Microsoft SEAL

Microsoft SEAL is an easy-to-use open-source (MIT licensed) homomorphic encryption library developed by the Cryptography and Privacy Research group at Microsoft. Microsoft SEAL is written in modern standard C++ and is easy to compile and run in many different environments. For more information about the Microsoft SEAL project, see sealcrypto.org.

This document pertains to Microsoft SEAL version 3.6. Users of previous versions of the library should look at the list of changes.

Contents

• Microsoft SEAL
  • Contents
  • Introduction
    • Building Microsoft SEAL
    • Optional Dependencies

      - [Windows](#windows)
      

      - [Linux, macOS, and FreeBSD](#linux-macos-and-freebsd)
      

      - [Android](#android)
      

  • Microsoft SEAL for .NET
    • From NuGet package
    • Windows

      - [Linux and macOS](#linux-and-macos)
      

      - [Android](#android-1)
      

  • Getting Started
  • Contributing
  • Citing Microsoft SEAL

Introduction

Core Concepts

Most encryption schemes consist of three functionalities: key generation, encryption, and decryption. Symmetric-key encryption schemes use the same secret key for both encryption and decryption; public-key encryption schemes use separately a public key for encryption and a secret key for decryption. Therefore, public-key encryption schemes allow anyone who knows the public key to encrypt data, but only those who know the secret key can decrypt and read the data. Symmetric-key encryption can be used for efficiently encrypting very large amounts of data, and enables secure outsourced cloud storage. Public-key encryption is a fundamental concept that enables secure online communication today, but is typically much less efficient than symmetric-key encryption.

While traditional symmetric- and public-key encryption can be used for secure storage and communication, any outsourced computation will necessarily require such encryption layers to be removed before computation can take place. Therefore, cloud services providing outsourced computation capabilities must have access to the secret keys, and implement access policies to prevent unauthorized employees from getting access to these keys.

Homomorphic Encryption

Homomorphic encryption refers to encryption schemes that allow the cloud to compute directly on the encrypted data, without requiring the data to be decrypted first. The results of such encrypted computations remain encrypted, and can be only decrypted with the secret key (by the data owner). Multiple homomorphic encryption schemes with different capabilities and trade-offs have been invented over the past decade; most of these are public-key encryption schemes, although the public-key functionality may not always be needed.

Homomorphic encryption is not a generic technology: only some computations on encrypted data are possible. It also comes with a substantial performance overhead, so computations that are already very costly to perform on unencrypted data are likely to be infeasible on encrypted data. Moreover, data encrypted with homomorphic encryption is many times larger than unencrypted data, so it may not make sense to encrypt, e.g., entire large databases, with this technology. Instead, meaningful use-cases are in scenarios where strict privacy requirements prohibit unencrypted cloud computation altogether, but the computations themselves are fairly lightweight.

Typically, homomorphic encryption schemes have a single secret key which is held by the data owner. For scenarios where multiple different private data owners wish to engage in collaborative computation, homomorphic encryption is probably not a reasonable solution.

Homomorphic encryption cannot be used to enable data scientist to circumvent GDPR. For example, there is no way for a cloud service to use homomorphic encryption to draw insights from encrypted customer data. Instead, results of encrypted computations remain encrypted and can only be decrypted by the owner of the data, e.g., a cloud service customer.

Microsoft SEAL

Microsoft SEAL is a homomorphic encryption library that allows additions and multiplications to be performed on encrypted integers or real numbers. Other operations, such as encrypted comparison, sorting, or regular expressions, are in most cases not feasible to evaluate on encrypted data using this technology. Therefore, only specific privacy-critical cloud computation parts of programs should be implemented with Microsoft SEAL.

