide the residual parameters and the parameterization of the bootstrapping, and the constructor will do the rest, managing these parameters without exposing them directly to the user.
• Support for the Conjugate-Invariant ring.
• Support for batch-bootstrapping of ciphertexts of lower degree and/or with sparse packing with automatic repacking/unpacking.
• High parameterization granularity of 16 tunable parameters.
• Full support of META-BTS, providing arbitrary precision iterated bootstrapping by reserving only one additional small prime.

Examples for the bootstrapping can be found in examples/he/hefloat/bootstrapping.

Refactoring of the Evaluation-Keys

Up to v4, the evaluation keys were defined by the struct rlwe.SwitchingKey. Although applying an evaluation key on a ciphertext does indeed serve the purpose of public re-encryption, user feedback has shown that this naming approach can lead to confusion and lacks an intuitive hierarchy among the different objects which are derived from the rlwe.SwitchingKey struct (and it does not provide a direct mapping with the literature). This is notably caused by the fact that public re-encryption is hardly ever used to change the access structure of a ciphertext, but as a means to ensure ciphertext compactness and decryption correctness during the different evaluation phases of a circuit.

To remedy to this issue, the struct rlwe.SwitchingKey has been renamed rlwe.EvaluationKey, and a comprehensive documentation on the generation, usage, and all capabilities of this object, as well as code comments, have been added. Additionally, the method SwitchKeys has been renamed ApplyEvaluationKey.

The goal is to better convey that rlwe.EvaluationKey is a special type of public key that is used during the evaluation phase of a circuit with different purposes (relinearization, automorphisms, etc...).

The struct rlwe.RotationKeySet has been removed. It is now replaced by the type rlwe.GaloisKey, which is a wrapper of rlwe.EvaluationKey and stores a single rlwe.EvaluationKey along with some meta data to help identify which automorphism it enables.

There is now a simple and much more intuitive hierarchy among rlwe.EvaluationKeys:

rlwe.EvaluationKey 
         |
         |-> rlwe.RelinearizationKey
         └-> rlwe.GaloisKey

To be able to manage multiple rlwe.EvaluationKeys, the rlwe.EvaluationKeySet interface has been added. The (bfv/bgv/ckks).Evaluator types now use this interface to access evaluation keys when required, which enables the users to define their own loading/saving/persistence policies for rlwe.RelinearizationKey and rlwe.GaloisKeys. The rlwe.MemEvaluationKeySet struct was added as a simple, memory-backed implementation of the rlwe.EvaluationKeySet interface.

Additionally, it is now possible to generate evaluation keys with specific levels for the moduli Q and P, as well as specific power of two decomposition, by passing the optional struct rlwe.EvaluationKeyParameters to the key-generator. This also means that the power of two decomposition for the evaluation keys is not a field of the cryptographic parameters anymore.

Test Coverage and Consistency

Many tests and benchmarks located in the bfv, bgv and ckks packages were merely wrappers of methods of the package rlwe, and thus didn't serve any meaningful purpose. Additionally, many methods in the rlwe package were not comprehensively tested.

To remedy to this issue, all tests and benchmarks in the bfv, bgv and ckks packages that were solely wrappers of a method located in rlwe have been removed. The test coverage of the rlwe package has been substantially increased by adding tests and expanding the range of parameters for which those methods are tested.

An example is the tests for automorphisms. These were tested in each of the schemes by checking that applying a specific automorphism on a ciphertext encrypting an encoded plaintext would result in specific rotations in the plaintext decoded domain. Although such test does ensure the functionality full pipeline behaves as expected, it made its debugging difficult by not being able to easily pinpoint where the correctness error could come from.

Instead, these kind of functionalities have been broken down into their elementary operations, testing each of them separately. Going back to the tests for the automorphisms, the rlwe package will now test that a Galois key is correctly generated, that the homomorphic automorphism applies the correct Galois automorphism on the polynomial coefficients, and that it produces the expected noise; and the schemes will only test that an automorphism on an encoded plaintext results in the correct rotation on the decoded plaintext.

Finally, all relevant methods of rlwe now have a benchmark function and the noise bounds for the tests in the packages rlwe and mhe have been substantially improved.

Arbitrary Precision Arithmetic & Polynomial Interpolation

A new package utils/bignum has been added. It provides arbitrary precision arithmetic and polynomial interpolation (Chebyshev & Multi-Interval Remez) over the real and complex numbers.

New Algorithm For Blind Rotations

The CGGI algorithm has been replaced by LMKCDEY's algorithm, enabling faster blind-rotations, smaller keys, and arbitrary key-distribution.

Improved Serialization

In addition to the previously available encoding.BinaryMarshaler and encoding.BinaryUnmarshaler interfaces, relevant Lattigo objects now implement the io.ReaderFrom and io.WriterTo interfaces to read/write objects directly from/to io.Reader and io.Writer. Moreover, the new methods have been optimized for buffers that provide transient access to their internal buffer (through the buffer.Writer interface, see below).

This is supported by two new packages devoted to serialization: utils/buffer and utils/structs. The package utils/buffer features low-level custom methods to efficiently write and read slices on any writer or reader that also expose their internal buffer. The package utils/structs implements generic map, vector and matrix structs of any type, as well as their serialization.

How to Switch from V4 to V5

• lattigo/v4/ckks -> lattigo/v5/he/hefloat
• lattigo/v4/[bfv/bgv] -> lattigo/v5/he/heint
• lattigo/v4/rgsw/lut -> lattigo/v5/he/hebin
• lattigo/v4/drlwe -> lattigo/v5/mhe
• lattigo/v4/dckks -> lattigo/v5/mhe/mhefloat
• lattigo/v4/[dbfv/dbgv] -> lattigo/v5/mhe/mheint
• lattigo/v4/rlwe -> lattigo/v5/core/rlwe
• lattigo/v4/rgsw -> lattigo/v5/core/rgsw
• lattigo/v4/ring -> lattigo/v5/ring

If needed, the bfv, bgv and ckks standalone schemes are still available, although they are not intended to be the front-end of the library:

• lattigo/v4/ckks -> lattigo/v5/schemes/ckks
• lattigo/v4/bfv -> lattigo/v5/schemes/bfv
• lattigo/v4/bgv -> lattigo/v5/schemes/bgv

Release Overview

The following sections give an overview of the main changes brought by the v5. This list is not exhaustive and we recommend taking a look at the CHANGELOG.md for the full list of changes.

