This is a software to benchmark various secure multi-party computation (MPC) protocols in a variety of security models such as honest and dishonest majority, semi-honest/passive and malicious/active corruption. The underlying technologies span secret sharing, homomorphic encryption, and garbled circuits.
Filing an issue on GitHub is the preferred way of contacting us, but you can also write an email to mp-spdz@googlegroups.com (archive). Before reporting a problem, please check against the list of known issues and possible solutions.
Please file complete code examples because it's usually not possible to reproduce problems from incomplete code, and please include which protocol you have used (if applicable) because there are considerable differences between the various protocols.
The documentation contains section on a number of frequently asked topics as well as information on how to solve common issues.
This requires either a Linux distribution originally released 2014 or later (glibc 2.17) or macOS High Sierra or later as well as Python 3 and basic command-line utilities.
Download and unpack the distribution, then execute the following from the top folder:
Scripts/tldr.sh
echo 1 2 3 4 > Player-Data/Input-P0-0
echo 1 2 3 4 > Player-Data/Input-P1-0
Scripts/compile-run.py -E mascot tutorial
This runs the tutorial with two parties and malicious security.
On Linux, this requires a working toolchain and all requirements. On Ubuntu, the following might suffice:
sudo apt-get install automake build-essential clang cmake git libboost-dev libboost-thread-dev libgmp-dev libntl-dev libsodium-dev libssl-dev libtool python3
On MacOS, this requires brew to be installed, which will be used for all dependencies. It will execute the tutorial with two parties and malicious security.
make setup
echo 1 2 3 4 > Player-Data/Input-P0-0
echo 1 2 3 4 > Player-Data/Input-P1-0
Scripts/compile-run.py -E mascot tutorial
On strong enough hardware setups (several cores and GB of RAM), you
can speed up the last step by running make -j8 mascot-party.x beforehand.
Build a docker image for mascot-party.x:
docker build --tag mpspdz:mascot-party --build-arg machine=mascot-party.x .
Run the the tutorial:
docker run --rm -it mpspdz:mascot-party ./Scripts/mascot.sh tutorial
See the Dockerfile for examples of how it can be used.
The primary aim of this software is to run the same computation in various protocols in order to compare the performance. All protocols in the matrix below are fully implemented. However, this does not mean that the software has undergone a security review as should be done with critical production code.
The following table lists all protocols that are fully supported.
| Security model | Mod prime / GF(2^n) | Mod 2^k | Bin. SS | Garbling |
|---|---|---|---|---|
| Malicious, dishonest majority | MASCOT / LowGear / HighGear | SPDZ2k | Tiny / Tinier | BMR |
| Covert, dishonest majority | CowGear / ChaiGear | N/A | N/A | N/A |
| Semi-honest, dishonest majority | Semi / Hemi / Temi / Soho | Semi2k | SemiBin | Yao's GC / BMR |
| Malicious, honest majority | Shamir / Rep3 / PS / SY | Brain / Rep3 / PS / SY | Rep3 / CCD / PS | BMR |
| Semi-honest, honest majority | Shamir / ATLAS / Rep3 | Rep3 | Rep3 / CCD | BMR |
| Malicious, honest supermajority | Rep4 | Rep4 | Rep4 | N/A |
| Semi-honest, dealer | Dealer | Dealer | Dealer | N/A |
Modulo prime and modulo 2^k are the two settings that allow integer-like computation. For k = 64, the latter corresponds to the computation available on the widely used 64-bit processors. GF(2^n) denotes Galois extension fields of order 2^n, which are different to computation modulo 2^n. In particular, every element has an inverse, which is not the case modulo 2^n. See this article for an introduction. Modulo prime and GF(2^n) are lumped together because the protocols are very similar due to the mathematical properties.
Bin. SS stands for binary secret sharing, that is secret sharing modulo two. In some settings, this requires specific protocols as some protocols require the domain size to be larger than two. In other settings, the protocol is the same mathematically speaking, but a specific implementation allows for optimizations such as using the inherent parallelism of bit-wise operations on machine words.
A security model specifies how many parties are "allowed" to misbehave in what sense. Malicious means that not following the protocol will at least be detected while semi-honest means that even corrupted parties are assumed to follow the protocol. See this paper for an explanation of the various security models and a high-level introduction to multi-party computation.
Lower security requirements generally allow for more efficient protocols. Within the same security model (line in the table above), there are a few things to consider:
-
Computation domain: Arithmetic protocols (modulo prime or power of two) are preferable for many applications because they offer integer addition and multiplication at low cost. However, binary circuits might be a better option if there is very little integer computation. See below to find the most efficient mixed-circuit variant. Furthermore, local computation modulo a power of two is cheaper, but MP-SPDZ does not offer this domain with homomorphic encryption.