It is not always easy or straightfoward to translate an unencrypted computation into a computation on encrypted data, for example, it is not possible to branch on encrypted data. Microsoft SEAL itself has a steep learning curve and requires the user to understand many homomorphic encryption specific concepts, even though in the end the API is not too complicated. Even if a user is able to program and run a specific computation using Microsoft SEAL, the difference between efficient and inefficient implementations can be several orders of magnitude, and it can be hard for new users to know how to improve the performance of their computation.

Microsoft SEAL comes with two different homomorphic encryption schemes with very different properties. The BFV scheme allows modular arithmetic to be performed on encrypted integers. The CKKS scheme allows additions and multiplications on encrypted real or complex numbers, but yields only approximate results. In applications such as summing up encrypted real numbers, evaluating machine learning models on encrypted data, or computing distances of encrypted locations CKKS is going to be by far the best choice. For applications where exact values are necessary, the BFV scheme is the only choice.

Building Microsoft SEAL

Optional Dependencies

Microsoft SEAL has no required dependencies, but certain optional features can be enabled if it is compiled with support for specific third-party libraries such as Microsoft GSL, ZLIB, and Google Test. In SEAL >= 3.5.0 third-party libraries are (if enabled) downloaded, configured, and built as CMake external projects defined in thirdparty/*/CMakeLists.txt. This workflow is carried out automatically by the CMake toolchain or pre-build commands defined in native/src/SEAL.vcxproj, and as such requires no manual steps from the user.

Microsoft GSL

Microsoft GSL (Guidelines Support Library) is a header-only library that implements gsl::span: a view type that provides safe (bounds-checked) array access to memory. For example, if Microsoft GSL is available, Microsoft SEAL can allow BatchEncoder and CKKSEncoder to encode from and decode to a gsl::span instead of std::vector, which can in some cases have a significant performance benefit.

NOTE: Microsoft SEAL >= 3.5.0 is compatible with Microsoft GSL >= 3.0.0, and does not use an existing Microsoft GSL installed on the system. Microsoft SEAL < 3.5.0 is compatible with Microsoft GSL < 3.0.0, and can use an existing Microsoft GSL installed on the system.

ZLIB

ZLIB is a widely used compression library that implements the DEFLATE compression algorithm. Microsoft SEAL can use ZLIB (if present) to automatically compress data that is serialized. Ciphertext objects consist of a large number of integers modulo specific prime numbers (coeff_modulus primes). When using the CKKS scheme, although these prime numbers can often be quite small (e.g., 30 bits), the numbers are nevertheless serialized as 64-bit integers. In this case, more than half of data in a ciphertext are zeros that can be compressed away with a compression library, such as ZLIB. The BFV scheme benefits typically less from this technique, because the prime numbers used for the coeff_modulus encryption parameter tend to be larger, and integers modulo these prime numbers fill more of each 64-bit word. The compression is not only applied to Ciphertext objects, but to every serializable Microsoft SEAL object.

If ZLIB is available, it will be automatically used for serialization (see Serialization::compr_mode_default in native/src/seal/serialization.h. However, it is always possible to explicitly pass compr_mode_type::none to serialization methods to disable compression.

WARNING: The compression rate for a SecretKey can (in theory at least) reveal information about the key. In most common applications of Microsoft SEAL the size of a SecretKey would not be deliberately revealed to untrusted parties. If this is a concern, one can always save the SecretKey in an uncompressed form by passing compr_mode_type::none to SecretKey::save.

Zstandard

ZLIB compression can be extremely slow. In Microsoft SEAL >= 3.6.0 Zstandard is supported and preferred as an alternative. It is easy to compile Microsoft SEAL to support one or both of the compression libraries. This will ensure that any received ciphertext can be decompressed and used.

Windows

Microsoft SEAL comes with a Microsoft Visual Studio 2019 solution file SEAL.sln that can be used to conveniently build the library, examples, and unit tests. Visual Studio 2019 is required to build Microsoft SEAL.

Platform

The Visual Studio solution SEAL.sln is configured to build Microsoft SEAL both for Win32 and x64 platforms. Please choose the right platform before building Microsoft SEAL. The SEAL_C project and the .NET wrapper library SEALNet can only be built for x64.

