Simple Encrypted Arithmetic Library (SEAL)



The Simple Encrypted Arithmetic Library (SEAL) is an easy-to-use but powerful open-source homomorphic encryption library, developed by researchers in the Cryptography Research Group at Microsoft Research. SEAL is written in standard C++; it has no external dependencies, so it is easy to compile in many different environments. SEAL is licensed under the MIT license.


12/2/2018: SEAL 3.1.0 released on GitHub under MIT license

In addition to the license change, this release brings many internal and a few API updates.

  • Changed to use Google Test framework for unit tests
  • Added support for 32-bit platforms
  • Cleaned up source code from unnecessary files and functions; improved build time
  • Changed directory structure to be more descriptive
  • Visual Studio solution now uses CMake to configure SEAL on Windows
  • Fixed multiple bugs
  • New capabilities, including:
    • Option of not expanding modulus chain when it is not needed
    • Easier to generate Galois keys for specific rotations
    • Loading now validates the correctness of plaintexts, ciphertexts, and keys for given SEALContext
    • New EncryptionParameterQualifiers flag indicating security standard compliance for parameters; option of enforcing the security standard
    • Secret key data is now cleared automatically from memory by destructors of SecretKey, KeyGenerator, and Decryptor


10/19/2018: Hotfix to SEAL 3.0

Due to a minor mistake SEAL 3.0 did not compile with OS X toolchains. This problem has now been fixed.


10/17/2018: SEAL 3.0 released

SEAL 3.0 is finally ready! Among other things, this major release adds support for the `FullRNS’ variant of the Cheon-Kim-Kim-Song (CKKS) approximate arithmetic scheme.

Main changes:

  • Added support for the CKKS encryption scheme (;
  • SEAL can now be compiled purely as C++14 if necessary although C++17 is recommended;
  • Added support for modulus switching (for both BFV and CKKS schemes);
  • Added seeded AES-NI-based PRNG for faster pseudo-randomness.
  • Improved performance when compiling on g++ and clang++;
  • Big improvements to the memory pooling system: the MemoryManager class now automatically hands out MemoryPoolHandle objects according to a customizable profile (MMProf class);
  • Big improvements to SEALExamples, e.g. multiple new examples;
  • Renamed `hash_block’ to `parms_id’;
  • Renamed EvaluationKeys to RelinKeys;
  • Renamed PolyCRTBuilder to BatchEncoder;
  • Removed Simulation, and Chooser, and related classes;
  • Removed .NET Framework wrappers and related projects;
  • Many bug fixes and improvements to the internals.

Let us know if you have any comments! For technical questions that can be of general interest, please ask on StackOverflow using the tag [seal]. For other communication, contact us at

P.S.: A big thank you to everyone who submitted bug reports for SEAL 2.3.1 and earlier versions.


6/20/2018: SEAL 2.3.1 released

A shiny new version of SEAL is now available! Here are the main changes:

  • SEAL requires C++17; it has been tested on Visual Studio 2017, g++-6 and newer, and clang++-5.0 and newer.
  • Added support for clang++ and fixed bug that caused incorrect results with g++-8.
  • Added CMake support for Linux and OS X. See INSTALL.txt for instructions for installing SEAL on Linux and OS X, and SEALExamples/CMakeLists.txt for an example of linking it with your projects.
  • Added performance tests to SEALNETExamples.
  • Enabled all Galois automorphisms in Evaluator/KeyGenerator.
  • Fixed bug that caused incorrect results with large plaintext modulus.
  • Simplified many class constructors: MemoryPoolHandle is no longer an optional parameter.
  • Thread-unsafe memory pools are no longer available by default (too dangerous).
  • Added experimental support for Microsoft GSL (gsl::span and gsl::multi_span).
  • Of course a huge number of internal bug fixes and improvements have been made.

Feel free to email if you find any bugs, or if you have feature requests or other suggestions.


12/1/2017: SEAL v2.3.0-4 available

A new update v2.3.0-4 fixing several major bugs and issues has been released. Important changes include:

  • The problem with GCC-7.2 has been fixed. SEAL also works with GCC-5 now and uses only C++11 (no C++14).
  • Homomorphic multiplication of ciphertexts of size larger than 2 gave incorrect results. This problem has been fixed now.
  • SEALNET EvaluationKeys|GaloisKeys::Save|Load now work correctly.
  • Problems with global memory pool in SEALNET have been fixed. There is no longer need to manually destroy the global memory pool on application exit.
  • In SEALNET, EncryptionParameters::SetX(…) functions have been removed and changed into setters for the corresponding properties.
  • Downloadable Linux (.tar.gz) and Windows (.zip) versions are available separately.


11/17/2017: Small updates

As some of you may have noticed, we’ve been pushing a lot of small (and big) bug fixes and other updates since the initial release of v2.3.0. We just released SEAL v2.3.0-3 which—in addition to the bug fixes—brings substantial improvements to memory locality and subsequently has a major impact on performance with larger parameters.