Reorganization of the Library

The library has been fully reorganized to provide a better user experience. The new organization of the packages is as follow, from the highest level to the lowest level:

• he: The highest level package which is intended to be the user facing part of the library for most applications. It contains three sub-packages which provide homomorphic encryption functionalities based on the plaintext domain:
  • hefloat: Homomorphic encryption for fixed-point approximate encrypted arithmetic over the complex or real numbers. This package is implemented as a wrapper over the schemes/ckks package.
    • bootstrapping: State-of-the-Art bootstrapping for fixed-point approximate arithmetic over the real
      and comples numbers.
  • heint: Homomorphic encryption for modular encrypted arithmetic over the integers. This package is implemented as wrapper of the schemes/bgv package.
  • hebin: Blind rotations (a.k.a Lookup Tables).
• mhe: This package implements scheme agnostic RLWE-based multiparty key-generation and proxy re-encryption.
  • mhefloat: Homomorphic decryption from RLWE to Linear-Secret-Sharing-Shares (LSSS) and homomorphic re-encryption from LSSS to RLWE, as well as interactive bootstrapping for he/hefloat .
  • mheint: Homomorphic decryption from RLWE to Linear-Secret-Sharing-Shares (LSSS) and homomorphic re-encryption from LSSS to RLWE, as well as interactive bootstrapping for he/heint.
• schemes: This package regroups all the homomorphic encryption schemes implemented in the library. It currently contains the following schemes:
  • bgv: A Full-RNS generalization of the Brakerski-Fan-Vercauteren scale-invariant (BFV) and Brakerski-Gentry-Vaikuntanathan (BGV) 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.
  • ckks: A Full-RNS variant of Homomorphic Encryption for Arithmetic for Approximate Numbers (HEAAN, a.k.a. CKKS) scheme.
• core : This package implements the core homomorphic cryptographic functionalities of the library which are common to all the RLWE and LWE schemes.
  • rlwe: A package that implements the generic cryptographic functionalities and operations that are common to all RLWE-based homomorphic encryption schemes.
  • rgsw: A package that provides support for Ring-GSW encryption and the external product.
• ring: A package implementing arithmetic for power-of-two cyclotomic rings.
• utils: A package implementing various utility functions, secure sampling, serialization and linear algebra.

Modular Implementation of High Level Functionalities

The package lattigo/he provides scheme agnostic interfaces for basic homomorphic operations and generic implementations for higher level operations such as polynomial evaluation and linear transformations. These are used to implement scheme specific functionalities in he/hebin, he/heint and he/hefloat in a way that enables user to easily provide custom implementations of sub-routines (e.g. adding concurrency).

Hybrid BFV/BGV Scheme

The implementation of the BGV scheme has been entirely rewritten to provide a unified variant of the BFV and BGV schemes. The proposed implementation provides all the functionalities of the BFV and BGV schemes under a unified framework. This is enabled by the equivalency between the LSB and MSB encodings when the plaintext modulus $t$ is coprime with the ciphertext modulus $Q$. In other words, if $t$ is coprime with $Q$, then the BFV and BGV schemes are indistinguishable up to a factor of $t^{-1} \mod Q$.

In this hybrid implementation, the BGV plaintext is scaled by $t^{-1} \mod Q$ (MSB encoding) instead of the error being scaled by $t$ (LSB encoding). This approach enables an implementation that behaves exactly like both schemes in terms of noise growth and performance depending on which multiplication is used: the regular tensoring (BGV/CKKS) or the scale-invariant tensoring (BFV).

For backward compatibility, the standalone implementation of the BFV scheme still exists, but is now instantiated as a wrapper of the new hybrid BGV scheme which essentially restricts the multiplication to only the scale invariant tensoring. The functionalities and noise growth are identical to the original BFV implementation, except that the plaintext modulus must be coprime with the ciphertext modulus.

High-Precision Approximate Homomorphic Encryption & Advanced Arithmetic

The implementation of the CKKS scheme now supports a scaling factor of up to 120 bits, enabling high precision fixed-point approximate arithmetic. Additionally the following advanced arithmetic operations have been improved/added in the package he/hefloat:

• Polynomial Evaluation
• Linear Transformations
• Homomorphic Encoding/Decoding
• Homomorphic Modular Reduction
• Full domain division
• Composite Minimax Polynomial Evaluation
• Sign and Step piece-wise functions
• Min/Max

Improvements to the Bootstrapping for Approximate Homomorphic Encryption

The generic interface he.Bootstrapper[CiphertextType any] has been added to the package he, enabling easy plug-and-play black-box bootstrapping in any implementation defining the bootstrapping via this interface.

The usability and range of parameterization of the bootstrapping for fixed-point approximate homomorphic encryption over complex and real numbers has been substantially improved:

• Decorrelation between the bootstrapping parameters (parameters used during the bootstrapping) and the residual parameters (parameters outside of the bootstrapping). The user only needs to provide the residual parameters and the parameterization of the bootstrapping, and the constructor will do the rest, managing these parameters without exposing them directly to the user.
• Support for the Conjugate-Invariant ring.
• Support for batch-bootstrapping of ciphertexts of lower degree and/or with sparse packing with automatic repacking/unpacking.
• High parameterization granularity of 16 tunable parameters.
• Full support of META-BTS, providing arbitrary precision iterated bootstrapping by reserving only one additional small prime.

Examples for the bootstrapping can be found in examples/he/hefloat/bootstrapping.

Refactoring of the Evaluation-Keys

Up to v4 the evaluation keys were defined by the struct rlwe.SwitchingKey. Although applying an evaluation key on a ciphertext does indeed serves the purpose of public re-encryption, user feedback has shown that this naming approach can lead to confusion and lacks an intuitive hierarchy among the different objects which are derived from the rlwe.SwitchingKey struct (and does not provide a comprehensive mapping with the literature). This is notably caused by the fact that public re-encryption is hardly ever used to change the access structure of a ciphertext, but as a mean to ensure ciphertext compactness and decryption correctness during the different evaluation phases of a circuit.