Building Microsoft SEAL

Build the SEAL project native\src\SEAL.vcxproj from SEAL.sln. This results in the static library seal.lib to be created in lib\$(Platform)\$(Configuration). When linking with applications, you need to add native\src\ (full path) as an include directory for Microsoft SEAL header files.

[Optional] Debug and Release builds

You can easily switch from Visual Studio build configuration menu whether Microsoft SEAL should be built in Debug mode (no optimizations) or in Release mode. Please note that Debug mode should not be used except for debugging Microsoft SEAL itself, as the performance will be orders of magnitude worse than in Release mode.

[Optional] Microsoft GSL

By default Microsoft GSL is downloaded as part of Microsoft SEAL library. Microsoft GSL's header files are copied to native\src\GSL to be portable with Microsoft SEAL at the time of installation. You can disable the dependency on Microsoft GSL by commenting out #cmakedefine SEAL_USE_MSGSL in native\src\seal\util\config.h.in.

[Optional] ZLIB

By default ZLIB is downloaded and compiled as part of Microsoft SEAL library. ZLIB's static archive is included in Microsoft SEAL's static or shared target object. You can disable the dependency on ZLIB by commenting out #cmakedefine SEAL_USE_ZLIB in native\src\seal\util\config.h.in.

[Optional] Zstandard

By default Zstandard is downloaded and compiled as part of Microsoft SEAL library. Zstandard's static archive is included in Microsoft SEAL's static or shared target object. You can disable the dependency on Zstandard by commenting out #cmakedefine SEAL_USE_ZSTD in native\src\seal\util\config.h.in.

Building Examples

Build the SEALExamples project native\examples\SEALExamples.vcxproj from SEAL.sln. This results in an executable sealexamples.exe to be created in bin\$(Platform)\$(Configuration).

Building Unit Tests

The unit tests require the Google Test framework to be installed. The appropriate NuGet package is already listed in native\tests\packages.config, so once you attempt to build the SEALTest project native\tests\SEALTest.vcxproj from SEAL.sln Visual Studio will automatically download and install it for you.

Linux, macOS, and FreeBSD

Microsoft SEAL is very easy to configure and build in Linux and macOS using CMake (>= 3.12). A modern version of GNU G++ (>= 6.0) or Clang++ (>= 5.0) is needed. In macOS the Xcode toolchain (>= 9.3) will work.

In macOS you will need CMake with command line tools. For this, you can either

1. install the cmake package with Homebrew, or
2. download CMake directly from cmake.org/download and enable command line tools.

Below we give instructions for how to configure, build, and install Microsoft SEAL either system-wide (global install), or for a single user (local install). A system-wide install requires elevated (root) privileges.

NOTE: Microsoft SEAL compiled with Clang++ has much better runtime performance than that compiled with GNU G++.

Building Microsoft SEAL

We assume that Microsoft SEAL has been cloned into a directory called SEAL and all commands presented below are assumed to be executed in the directory SEAL.

You can build Microsoft SEAL library for your machine by executing the following commands:

cmake .
make

[Optional] Debug and Release Modes

By default Microsoft SEAL is built in Release mode. You can easily switch between Debug mode (no optimizations) or Release mode in CMake configuration options as follows:

cmake . -DCMAKE_BUILD_TYPE=Debug
make

Please note that Debug mode should not be used except for debugging Microsoft SEAL itself, as the performance will be orders of magnitude worse than in Release mode.