-
Secret sharing vs garbled circuits: Computation using secret sharing requires a number of communication rounds that grows depending on the computation, which is not the case for garbled circuits. However, the cost of integer computation as a binary circuit often offset this. MP-SPDZ only offers garbled circuit with binary computation.
-
Underlying technology for dishonest majority: While secret sharing alone suffice honest-majority computation, dishonest majority requires either homomorphic encryption (HE) or oblivious transfer (OT). The two options offer a computation-communication trade-off: While OT is easier to compute, HE requires less communication. Furthermore, the latter requires a certain of batching to be efficient, which makes OT preferable for smaller tasks.
-
Malicious, honest-majority three-party computation: A number of protocols are available for this setting, but SY/SPDZ-wise is the most efficient one for a number of reasons: It requires the lowest communication, and it is the only one offering constant-communication dot products.
-
Fixed-point multiplication: Three- and four-party replicated secret sharing as well semi-honest full-threshold protocols allow a special probabilistic truncation protocol (see Dalskov et al. and Dalskov et al.). You can activate it by adding
program.use_trunc_pr = Trueat the beginning of your high-level program. -
Larger number of parties: ATLAS scales better than the plain Shamir protocol, and Temi scale better than Hemi or Semi.
-
Minor variants: Some command-line options change aspects of the protocols such as:
--bucket-size: In some malicious binary computation and malicious edaBit generation, a smaller bucket size allows preprocessing in smaller batches at a higher asymptotic cost.--batch-size: Preprocessing in smaller batches avoids generating too much but larger batches save communication rounds.--direct: In dishonest-majority protocols, direct communication instead of star-shaped saves communication rounds at the expense of a quadratic amount. This might be beneficial with a small number of parties.--bits-from-squares: In some protocols computing modulo a prime (Shamir, Rep3, SPDZ-wise), this switches from generating random bits via XOR of parties' inputs to generation using the root of a random square.
The design of MP-SPDZ is described in this paper. If you use it for an academic project, please cite:
@inproceedings{mp-spdz,
author = {Marcel Keller},
title = {{MP-SPDZ}: A Versatile Framework for Multi-Party Computation},
booktitle = {Proceedings of the 2020 ACM SIGSAC Conference on
Computer and Communications Security},
year = {2020},
doi = {10.1145/3372297.3417872},
url = {https://doi.org/10.1145/3372297.3417872},
}
The software started out as an implementation of the improved SPDZ protocol. The name SPDZ is derived from the authors of the original protocol.
This repository combines the functionality previously published in the following repositories:
- https://github.com/bristolcrypto/SPDZ-2
- https://github.com/mkskeller/SPDZ-BMR-ORAM
- https://github.com/mkskeller/SPDZ-Yao
For the actual computation, the software implements a virtual machine that executes programs in a specific bytecode. Such code can be generated from high-level Python code using a compiler that optimizes the computation with a particular focus on minimizing the number of communication rounds (for protocols based on secret sharing) or on AES-NI pipelining (for garbled circuits).
The software uses two different bytecode sets, one for arithmetic circuits and one for boolean circuits. The high-level code slightly differs between the two variants, but we aim to keep these differences a at minimum.
In the section on computation we will explain how to compile a high-level program for the various computation domains and then how to run it with different protocols.
The section on offline phases will explain how to benchmark the offline phases required for the SPDZ protocol. Running the online phase outputs the amount of offline material required, which allows to compute the preprocessing time for a particular computation.
- GCC 5 or later (tested with up to 11) or LLVM/clang 6 or later (tested with up to 14). The default is to use clang because it performs better. Note that GCC 5/6 and clang 9 don't support libOTe, so you need to deactivate its use for these compilers (see the next section).