To remedy to this issue, the struct rlwe.SwitchingKey has been renamed rlwe.EvaluationKey, and a comprehensive documentation on the generation, usage and all capabilities of this object, as well as code comments, have been added. Additionally, the method SwitchKeys has been renamed ApplyEvaluationKey.

The goal is to better convey that rlwe.EvaluationKey is a special type of public key that is used during the evaluation phase of a circuit, with different purposes (relinearization, automorphisms, etc...).

The struct rlwe.RotationKeySet has been removed. It is now replaced by the type rlwe.GaloisKey, which is a wrapper of rlwe.EvaluationKey and stores a single rlwe.EvaluationKey along with some meta data to help identify which automorphism it enables.

There is now a simple and much more intuitive hierarchy among rlwe.EvaluationKeys:

rlwe.EvaluationKey 
         |
         |-> rlwe.RelinearizationKey
         └-> rlwe.GaloisKey

To be able to manage multiple rlwe.EvaluationKeys, the rlwe.EvaluationKeySet interface has been added. The (bfv/bgv/ckks).Evaluator types are now using this interface to access evaluation keys when required, which enables the users to define their own loading/saving/persistence policies for rlwe.RelinearizationKey and rlwe.GaloisKeys. The rlwe.MemEvaluationKeySet struct was added as a simple, memory-backed implementation of the rlwe.EvaluationKeySet interface .

Test Coverage and Consistency

Many tests and benchmarks located in the bfv, bgv and ckks packages were merely wrappers of methods of the package rlwe, and thus didn't serve any meaningful purpose. Additionally, many methods in the rlwe package where not fully tested or not tested at all.

To remedy to this issue, all tests and benchmarks in the bfv, bgv and ckks packages that were solely wrappers of a method located in rlwe have been removed. The test coverage of the rlwe package has been substantially increased by adding tests and expanding the range of parameters for which those methods are tested.

An example is the tests for automorphisms. These were tested in each of the schemes by checking that applying a specific automorphism on a ciphertext encrypting an encoded plaintext would result in a specific rotations in the plaintext decoded domain. Although such test does ensure the functionality full pipeline behaves as expected, it was making its debugging difficult by not being able to easily pin-point where the correctness error could come from.

Instead these kind of functionalities have been broken down in their elementary operations, testing each of them separately. Going back to the tests for the automorphisms, the rlwe package will now test that a Galois key is correctly generated, that the homomorphic automorphism applies the correct Galois automorphism on the polynomial coefficients and that it produces the expected noise; and the schemes will only test that an automorphism on an encoded plaintext results in the correct rotation on the decoded plaintext.

Finally, all relevant methods of rlwe now have a benchmark function and the noise bounds for the tests in the packages rlwe and mhe have been substantially improved.

Arbitrary Precision Arithmetic & Polynomial Interpolation

A new package utils/bignum has been added. It provides arbitrary precision arithmetic and polynomial interpolation (Chebyshev & Multi-Interval Remez) over the real and complex numbers.

Improved Serialization

In addition to the previously available encoding.BinaryMarshaler and encoding.BinaryUnmarshaler interfaces, relevant Lattigo objects now implement the io.ReaderFrom and io.WriterTo interfaces to read/write object directly from/to io.Reader and io.Writer. Moreover, the new methods have been optimized for buffers that provide transient access to their internal buffer (through the buffer.Writer interface, see below).

This is supported by two new packages dedicated to serialization: utils/buffer and utils/structs. The package utils/buffer provides low-level custom methods to efficiently write and read slices on any writer or reader that also expose their internal buffer. The package utils/structs implements generic map, vector and matrix structs of any type, as well as their serialization.