[Optional] Microsoft GSL

By default Microsoft GSL is downloaded as part of Microsoft SEAL library. Microsoft GSL's header files are copied to native/src/GSL to be portable with Microsoft SEAL at the time of installation. You can disable the dependency on Microsoft GSL in CMake configuration options as follows:

cmake . -DSEAL_USE_MSGSL=OFF
make

[Optional] ZLIB

By default ZLIB is downloaded and compiled as part of Microsoft SEAL library. ZLIB's static archive is included in Microsoft SEAL's static or shared target object. You can disable the dependency on ZLIB in CMake configuration options as follows:

cmake . -DSEAL_USE_ZLIB=OFF
make

[Optional] Zstandard

By default Zstandard is downloaded and compiled as part of Microsoft SEAL library. Zstandard's static archive is included in Microsoft SEAL's static or shared target object. You can disable the dependency on Zstandard in CMake configuration options as follows:

cmake . -DSEAL_USE_ZSTD=OFF
make

[Optional] Shared Library

By default Microsoft SEAL builds only a static library that is libseal-3.6.a on Unix-like platforms. You can enable building a shared library, libseal.so* in Linux or libseal*.dylib in macOS, in CMake configuration options as follows:

cmake . -DBUILD_SHARED_LIBS=ON
make

Building Examples

By default Microsoft SEAL does not build examples. You can enable building examples in CMake configuration options as follows:

cmake . -DSEAL_BUILD_EXAMPLES=ON
make

The sealexamples executable is located in native/bin/.

Building Unit Tests

By default Microsoft SEAL does not build tests. You can enable building tests in CMake configuration options as follows:

cmake . -DSEAL_BUILD_TESTS=ON
make

This downloads and compiles the GoogleTest framework as a part of Microsoft SEAL. The sealtest executable is located in native/bin/. All unit tests should pass successfully.

Installing Microsoft SEAL

If you have root access to the system you can install Microsoft SEAL system-wide as follows:

cmake .
make
sudo make install

To instead install Microsoft SEAL locally, e.g., to ~/mylibs/, do the following:

cmake . -DCMAKE_INSTALL_PREFIX=~/mylibs
make
make install

Linking with Microsoft SEAL through CMake

It is very easy to link your own applications and libraries with Microsoft SEAL if you use CMake. Simply add the following to your CMakeLists.txt:

find_package(SEAL 3.6 REQUIRED)
target_link_libraries(<your target> SEAL::seal)

If Microsoft SEAL was installed globally, the above find_package command will likely find the library automatically. To link with a locally installed Microsoft SEAL, e.g., installed in ~/mylibs as described above, you may need to tell CMake where to look for Microsoft SEAL when you configure your application by running:

cd <directory containing your CMakeLists.txt>
cmake . -DCMAKE_PREFIX_PATH=~/mylibs

Android

Microsoft SEAL can be compiled for Android. Under the android directory of the source tree you will find an Android Studio project that you can use to compile the library for Android. This project is meant only to generate native libraries that can then be called through the .NET library described in the following sections. Specifically, it does not contain any wrappers that can be used from the Java language.

Microsoft SEAL for .NET

Microsoft SEAL provides a .NET Standard library that wraps the functionality in Microsoft SEAL for use in .NET development.

From NuGet package

For .NET developers the easiest way of installing Microsoft SEAL is by using the multi-platform NuGet package available at NuGet.org. Simply add this package into your .NET project as a dependency and you are ready to go.

Windows

The Microsoft Visual Studio 2019 solution file SEAL.sln contains the projects necessary to build the .NET assembly, a backing native shared library, .NET examples, and unit tests.

Native Library

Microsoft SEAL for .NET requires a native library that is invoked by the managed .NET library. Build the SEAL_C project native\src\SEAL_C_.vcxproj from SEAL.sln. Building SEAL_C results in the dynamic library sealc.dll to be created in lib\$(Platform)\$(Configuration). This library is meant to be used only by the .NET library, not by end users, and needs to be present in the same directory as your executable when running a .NET application.

.NET Library

Once you have built the shared native library (see above), build the SEALNet project dotnet\src\SEALNet.csproj from SEAL.sln. Building SEALNet results in the assembly SEALNet.dll to be created in lib\dotnet\$(Configuration)\netstandard2.0. This is the assembly you can reference in your application.