- For protocols using oblivious transfer, libOTe with the necessary
patches
but without SimplestOT. The easiest way is to run
make libote, which will install it as needed in a subdirectory. libOTe requires CMake of version at least 3.15, which is not available by default on older systems such as Ubuntu 18.04. You can runmake cmaketo install it locally. libOTe also requires boost of version at least 1.75, which is not available by default on relatively recent systems such as Ubuntu 22.04. You can install it locally by runningmake boost. - GMP library, compiled with C++ support (use flag
--enable-cxxwhen running configure). Tested against 6.2.1 as supplied by Ubuntu. - libsodium library, tested against 1.0.18
- OpenSSL, tested against 3.0.2
- Boost.Asio with SSL support (
libboost-devon Ubuntu), tested against 1.81 - Boost.Thread for BMR (
libboost-thread-devon Ubuntu), tested against 1.81 - x86 or ARM 64-bit CPU (the latter tested with AWS Gravitron and Apple Silicon)
- Python 3.5 or later
- NTL library for homomorphic encryption (optional; tested with NTL 11.5.1)
- If using macOS, Sierra or later
- Windows/VirtualBox: see this issue for a discussion
-
Edit
CONFIGorCONFIG.mineto your needs:- On x86, the binaries are optimized for the CPU you are compiling
on. For all optimizations on x86, a CPU supporting AES-NI,
PCLMUL, AVX2, BMI2, ADX is required. This includes mainstream
processors released 2014 or later. If you intend to run on a
different CPU than compiling, you might need to change the
ARCHvariable inCONFIGorCONFIG.mineto-march=<cpu>. See the GCC documentation for the possible options. To run on CPUs without AVX2 (CPUs from before 2014), you should also addAVX_OT = 0toCONFIG.mine. - For optimal results on Linux on ARM, add
ARCH = -march=armv8.2-a+cryptotoCONFIG.mine. This enables the hardware support for AES. See the GCC documentation on available options. - To benchmark online-only protocols or Overdrive offline phases, add the following line at the top:
MY_CFLAGS = -DINSECURE PREP_DIRshould point to a local, unversioned directory to store preprocessing data (the default isPlayer-Datain the current directory).SSL_DIRshould point to a local, unversioned directory to store ssl keys (the default isPlayer-Datain the current directory).- For homomorphic encryption with GF(2^40), set
USE_NTL = 1. - To use KOS instead of SoftSpokenOT, add
USE_KOS = 1andSECURE = -DINSECUREtoCONFIG.mine. This is necessary with GCC 5 and 6 because these compilers don't support the C++ standard used by libOTe. - On macOS, there have been issues with non-system compilers. Add
CXX = /usr/bin/g++to fix them.
- On x86, the binaries are optimized for the CPU you are compiling
on. For all optimizations on x86, a CPU supporting AES-NI,
PCLMUL, AVX2, BMI2, ADX is required. This includes mainstream
processors released 2014 or later. If you intend to run on a
different CPU than compiling, you might need to change the
-
Run
maketo compile all the software (use the flag-jfor faster compilation using multiple threads). See below on how to compile specific parts only. Remember to runmake cleanfirst after changingCONFIGorCONFIG.mine.
See Programs/Source/ for some example MPC programs, in particular
tutorial.mpc. Furthermore, Read the
Docs hosts a more
detailed reference of all aspects of MP-SPDZ.
There are three ways of running computation:
-
Separate compilation and execution. This is the default in the further documentation. It allows to run the same program several times while only compiling once, for example:
./compile.py <program> <argument> Scripts/mascot.sh <program>-<argument> [<runtime-arg>...] Scripts/mascot.sh <program>-<argument> [<runtime-arg>...] -
One-command local execution. This compiles the program and the virtual machine if necessary before executing it locally with the given protocol. The name of the protocols correspond to the script names below (without the
.sh). Furthermore, some protocol-specific optimization options are automatically used as well as required options.Scripts/compile-run.py -E mascot <program> <argument> -- [<runtime-arg>...] -
One-command remote execution. This compiles the program and the virtual machine if necessary before uploading them together with all necessary input and certificate files via SSH.
Scripts/compile-run.py -H HOSTS -E mascot <program> <argument> -- [<runtime-arg>...]HOSTShas to be a text file in the following format:[<user>@]<host0>[/<path>] [<user>@]<host1>[/<path>] ...If does not start with
/(only one/after the hostname), the path with be relative to the home directory of the user. Otherwise (//after the hostname it will be relative to the root directory.It is assumed that the SSH login is possible without password.
Even with the integrated execution it is important to keep in mind
that there are two different phases, the compilation and the run-time
phase. Any secret data is only available in the second phase, when the
Python compilation has concluded. Therefore, the types like sint and
sfix are mere placeholders for data to be used later, and they don't
contain any shares. See also the
documentation
for what this means when using Python data structures and Python
language features.
There are three computation domains, and the high-level programs have to be compiled accordingly.
./compile.py [-F <integer bit length>] [-P <prime>] <program>
The integer bit length defaults to 64, and the prime defaults to none
given. If a prime is given, it has to be at least two bits longer than
the integer length. Note that -P is optional, and it involves
algorithms that are more expensive while allowing for a wider range of
integer lengths.
Note that in this context integers do not wrap around according to the bit integer bit length but the length is used for non-linear computations such as comparison. Overflow in secret integers might have security implications if no concrete prime is given.