• Added BGV/DBGV schemes.
• ALL: added default parameters for LogN=11 and LogN=10.
• RING: prime generation no longer skips the first candidate.
• RING: reworked marshalling of ring.Poly object. The new available methods are:
  • ring.Poly now has a .Buff 1-dimensional slice which is the only heavy allocation of a ring.Poly. The .Coeffs 2-dimensional slice is a re-slicing of .Buff.
  • GetDataLen64 and GetDataLen32: gets the length in bytes of an encoded ring.Poly object.
  • WriteTo64 and WriteTo32: encodes a ring.Poly object on a pre-allocated slice of bytes.
  • WriteCoeffsTo64 and WriteCoeffsTo32: encodes a slice of coefficients on a pre-allocated slice of bytes.
  • DecodeCoeffs64 and DecodeCoeffs32: decodes a slice of bytes on a slice of coefficients.
  • DecodePoly64 and DecodePoly32: decodes a slice of bytes on a pre-allocated ring.Poly object.
• RING: renamed ring.Poly.Degree() to ring.Poly.N() for consistency.
• RING: removed ring.Poly.LenModuli() deprecated method.
• RING: changed ring.NewPoly to take the level as argument instead of the number of moduli, for consistency.
• RLWE: added several types of ciphertexts:
  • rlwe.CiphertextQP represents a ciphertext that is encrypted in the extended ring R_QP.
  • rlwe.GadgetCiphertext represents an encryption in the extended ring R_QP of a plaintext that is decomposed in the CRT and power-of-two basis (e.g., plublic switching keys).
• RLWE: changed representation of rlwe.PublicKey types which are now stored in Montgomerry form, consistently with all other key types.
• RLWE: changed rlwe.SwitchingKey type to use rlwe.GadgetCiphertext internally.
• RLWE: generalized rlwe.KeySwitcher into rlwe.Evaluator, which provides new functionalities:
  • DecomposeNTT: decomposes a polynomial modulo the special RNS basis and extends its basis from Q to QP.
  • DecomposeSingleNTT: decomposes a polynomial modulo a single power of the special RNS basis and extends its basis from Q to QP.
  • ExpandRLWE: extracts each coefficient of a RLWE sample to the degree-0 coefficient of multiple RLWE samples.
  • MergeRLWE: merges the degree-0 coefficient of multiple RLWE samples into a single RLWE sample.
  • GadgetProduct: evaluates ring.Poly x gadget.Ciphertext -> RLWE, where gadget.Ciphertext is a matrix of RLWE samples encrypting scaled plaintext by the special RNS basis and a modulus P.
  • GadgetProductNoModDown: evaluates ring.Poly x gadget.Ciphertext -> RLWE but without the division by P (the result is given mod QP).
  • GadgetProductSinglePAndBitDecompNoModDown: evaluates ring.Poly x gadget.Ciphertext -> RLWE, where gadget.Ciphertext is a matrix of RLWE samples encrypting scaled plaintext by the special RNS basis along with a base-2 basis and an optional prime P.
  • Relinearize: reduces the degree of a rlwe.Ciphertext to one by homomorphically evaluating the decryption of the higher-degree terms.
  • KeySwitch: homomorphically re-encrypts a rlwe.Ciphertext under a new secret.
  • KeyswitchHoisted: homomorphically re-encrypts a rlwe.Ciphertext under a series of new secrets, returning a new ciphertext for each secret.
  • KeyswitchHoistedNoModDown: homomorphically re-encrypts a rlwe.Ciphertext under a series of new secrets, returning a new ciphertext for each secret, but without the division by P (the result is given mod QP).
  • Automorphism: homomorphically evaluates the map X -> X^k.
  • AutomorphismHoisted: homomorphically evaluates multiple maps of the type X -> X^k, returning a new ciphertext for each map.
  • AutomorphismHoistedNoModDown: homomorphically evaluates multiple maps of the type X -> X^k, returning a new ciphertext for each map, but without the division by P (result is given mod QP).
  • Trace: homomorphically evaluates the map X -> sum((-1)^i * X^{i*n+1}) for n <= i < N.
  • ExternalProduct: evaluates rlwe.Ciphertext x rgsw.Ciphertext -> rlwe.Ciphertext.
• RLWE: re-enabled bit-decomposition, on top of RNS decomposition, for the inner-product between rlwe.Ciphertext and gadget.Ciphertext.
  • This functionality can be enabled by setting Pow2Base to the desired power of two basis.
  • This functionality can be used in conjunction with the RNS hybrid decomposition (with a modulus P) only when P is composed of a single prime.
  • This functionality is disabled if Pow2Base is set to zero (default value).
• RLWE: enabled instantiation of rlwe.Parameters without the modulus P.
• RLWE: revamped the rlwe.Encryptor interface and implementing structs:
  • Added the .EncryptZero method to generate encryptions of zeros.
  • The .Encrypt and .EncryptZero now accept ct interface{} as their ciphertext argument and determine the type of encryption to be performed according to the runtime type of ct.
• RLWE: added the PRNGEncryptor type, which supports secret-key encryption from a user-specified PRNG.
• RLWE: rlwe.KeyGenerator now uses an rlwe.Encryptor internally, to generate secret keys, encryption keys and evaluation keys.
• RLWE: extracted the rlwe/ringqp sub-package which provides the ringqp.Ring and ringqp.Poly types to respectively replace the former types rlwe.RingQP and rlwe.PolyQP.
• DRLWE: added the Thresholdizer and Combiner types for t-out-of-N-threshold schemes through Shamir secret-sharing.
• DRLWE: added a README.md providing package overview and usage instructions.
• DRLWE: removed the obsolete CollectivePublicKeyGenerator, RelinearizationKeyGenerator, RotationKeyGenerator, PublicKeySwitchingProtocol and KeySwitchingProtocol interfaces.
• DRLWE: renamed AggregateShare methods to AggregateShares.
• RGSW: added package rgsw, which provides a partial implementation of the RLWE-based RGSW encryption scheme. This incluides:
  • rgsw.Encryptor and the rgsw.Ciphertext types.
  • rgsw.Evaluator to support the external product RLWE x RGSW -> RLWE.
  • rgsw/lut sub-package that provides evaluation of Look-Up-Tables (LUT) on rlwe.Ciphertext types.
• BFV: renamed Encoder.DecodeRingT to Encoder.SwitchToRingT to better reflect the purpose of the method.
• CKKS: fixed MulAndAdd correctness for non-identical inputs.
• CKKS: added advanced.EncodingMatrixLiteral.RepackImag2Real optional field to repack the imaginary part into the right n real slots.
• CKKS: Trace now only takes as input the logSlots of the encrypted plaintext.
• CKKS: replaced the public variable .Scale with .scale, it can now be accessed with .Scale() and set to a new value with .SetScale().
• CKKS: renamed the methods ScalingFactor and SetScalingFactor of the interface Operand to Scale and SetScale respectively.
• CKKS/bootstrapping: renamed method Bootstrapp to Bootstrap.
• BFV/CKKS: key-switching functionalities (such as rotations, relinearization and key-switching) are now all based on the rlwe.Evaluator.
• BFV/CKKS: the parameters now are based on the sub-type rlwe.Parameters.
• BFV/CKKS: removed deprecated methods EncryptFromCRP and EncryptFromCRPNew, users should now use the PRNGEncryptor interface.
• BFV/CKKS: fixed a panic happening during the benchmark testing.
• DBFV/DCKKS: removed the dbfv/dckks.CKGProtocol, dbfv/dckks.RKGProtocol and dbfv/dckks.RTGProtocol types. Users should use the corresponding drlwe types instead.
• DBFV/DCKKS: MaskedTransformFunc is now a struct and takes as additional input to the linear transform two Boolean flags to parameterize if the decoding/encoding process must be done before/after the linear transform.
• DBFV/DCKKS: refresh and maskedTransform protocols now allow the user to specify the output parameters, enabling parameter switching.
• DCKKS: fixed dckks.RefreshProtocol correctness when the output scale is different from the input scale.
• Examples: added examples/ckks/advanced/lut, which is an example that performs homomorphic decoding -> LUT -> homomorphic encoding on a ckks.Ciphertext.
• Examples: removed examples/ckks/advanced/rlwe_lwe_bridge_LHHMQ20, which is replaced by examples/ckks/advanced/lut.
• Examples: removed examples/rlwe/lwe_bridge since the code of this example is now part of rlwe.Evaluator and showcased in examples/ckks/advanced/lut.
• CI: revamped Makefile to no longer require github.com/dedis/coding and integrated linting/vet checks.

