Multi-Key Homomophic Encryption from TFHE

MK-TFHE is a proof-of-concept implementation of a multi-key version of TFHE. The code is written on top of the TFHE library (https://tfhe.github.io/tfhe/).

MK-TFHE is described in the paper "Multi-Key Homomophic Encryption from TFHE" by Hao Chen, Ilaria Chillotti, Yongsoo Song (https://eprint.iacr.org/2019/116).

We report below the TFHE readme, giving details on the original library and instructions for the dependencies and installation. We refer to their webpage for more details.

Fast Fully Homomorphic Encryption Library over the Torus

version 1.0 -- first release date: 2017.05.02

version 1.0-rc1 -- first pre-release date: 2017.04.05

version 0.1 -- Proof of concept release date: 2016.08.18

TFHE is open-source software distributed under the terms of the Apache 2.0 license. The scheme is described in the paper "Faster fully homomorphic encryption: Bootstrapping in less than 0.1 seconds" presented at the IACR conference Asiacrypt 2016 by Ilaria Chillotti, Nicolas Gama, Mariya Georgieva, Malika Izabachène.

The TFHE library implements a very fast gate-by-gate bootstrapping, based on [CGGI16]. Namely, any binary gate is evaluated homomorphically in about 13 milliseconds on a single core which improves [DM15] by a factor 50, and the mux gate takes about 26 CPU-ms (or 13ms on 2 cores).

The library implements a Ring-variant of the GSW [GSW13] cryptosystem and makes many optimizations described in [DM15] and [CGGI16].

It also implements a dedicated Fast Fourier Transformation for the anticyclic ring R[X]/(X^N+1), and uses AVX, AVX2 and FMA assembly vectorization instructions. The default parameter set achieves at least 110-bit of cryptographic security, based on ideal lattice assumptions.

From the user point of view, the library can evaluate a net-list of binary gates homomorphically at a rate of about 50 gates per second per core, without decrypting its input. It suffices to provide the sequence of gates, as well as ciphertexts of the input bits. And the library computes ciphertexts of the output bits.

Unlike other libraries, TFHE has no restriction on the number of gates or on their composition. This makes the library usable with either manually crafted circuits, or with the output of automated circuit generation tools. For TFHE, optimal circuits have the smallest possible number of gates, and to a lesser extent, the possibility to evaluate them in parallel.

The library interface can be used in a regular C code. However, to compile the core of the library you will need a standard C++11 compiler. Currently, the project has been tested with the g++ >= 5.2 compiler and clang >=3.8 under Linux, as well as clang under MacOS. In the future, we plan to extend the compatibility to other compilers, platforms and operating systems.

At least one FFT processor is needed to run the project:

• The default processor comes from Project Nayuki, who proposes two implementations of the fast Fourier transform - one in portable C, and the other using the AVX assembly instructions. This component is licensed under the MIT license, and we added the code of the reverse FFT (both in C and in assembly). Original source: https://www.nayuki.io/page/fast-fourier-transform-in-x86-assembly
• we provide another processor, named the spqlios processor, which is written in AVX and FMA assembly in the style of the nayuki processor, and which is dedicated to the ring R[X]/(X^N+1) for N a power of 2.
• We also provide a connector for the FFTW3 library: http://www.fftw.org. With this library, the performance of the FFT is between 2 and 3 times faster than the default Nayuki implementation. However, you should keep in mind that the library FFTW is published under the GPL License. If you choose to use this library in a final product, this product may have to be released under GPL License as well (other commercial licenses are available on their web site)
• We plan to add other connectors in the future (for instance the Intel’s IPP Fourier Transform, which should be 1.5× faster than FFTW for 1D real data)

To build the library with the default options, run make and make install from the top level directory of the TFHE project. This assumes that the standard tool cmake is already installed on the system, and an up-to-date c++ compiler (i.e. g++ >=5.2 or clang >= 3.8) as well. It will compile the shared library in optimized mode, and install it to the /usr/local/lib folder.

If you want to choose additional compile options (i.e. other installation folder, debug mode, tests, fftw), you need to run cmake manually and pass the desired options:

mkdir build
cd build
cmake ../src -DENABLE_TESTS=on -DENABLE_FFTW=on -DCMAKE_BUILD_TYPE=debug
make

The available options are the following:

[CGGI16]: I. Chillotti, N. Gama, M. Georgieva, and M. Izabachène. Faster fully homomorphic encryption: Bootstrapping in less than 0.1 seconds. In Asiacrypt 2016, pages 3-33.

[DM15]: L. Ducas and D. Micciancio. FHEW: Bootstrapping homomorphic encryption in less than a second. In Eurocrypt 2015, pages 617-640.

[GSW13]: C. Gentry, A. Sahai, and B. Waters. Homomorphic encryption from learning with errors: Conceptually-simpler, asymptotically-faster, attribute-based. In Crypto 2013, pages 75-92