.NET Examples

Build the SEALNetExamples project dotnet\examples\SEALNetExamples.csproj from SEAL.sln. This results in the assembly SEALNetExamples.dll to be created in bin\dotnet\$(Configuration)\netcoreapp3.1. The project takes care of copying the native SEAL_C library to the output directory.

.NET Unit Tests

Build the SEALNetTest project dotnet\tests\SEALNetTest.csproj from SEAL.sln. This results in the assembly SEALNetTest.dll to be created in bin\dotnet\$(Configuration)\netcoreapp3.1. The project takes care of copying the native SEAL_C library to the output directory.

Using Microsoft SEAL for .NET in Your Own Application

To use Microsoft SEAL for .NET in your own application you need to:

1. add a reference in your project to SEALNet.dll;
2. ensure sealc.dll is available for your application when run. The easiest way to ensure this is to copy sealc.dll to the same directory where your application's executable is located.

Building Your Own NuGet Package

You can build your own NuGet package for Microsoft SEAL by following the instructions in NUGET.md.

Linux and macOS

Microsoft SEAL for .NET relies on a native shared library that can be easily configured and built using CMake (>= 3.12) and a modern version of GNU G++ (>= 6.0) or Clang++ (>= 5.0). In macOS the Xcode toolchain (>= 9.3) will work.

For compiling .NET code you will need to install a .NET Core SDK (>= 3.1). You can follow these instructions for installing in Linux, or for installing in macOS.

Native Library

If you only intend to run the examples and unit tests provided with Microsoft SEAL, you do not need to install the native shared library. You only need to compile it. The SEALNetExamples and SEALNetTest projects take care of copying the native shared library to the appropriate assembly output directory.

Microsoft SEAL by default does not build SEAL_C. You can enable it in CMake configuration options as follows:

cmake . -DSEAL_BUILD_SEAL_C=ON
make

This results in a shared native library libsealc.so* in Linux or libsealc*.dylib in macOS.

If you have root access to the system, you have the option to install the native shared library globally. Then your application will always be able to find and load it. Assuming Microsoft SEAL is build and installed globally, you can install the shared native library globally as follows:

sudo make install

.NET Library

To build the .NET Standard library, do the following:

dotnet build dotnet/src --configuration <Debug|Release>

This will result in a SEALNet.dll assembly to be created in lib/dotnet/$(Configuration)/netstandard2.0. This assembly is the one you will want to reference in your own projects. The optional dotnet parameter --configuration <Debug|Release> can be used to build either a Debug or Release version of the assembly.

.NET Examples

To build and run the .NET examples, do:

dotnet run -p dotnet/examples

As mentioned before, the .NET project will copy the shared native library to the assembly output directory. You can use the dotnet parameter --configuration <Debug|Release> to run either Debug or Release versions of the examples.

.NET Unit Tests

To build and run the .NET unit tests, do:

dotnet test dotnet/tests

All unit tests should pass. You can use the dotnet parameter --configuration <Debug|Release> to run Debug or Relase unit tests. And you can use --verbosity detailed to print the list of unit tests that are being run.

Using Microsoft SEAL for .NET in Your Own Application

To use Microsoft SEAL for .NET in your own application you need to:

1. add a reference in your project to SEALNet.dll;
2. ensure the native shared library is available for your application when run. The easiest way to ensure this is to copy the native shared library to the same directory where your application's executable is located.

Android

You can use Android Studio to build the native shared library used by the .NET Standard wrapper library. However, the easiest and recommended way to use Microsoft SEAL in Android is through the multiplatform NuGet package you can find at NuGet.org. Just add this package to your Xamarin project in order to develop mobile applications using Microsoft SEAL and .NET. The native shared library and the .NET wrapper compile only for 64 bits, so only arm64-v8a and x86_64 Android ABIs are supported.