• CKKS: Baby-Step Giant-Step Polynomial Evaluation Algorithm (BSGSPEA):
  • Added PolynomialBasis, a struct to generate powers of monomials. This struct can be marshalled.
  • Renamed former PolynomialBasis enumerated type to BasisType.
  • EvaluatePoly and EvaluatePolyVector now both accept pre-computed PolynomialBasis as input in addition to Ciphertext.
  • Fixed correctness error and panic when a non-relinearized ciphertext and a plaintext were given to Mul and MulAndAdd.
  • Fixed automatic-scale matching in BSGS that wasn't reliably ensuring that scales between two ciphertext to be added was the same.
  • Improved BSGSPEA with lazy relinearization and lazy rescaling.
  • Overall the precision of the BSGSPEA is greatly improved and its complexity is reduced. This also improves the precision of the bootstrapping.

• CKKS: updated the bootstrapping circuit to use the key-encapsulation mechanism of Bootstrapping for Approximate Homomorphic Encryption with Negligible Failure-Probability by Using Sparse-Secret Encapsulation. The previous bootstrapping circuit can be run by setting EphemeralSecretDensity=0.
• BFV: added the Evaluator.Rescale and Evaluator.RescaleTo methods to switch BFV ciphertexts to lower levels.
• BFV: all Evaluator methods on ciphertext support all arithmetic operations at lower levels, but require that operands are at the same level.
• BFV: the plaintext modulus T can now equal to the level-zero modulus Q[0] (i.e., be a factor of the ciphertext modulus Q).
• BFV: added the methods NewCiphertextLvl, NewPlaintextLvl, NewPlaintextMulLvl, Evaluator.AddScalar and Evaluator.MulScalarAndAdd.
• BFV: merged []uint64 and []int64 plaintext encoding methods (e.g. EncodeUint and EncodeInt are replaced by Encode) and added the respective [...]New methods.
• BFV: added the methods EvaluatePoly and EvaluatePolyVector for homomorphic polynomial evaluation.
• BFV/RING: moved RNSScaler from ring to bfv.
• RING: removed deprecated SimpleScaler.

• Fixed sparse ternary sampler to properly sample on non-zero poly.

Changelog

• RLWE/CKKS/BFV: added the H field and HammingWeight method in parameters-related structs, to specify distribution of all secrets in the schemes.
• RLWE/DRLWE: all secrets in the ternary distribution are now sampled with a fixed hamming weight, according to the parameters.
• CKKS: encoder is now about 3.5x faster (without taking the NTT into account).

Changelog

• RING: renamed FastBasisExtender to BasisExtender.
• RING: .PolyToBigint[...](*) now take as input gap which defines the multiples of X^{i*gap} to reconstruct.
• RLWE: removed FastEncryptor. Encryption without rescaling by P is now automatically used by Encryptor if no P is specified in the parameters.
• RLWE: NewAdditiveShareBigint now takes as input the size of the share.
• RLWE/CKKS/BFV: added .ShallowCopy(), .WithKey() (shallow copy with new key) to Encryptor and Decryptor.
• BFV/CKKS: added .ShallowCopy() to Encoder and EncoderBigComplex (only CKKS).
• DRLWE/DCKKS/DBFV: added .ShallowCopy() to all protocols.
• DLRWE/DCKKS/DBFV: protocols drlwe.CKSProtocol and drlwe.PCKSProtocol and sub-protocols based on these two protocols now only take a polynomial as input for the share generation instead of the full ciphertext.
• DRLWE/DCKKS/DBFV: uniformized API of share generation and aggregation to .GenShare(*) and .AggregateShare(*).

Changelog

• RING: added support for ring operations over the conjugate invariant ring.
• RING: added support for custom NTT via the NumberTheoreticTransformer interface.
• RLWE: added support for RLWE primitives over the conjugate invariant ring.
• RLWE: added encoding.BinaryMarshaler implementation for rlwe.Ciphertext types.
• RLWE: added an example implementation of homomorphic RLWE slot shuffling based on RLWE<->LWE conversion.
• RLWE: increased the maximum supported polynomial degree to 2^17.
• CKKS: Trace does not multiply the output by (N/n)^-1 anymore.
• CKKS: added support for the CKKS scheme over the conjugate invariant ring.
• CKKS: renamed Scale to DefaultScale in Parameters and ParametersLiteral.
• CKKS: added the Evaluator.Average method.
• CKKS: added DomainSwitcher type for conversion between Standard and Conjugate Invariant variants of CKKS.
• CKKS: added support for both []complex128 and []float64 as input to Encoder.Encode* methods.
• CKKS: added support for []float64 as input to GetPrecisionStats.
• CKKS: added support for func(float64)float64 and func(complex128)complex128 as input to Approximate.
• CKKS: uniformized the arguments' position for all methods of the Encoder interface.
• CKKS: renamed Encoder.EncodeNTT/New to Encoder.Encode/Newand added Encoder.EncodeSlots, Encoder.DecodeSlots and Encoder.DecodeSlotsPublic.
• CKKS: added EncodeSlotsQP to encode on rlwe.PolyQP to support the new LinearTransform interface.
• CKKS: improved Encoder implementation; it is now much faster when encoding sparse plaintexts.
• CKKS: changed the approximation intervals from complex128 to float64.
• CKKS: renamed PtDiagMatrix to LinearTransform.
• CKKS: added LinearTransform.Rotations() to get the required rotation for the reciever plaintext linear tranform.
• CKKS: added Parameters.RotationsForLinearTransform to get the required rotation for the given plaintext linear tranform.
• CKKS: added NewLinearTransform, EncodeNewLinearTransform, GenLinearTransform and GenLinearTransformBSGS to allocate and initialize plaintext linear transforms.
• CKKS: removed plaintext linear transforms (old PtDiagMatrix) constructors and initializers from Encoder.
• CKKS: added Evaluator.EvaluatePolyVector to enable efficient evaluation of multiple different polynomials on the same ciphertext.
• CKKS: fixed a bug in the BSGS approach for linear transform where the selection of the ratio bettween giant step and baby step could lead to a ratio of N.
• CKKS: the EvalMod step of the bootstrapping now works for moduli of any size, regardless of Q[0] or MessageRatio.
• DCKKS: added support for multiparty CKKS over the conjugate invariant ring.
• DCKKS: fixed MaskedTransformProtocol correctness for sparse plaintexts.
• Examples: updated the ckks/sigmoid example to ckks/polyeval example, that now showcases the use of PolynomialVector.