11/9/2017: Direct download link

SEAL v2.3.0-2 can now be downloaded directly from


11/7/2017: SEAL v2.3.0 released

A new version of SEAL is available! This is the biggest update since the first release, and contains a huge number of improvements, including:

  • Implementation of the FullRNS variant of the FV scheme by Bajard et al. (SAC 2016)
  • Redesigned and improved memory management
  • Improved support for multi-threaded applications
  • Massive number of optimizations and improvements throughout the library
  • Row and column rotations of encrypted matrices (batching)
  • Completely revised SEALExamples/main.cpp; new example demonstrating multi-threaded use of SEAL
  • Better directory structure
  • Lots of bug fixes

A new SEAL manual will be available shortly.

We highly recommend all users (especially those familiar with older versions of SEAL) to go carefully over the examples in SEALExamples/main.cpp. There are several subtle but critical differences to SEAL v2.2, which are necessary to know to achieve the best performance.


7/21/2017: SEAL has found a new home

SEAL is now available at To get access, send us an email at, include an email address associated to your Microsoft Live Account, and tell us briefly what you are planning on using SEAL for. SEAL v2.3 will be available only through the new repository.


6/4/2017: SEAL v2.2 released

SEAL v2.2 has been released. It includes the changes from the experimental branch, and many other improvements. We have big plans for major improvements to be implemented this summer, so stay tuned!


10/13/2016: Experimental Branch

A new experimental branch has been created. This branch will get much more frequent updates than the master branch, but these updates may not have been tested as thoroughly as the code in the master branch, may introduce frequent API changes, and may contain incomplete functionality. This first experimental commit contains some significant performance improvements over SEAL v2.1.


9/30/2016: SEAL v2.1 released

Again a new version of SEAL has been released. This is a fairly large update, which focuses mostly on performance, but also introduces some small API changes.

To accompany the release and to explain the changes in SEAL v2.1, we have released a new version of the documentation, available here.


By far the best way of learning to use SEAL is by going over the examples in examples/examples.cpp. These examples are heavily commented and demonstrate much of the core functionality of SEAL. In particular, they will teach how to set secure parameters, and how to use the BFV and CKKS schemes for simple computations on encrypted data. Ideally, the user would read examples.cpp while at the same time looking at the output of the corresponding executable.

Older versions of SEAL came with an associated manual. The SEAL 2.3.1 manual is still partly relevant and contains more explanation of how the BFV scheme works.

Citing SEAL

When citing SEAL, please use the following BibTeX entries.

Version BibTex
	title = {{S}imple {E}ncrypted {A}rithmetic {L}ibrary (release 3.1.0)},
	howpublished = {\url{}},
	month = dec,
	year = 2018,
	note = {Microsoft Research, Redmond, WA.},
	key = {SEAL}
	title = {{S}imple {E}ncrypted {A}rithmetic {L}ibrary (release 3.0.0)},
	howpublished = {\url{}},
	month = oct,
	year = 2018,
	note = {Microsoft Research, Redmond, WA.},
	key = {SEAL}


We are always looking for talented Ph.D. student interns to work with us on the SEAL project, and related homomorphic encryption research. If you are interested in a fun and productive 12-week internship at Microsoft Research, send us an email at Internships can take place at any time of the year.

An ideal  intern candidate has a non-empty subset of the following:

  • Strong academic record; publications in top conferences/journals
  • Background in cryptography/homomorphic encryption
  • Excellent communication skills; ability to communicate difficult/technical topics to mixed audiences
  • Excellent teamwork skills; ability to work together with people of diverse backgrounds towards a common goal
  • Strong programming experience in C++; experience in writing fast code
  • Experience in a professional software engineering project, e.g. prior internship experience as a software developer
  • Experience in machine learning
  • Ability to learn new skills quickly when needed
  • Passion for solving real-life privacy problems with fresh new ideas


Current and past interns:

Ilia Iliashenko (KU Leuven) Ilaria Chillotti (Université de Versailles SQ)
Wei Dai (Worcester Polytechnic Institute) Sadegh Riazi (UC San Diego)
Zhicong Huang (EPFL) Amir Jalali (Florida Atlantic University)
Peter Rindal (Oregon State University) Kyoohyung Han (Seoul National University)
Gizem Cetin (Worcester Polytechnic Institute) Yuhou (Susan) Xia (Princeton University)
Nathan Dowlin (Princeton University) Rachel Player (Royal Holloway, University of London)


We believe strongly that (fully) homomorphic encryption is ripe for use in many real-world applications. Since the technology is still quite new, and the existing libraries are very diverse in their functionality and design, we believe that a clear and public standardization effort could help in

  • Making homomorphic encryption easier to use
  • Determining security levels for specific parameter sets
  • Explaining to the public the capabilities and possibilities of this technology
  • Making libraries more inter-operable

For more information, see

Contact Us

If you have any questions, suggestions, comments, or bug reports, please contact us by emailing For technical questions that can be of general interest, please ask on StackOverflow using the tag [seal].