Getting Started

Using Microsoft SEAL will require the user to invest some time in learning fundamental concepts in homomorphic encryption. The code comes with heavily commented examples that are designed to gradually teach such concepts as well as to demonstrate much of the API. The code examples are available (and identical) in C++ and C#, and are divided into several source files in native/examples/ (C++) and dotnet/examples/ (C#), as follows:

C++	C#	Description
examples.cpp	Examples.cs	The example runner application
1_bfv_basics.cpp	1_BFV_Basics.cs	Encrypted modular arithmetic using the BFV scheme
2_encoders.cpp	2_Encoders.cs	Encoding more complex data into Microsoft SEAL plaintext objects
3_levels.cpp	3_Levels.cs	Introduces the concept of levels; prerequisite for using the CKKS scheme
4_ckks_basics.cpp	4_CKKS_Basics.cs	Encrypted real number arithmetic using the CKKS scheme
5_rotation.cpp	5_Rotation.cs	Performing cyclic rotations on encrypted vectors in the BFV and CKKS schemes
6_serialization.cpp	6_Serialization.cs	Serializing objects in Microsoft SEAL
7_performance.cpp	7_Performance.cs	Performance tests

It is recommeded to read the comments and the code snippets along with command line printout from running an example. For easier navigation, command line printout provides the line number in the associated source file where the associated code snippets start.

WARNING: It is impossible to use Microsoft SEAL correctly without reading all examples or by simply re-using the code from examples. Any developer attempting to do so will inevitably produce code that is vulnerable, malfunctioning, or extremely slow.

Contributing

For contributing to Microsoft SEAL, please see CONTRIBUTING.md.

Citing Microsoft SEAL

To cite Microsoft SEAL in academic papers, please use the following BibTeX entries.

Version 3.6

    @misc{sealcrypto,
        title = {{M}icrosoft {SEAL} (release 3.6)},
        howpublished = {\url{https://github.com/Microsoft/SEAL}},
        month = sep,
        year = 2020,
        note = {Microsoft Research, Redmond, WA.},
        key = {SEAL}
    }

Version 3.5

    @misc{sealcrypto,
        title = {{M}icrosoft {SEAL} (release 3.5)},
        howpublished = {\url{https://github.com/Microsoft/SEAL}},
        month = apr,
        year = 2020,
        note = {Microsoft Research, Redmond, WA.},
        key = {SEAL}
    }

Version 3.4

    @misc{sealcrypto,
        title = {{M}icrosoft {SEAL} (release 3.4)},
        howpublished = {\url{https://github.com/Microsoft/SEAL}},
        month = oct,
        year = 2019,
        note = {Microsoft Research, Redmond, WA.},
        key = {SEAL}
    }

Version 3.3

    @misc{sealcrypto,
        title = {{M}icrosoft {SEAL} (release 3.3)},
        howpublished = {\url{https://github.com/Microsoft/SEAL}},
        month = jun,
        year = 2019,
        note = {Microsoft Research, Redmond, WA.},
        key = {SEAL}
    }

Version 3.2

    @misc{sealcrypto,
        title = {{M}icrosoft {SEAL} (release 3.2)},
        howpublished = {\url{https://github.com/Microsoft/SEAL}},
        month = feb,
        year = 2019,
        note = {Microsoft Research, Redmond, WA.},
        key = {SEAL}
    }

Version 3.1

    @misc{sealcrypto,
        title = {{M}icrosoft {SEAL} (release 3.1)},
        howpublished = {\url{https://github.com/Microsoft/SEAL}},
        month = dec,
        year = 2018,
        note = {Microsoft Research, Redmond, WA.},
        key = {SEAL}
    }

Version 3.0

    @misc{sealcrypto,
        title = {{M}icrosoft {SEAL} (release 3.0)},
        howpublished = {\url{http://sealcrypto.org}},
        month = oct,
        year = 2018,
        note = {Microsoft Research, Redmond, WA.},
        key = {SEAL}
    }