Changelog

• RING: added MapSmallDimensionToLargerDimensionNTT method which maps from Y = X^{N/n} to X in the NTT domain.
• RING: FastBasisExtender type can now extend the basis of polynomials of any level in base Q to polynomials of any level in base P.
• RING: changed RNS division Div[floor/round]BylastModulus[NTT] to Div[floor/round]BylastModulus[NTT]Lvl (the level of the last modulus must always be provided).
• RING: RNS division no longer modifies the output polynomial's level, this is to facilitate the usage of memory pools.
• RING: added the method MFormVector, which switches a slice of uint64 into the Montgomery domain.
• RING: RNS scaler (used in BFV) does not modify the input anymore.
• RLWE: GenSwitchingKey now accepts secret-keys of different dimensions and level as input to enable re-encryption between different ciphertext degrees.
• RLWE: added SwitchCiphertextRingDegreeNTT and SwitchCiphertextRingDegree to switch ciphertext ring degrees.
• RLWE: added the rlwe.RingQP type to represent the extended ring R_qp.
• RLWE: added the rlwe.PolyQP type to represent polynomials in the extended ring R_qp.
• DRLWE: added the CKGCRP, RKGCRP, RTGCRP and CKSCRP types to represent the common reference polynomials in these protocols.
• DRLWE: added the CRS interface for PRNGs that implement a common reference string among the parties.
• DRLWE: added the SampleCRP(crs CRS) method to each protocol types to sample their respective CRP type.
• BFV: changed the plaintext scaling from floor(Q/T)*m to round((Q*m)/T) to reduce the initial ciphertext noise.
• CKKS: added the ckks/advanced sub-package and moved the homomorphic encoding, decoding and modular reduction into it.
• CKKS: added the ckks/bootstrapping sub-package and moved the CKKS bootstrapping into it. This package now mostly relies on the ckks/advanced package.
• CKKS: renamed the ChebyshevInterpolation type to Polynomial.
• CKKS: removed the EvaluateCheby method that was redundant with the EvaluatePoly one.
• CKKS: optimized the EvaluatePoly to account for odd/even polynomials and fixed some small imprecisions in scale management occurring for some specific polynomial degrees.
• CKKS: some advanced methods related to automorphisms are now public to facilitate their external use.
• CKKS: improved the consistency of the API for in-place and [..]New methods.
• CKKS: added the method NewCiphertextAtLevelFromPoly, which creates a ciphertext at a specific level from two polynomials.
• CKKS: updated precision stats struct, added L2 norm in the statistics and improved the command line prints.
• CKKS: improved the algorithmic complexity of MultiplyByDiagMatrixBSGS and updated the bootstrapping parameters accordingly.
• CKKS: PermuteNTTHoistedNoModDown now returns [phi(P*c0 + c0'), phi(c1')] instead of [phi(c0'), phi(c1')].
• CKKS: Changed RotateHoistedNoModDown to RotateHoistedNoModDownNew for consistency.
• DBFV/DCKKS: both now use their respective CRP type for each protocol.
• EXAMPLE: added showcase of the ckks/advanced sub-package: a bridge between CKKS and FHEW ciphertexts using homomorphic decoding, ring dimension switching, homomorphic matrix multiplication and homomorphic modular reduction.

Changelog

• Added SECURITY.md
• ALL: when possible, public functions now use int instead of uint64 as parameters and return values.
• ALL: ring.Ring are not instantiated once in the parameters and read only. They are then accessed by other structs, like the encryptor or evaluator.
• RING: removed MulPoly and its related tests.
• RING: ring.Ring is now read-only and thread-safe.
• RING: RNS rescaling API is now in place and can take a different poly as output.
• RING: added ReadFromDistLvl and ReadAndAddFromDistLvl to Gaussian sampler API.
• RING: added IsNTT and IsMForm flags in the ring.Poly type. For now, these flags are never checked or changed by the ring package.
• RLWE: added a new rlwe package as common implementation base package for the Lattigo RLWE schemes.
• RLWE: extracted the rlwe.Parameters type as common base struct for BFV and CKKS parameters.
• RLWE: extracted the rlwe.KeyGenerator type as common key-generator for BFV and CKKS.
• RLWE: extracted the rlwe.Ciphertext type as common base struct for BFV and CKKS ciphertexts.
• RLWE: extracted the rlwe.Plaintext type as common base struct for BFV and CKKS plaintext.
• RLWE: extracted the rlwe.Encryptor type as common base interface for BFV and CKKS encryptors.
• RLWE: extracted the rlwe.Decryptor type as common base interface for BFV and CKKS decryptors.
• RLWE: extracted the rlwe.KeySwitcher type as a common key-switching implementation for BFV and CKKS evaluators.
• RLWE: renamed the Parameters.Copy() method to Parameters.CopyNew() for consistency.
• RLWE: added Parameter struct, that stores the relevant ring.Ring instances and has getter methods to access them.
• RLWE: added equality and inclusion check methods for the rlwe.RotatationKeySet type.
• RLWE: added tests for encryption, decryption, key-generation and key-switching.
• RLWE: moved keys related marshalling tests of bfv and ckks packages the rlwe package.
• DRLWE: added a new drlwe package as a common implementation base for the lattigo multiparty RLWE schemes.
• DRLWE: added tests for the protocols.
• DRLWE: moved keys-related marshalling tests of dbfv and dckks packages to the drlwe package.
• BFV/CKKS: the schemes now use a common implementation for their keys.
• BFV/CKKS: the rotation-keys are now indexed by their corresponding Galois automorphism.
• BFV/CKKS: the Evaluator interface now has a single method for all column rotations and one method for the row-rotation/conjugate.
• BFV/CKKS: the relinearization and rotation keys are now passed to the Evaluator constructor methods (and no longer to the operations methods).
• BFV/CKKS: added the ParameterLiteral type for literally specifying scheme parameters in Go programs.
• BFV/CKKS: removed the now obsolete Moduli and LogModuli types and their associated Parameters constructors.
• BFV/CKKS: Parameters types are now passed by value in most situations.
• BFV/CKKS: added encoding/json-compatible JSON serializers and deserializers for the Parameters types.
• BFV/CKKS: removed the scheme-specific key types.
• BFV/CKKS: added a -params=[params json] flag for all test and bench suites for specifying parameters from the command line.
• DBFV/DCKKS: added a common interface and implementation for each multiparty protocol.
• DBFV/DCKKS: added standalone Encryption-To-Shares (E2SProtocol) and Shares-To-Encryption (S2EProtocol) protocols for domain switching between encryptions and secret-shares.
• DBFV/DCKKS: generalized the Refresh-and-permute protocol into generic MaskedTransformProtocol that accepts an arbitrary linear function.
• DCKKS: public-refresh now takes a target desired output scale, which enables refreshing the ciphertext to the default scale.
• BFV: the moduli of ringQMul are now generated based on N andQ.
• CKKS: added Parameter methods that compute the required rotations for relevant Evaluator operations.
• CKKS: added methods for performing linear-transformations and improved several aspects listed below.
• CKKS: improved the tests for CoeffsToSlots and SlotsToCoeffs.

CKKS Bootstrapping

• The procedure now allows for a more granular parameterization.
• Added flag in bootstrapping parameters for bit-reversed inputs (with bit-reversed output) CoeffsToSlots and SlotsToCoeffs.
• Added optional Arcsine.
• The procedure now uses the new linear-transformation API.
• CoeffsToSlots and SlotsToCoeffs are now standalone public functions.

New CKKS Evaluator methods

• RotateHoisted: evaluates several rotations on a single ciphertext.
• LinearTransform: evaluates one or more PtDiagMatrix on a ciphertext using MultiplyByDiagMatrix or MultiplyByDiagMatrixBSGS according to the encoding of PtDiagMatrix.
• MultiplyByDiagMatrix: multiplies a ciphertext with a PtDiagMatrix using n rotations with single hoisting.
• MultiplyByDiagMatrixBSGS: multiplies a ciphertext with a PtDiagMatrix using 2sqrt(n) rotations with double-hoisting.
• InnerSumLog: optimal log approach that works for any value (not only powers of two) and can be parameterized to inner sum batches of values (sub-vectors).
• InnerSum: naive approach that is faster for small values but needs more keys.
• ReplicateLog: optimal log approach that works for any value (not only powers of two) and can be parameterized to replicate batches of values (sub-vectors).
• Replicate: naive approach that is faster for small values but needs more keys.

New CKKS Encoder methods

• PtDiagMatrix: struct that represents a linear transformation.
• EncodeDiagMatrixBSGSAtLvl: encodes a PtDiagMatrix at a given level, with a given scale for the BSGS algorithm.
• EncodeDiagMatrixAtLvl: encodes a PtDiagMatrix at a given level, with a given scale for a naive evaluation.
• DecodePublic: adds Gaussian noise of variance floor(sigma * sqrt(2*pi)) before the decoding step (see SECURITY.md).
• DecodeCoeffsPublic: adds Gaussian noise of variance floor(sigma * sqrt(2*pi)) before the decoding step (see SECURITY.md).
• GetErrSTDFreqDom : get the error standard deviation in the frequency domain (slots).
• GetErrSTDTimeDom: get the error standard deviation in the time domain (coefficients).

CKKS Fixes

• MultByi now correctly sets the output ciphertext scale.
• Relinearize now correctly sets the output ciphertext level.
• matrix-vector multiplication now correctly manages ciphertexts of higher level than the plaintext matrix.
• matrix-vector encoding now properly works for negative diagonal indexes.

Others

• PrecisionStats now includes the standard deviation of the error in the slots and coefficients domains.

Added

• BFV/CKKS : added a check for minimum polynomial degree when creating parameters.
• BFV : added the bfv.Element.Level method.
• RING : test for sparse ternary sampler.

Changed

• BFV/CKKS : pk is now (-as + e, a) instead of (-(as + e), a).
• BFV : harmonized the EvaluationKey setter from SetRelinKeys to Set
• CKKS : renamed BootstrappParams into BootstrappingParameters
• CKKS : the Evaluator.DropLevel, Parameters.SetLogSlots and Element.Copy methods no longer return errors
• RING : minimum poly degree modulus is 16 to ensure the NTT correctness.
• RING : isPrime has been replaced by big.ProbablyPrime, which is deterministic for integers < 2^64.

Fixed

• ALL : reduced cyclomatic complexity of several functions.
• ALL : fixed all instances reporeted by staticcheck and gosec excluding G103 (audit the use of unsafe).
• ALL : test vectors are now generated using the crypto/rand instead of math/rand package.
• ALL : fixed some unhandled errors.
• BFV/CKKS : improved the documentation: documentated several hardcoded values and fixed typos.
• RING : fixed bias in sparse ternary sampling for some parameters.
• RING : tests for the modular reduction algorithms are now deterministic.

Added

• BFV : special-purpose plaintext types (PlaintextRingT or PlaintextMul) for optimized ct-pt operations. See bfv/encoder.go and bfv/plaintext.go.
• BFV : allocation-free Encoder methods
• RING : GenNTTPrimes now takes the value Nth (for Nth primitive root) as input rather than logN.

Changed

• BFV : the Encoder.DecodeUint64 and Encoder.DecodeInt64 methods now take the output slice as argument.
• CKKS : API of Evaluator.RotateColumns becomes Evaluator.Rotate
• CKKS : the change of variable in Evaluator.EvaluateCheby isn't done automatically anymore and the user must do it before calling the function to ensure correctness.
• CKKS : when encoding, the number of slots must now be given in log2 basis. This is to prevent errors that would induced by zero values or non power of two values.
• CKKS : new encoder API : EncodeAtLvlNew and EncodeNTTAtLvlNew, which allow a user to encode a plaintext at a specific level.

Removed

• CKKS : removed method Evaluator.EvaluateChebySpecial
• BFV : removed QiMul field from bfv.Parameters. It is now automatically generated.

Performance

• Global 1.5x speed-up across all arithmetic (this does not include sampling).

Added

• BFV/CKKS: Added fast encryption (directly in Q without the rescaling by P).
• CKKS: Added full-RNS scale-invariant bootstrapping (https://eprint.iacr.org/2012/144).
• CKKS: Added parameterized tests for a range of experiments.
• CKKS: Added arbitrary precision encoding/decoding.
• CKKS: Added scale invariant polynomial evaluation.
• CKKS: Added encoding/decoding for coefficient packing.
• CKKS The user can now choose to encode a plaintext in or out of the NTT domain (the latter option leads to slightly faster encryptions).
• CKKS: Added secret-key gen with error distribution.
• DBFV: Added collective refresh with arbitrary permutation/linear transformation.
• DCKKS: Added collective refresh with arbitrary permutation/linear transformation.
• RING: Added arbitrary precision complex arithmetic, including cos and sin functions.
• RING: Added polynomial interpolation.
• RING: Added polynomial inversion.
• RING: Extracted interface type Scaler for polynomial coefficient scaling.
• RING: Added type RNSScaler as an efficient, cross-platform implementation of the Scaler interface.

Changed

• ALL: all tests now use "require".
• BFV/CKKS: Now parameters without P can be used, but the key-switching is disabled.
• BFV/CKKS: Now parameters do not use methods to access internal values.
• BFV/CKKS: New rotations keys optimized for hoisting rotations of the form (-phi^{-1}(s1)a + phi(s0) + e, a).
• BFV: The Decoder uses the RNSScaler implementation of the Scaler interface to perform the t/Q rescaling.
• CKKS: Simplified the code of the hybrid key-switching (does not affect user experience).
• CKKS: The encoding/decoding operations at level 0 are now 500% faster.
• CKKS: The encoder now accepts slices of complex values with length equal to or smaller than the specified number of slots.
• RING: Improved primes finding.
• RING: All Gaussian sampling now uses Ziggurat sampling.
• RING: Revamped polynomial samplers to make them more memory efficient, consistent user friendly, and to enable parallel sampling.
• RING: The SimpleScaler type now use slightly slower but cross-platform big.Int/Float.
• UTILS: Complete revamp of the PRNG (Blake2b XOF), to make it more user friendly and consistent.

Removed

• BFV/CKKS: Parameters API generation GenFromLogModuli() and GenFromModuli() have been removed and replaced by Gen().
• CKKS: EvaluatePolyFast(.) and EvaluatePolyEco(.) are replaced by EvaluatePoly(.).
• CKKS: EvaluateChebyFast(.) and EvaluateChebyEco(.) are replaced by EvaluatePolyCheby(.).
• CKKS: EvaluateChebyEcoSpecial(.) and EvaluateChebyFastSpecial(.) are replaced by EvaluatePolyChebySpecial(.).
• RING: The Float128 type was removed due to cross-platform incompatility.

Fixes

• BFV: Fixed multiplication that was failing when #Qi != #QMul.
• BFV: Fixed a mempool corruption when encrypting from SK.
• CKKS: The function mulrelin now always returns a fully reduced polynomial.
• CKKS: The encoder now correctly checks that the number of slots is a power of two.
• RING: Prevented a rare case of uint64 overflow during prime sampling.
• RING: Prevented a rare case where two identical primes could be returned when sampling primes.

Added

All schemes : new switching-keys and key-switching algorithm based on the concept presented in https://eprint.iacr.org/2019/688.pdf.
All schemes : new marshaling interface for all structures.
BFV/CKKS : new Parameters structs and API enabling a better customization and fine tuning for specific applications.
CKKS : new API for hoisted rotations, which is faster than sequential rotations.
DBFV/DCKKS : added collective refresh of a ciphertext (decentralized bootstrapping).
RING : added Ziggurat sampling, available from the context.
RING : enabled dense and sparse ternary polynomials sampling directly from the context.
RING : new API enabling "level" wise polynomial arithmetic.
RING : new API for modulus switching with flooring and rounding.
UTILS : utils now regroups all the utility methods which were previously duplicated among packages.

Removed

BFV/CKKS/DBFV/DCKKS : removed their respective context. Ring context remains public.
All schemes : removed key-switching with bit decomposition. This option will however be re-introduced at a later stage since applications using small parameters can suffer from this change.
BFV/CKKS/RING : removed redudant/irrelevant tests and benchmarks.
BFV : removed context QP as it is not any more used in the multiplication.
BFV : removed int encoder, now only batch encoding is supported.
CKKS : modulus switching is now located in Ring.
RING : removed the algorithms that needed Float128 during the BFV multiplication.
RING : removed most wrapping methods for bigInt, which are now replaced by the native math/big package.
RING : removed ternary sampler, which is now part of the context.

Changed

All schemes : Encryptor, Decryptor, Encoder, Evaluator, KeyGenerator are now interface types.
All schemes : Improved Godoc and error strings.
ALl schemes : greatly reduced the number of methods that could return an error.
All schemes : new tests and benchmarks with fully supported regex.
All schemes : coefficient wise arithmetic using double slices is now substentially faster.
BFV/CKKS : changed the name of the underlying ring contexts. Q now represents the ciphertext modulus (with QMul being the extended ciphertext modulus for BFV) and QP represents modulus of the keys (P being the special primes used during the new key-switching).
BFV/CKKS/DBFV/DCKKS : structures are now created using the parameters instead of the context.
BFV : quantization during multiplication doesn't use Float128 any more, resulting in a substential speed improvement.
BFV : BatchEncoder has been renamed Encoder.
CKKS : the scale is now stored as a float64 instead of a power of 2.
CKKS : rounding is applied instead of flooring when a real value is converted to an integer value. This change affects the rescaling and the encoding.
CKKS : previously needed one ring context per level, now only uses one context for all levels.
CKKS : new baby-step giant-step algorithm for evaluating polynomials in standard and Chebyshev basis.
CKKS : reduced the number of NTT needed during the encryption.
CKKS : API for MultConst is now MultByConst.
BFV/CKKS : new API for the rotation-keys generation.
DBFV/DCKKS : complete revamp of the API and interfaces enabling a much easier integration into larger systems.
DBFV/DCKKS : improved PCKS and CKS using the concept of the new key-switching technique which enables to reduces the added noise.
DCKKS : all protocols work for ciphertexts at any levels.
RING : faster MulScalarBigint (now similar to MulScalar).
UTILS : PRNG must be keyed to be forward secure.

Fixes

All packages : typos, godoc and golint.
CKKS : ciphertext rotation now correctly sets the scale of the output ciphertext.
DBFV/DCKKS : correctness is now ensured when the same protocol instance is used to generate multiples shares.