The parameters given together with the computation mandate some
restriction on the prime modulus, either an exact value or a minimum
length. The latter is roughly the integer length plus 40 (default
security parameter). The restrictions are communicated to the virtual
machines, which will use an appropriate prime if they have been
compiled accordingly. By default, they are compiled for prime bit
lengths up to 256. For larger primes, you will have to compile with
MOD = -DGFP_MOD_SZ=<number of limbs> in CONFIG.mine where the
number of limbs is the the prime length divided by 64 rounded up.
The precision for fixed- and floating-point computation are not
affected by the integer bit length but can be set in the code
directly. For fixed-point computation this is done via
sfix.set_precision().
./compile.py -R <integer bit length> <program>
The length is communicated to the virtual machines and automatically
used if supported. By default, they support bit lengths 64, 72, and
128 (the latter except for SPDZ2k). If another length is required, use
MOD = -DRING_SIZE=<bit length> in CONFIG.mine.
./compile.py -B <integer bit length> <program>
The integer length can be any number up to a maximum depending on the protocol. All protocols support at least 64-bit integers.
Fixed-point numbers (sfix) always use 16/16-bit precision by default in
binary circuits. This can be changed with sfix.set_precision. See
the tutorial.
If you would like to use integers of various precisions, you can use
sbitint.get_type(n) to get a type for n-bit arithmetic.
MP-SPDZ allows to mix computation between arithmetic and binary secret sharing in the same security model. In the compiler, this is used to switch from arithmetic to binary computation for certain non-linear functions such as comparison, bit decomposition, truncation, and modulo power of two, which are use for fixed- and floating-point operations. There are several ways of achieving this as described below.
You can activate this by adding -X when compiling arithmetic
circuits, that is
./compile.py -X [-F <integer bit length>] <program>
for computation modulo a prime and
./compile.py -X -R <integer bit length> <program>
for computation modulo 2^k.
Internally, this uses daBits described by Rotaru and Wood, that is secret random bits shared in different domains. Some security models allow direct conversion of random bits from arithmetic to binary while others require inputs from several parties followed by computing XOR and checking for malicious security as described by Rotaru and Wood in Section 4.1.
Extended daBits were introduced by Escudero et
al.. You can activate them by using
-Y instead of -X. Note that this also activates classic daBits
when useful.
This technique has been used by Mohassel and
Rindal as well as Araki et
al. for three parties and Demmler
et al. for two parties.
It involves locally
converting an arithmetic share to a set of binary shares, from which the
binary equivalent to the arithmetic share is reconstructed using a
binary adder. This requires additive secret sharing over a ring
without any MACs. You can activate it by using -Z <n> with the
compiler where n is the number of parties for the standard variant
and 2 for the special
variant by Mohassel and Rindal (available in Rep3 only).
Where available, local share conversion is likely the most efficient
variant. Otherwise, edaBits likely offer an asymptotic benefit. When
using edaBits with malicious protocols, there is a trade-off between
cost per item and batch size. The lowest cost per item requires large
batches of edaBits (more than one million at once), which is only
worthwhile for accordingly large computation. This setting can be
selected by running the virtual machine with -B 3. For smaller
computation, try -B 4 or -B 5, which set the batch size to ~10,000
and ~1,000, respectively, at a higher asymptotic cost. -B 4 is the
default.
Bristol Fashion is the name of a description format of binary circuits
used by
SCALE-MAMBA. You can
access such circuits from the high-level language if they are present
in Programs/Circuits. To run the AES-128 circuit provided with
SCALE-MAMBA, you can run the following:
make Programs/Circuits
./compile.py aes_circuit
Scripts/semi.sh aes_circuit
This downloads the circuit, compiles it to MP-SPDZ bytecode, and runs
it as semi-honest two-party computation 1000 times in parallel. It
should then output the AES test vector
0x3ad77bb40d7a3660a89ecaf32466ef97. You can run it with any other
protocol as well.
See the documentation for further examples.
You may prefer to not have an entirely static .mpc file to compile, and may want to compile based on dynamic inputs. For example, you may want to be able to compile with different sizes of input data without making a code change to the .mpc file. To handle this, the compiler an also be directly imported, and a function can be compiled with the following interface:
# hello_world.mpc
from Compiler.library import print_ln
from Compiler.compilerLib import Compiler
compiler = Compiler()
@compiler.register_function('helloworld')
def hello_world():
print_ln('hello world')
if __name__ == "__main__":
compiler.compile_func()You could then run this with the same args as used with compile.py:
python hello_world.mpc <compile args>This is particularly useful if want to add new command line arguments specifically for your .mpc file. See test_args.mpc for more details on this use case.
Note that when using this approach, all objects provided in the high level interface (e.g. sint, print_ln) need to be imported, because the .mpc file is interpreted directly by Python (instead of being read by compile.py.)
Programs can also be edited, compiled and run from any directory with
the above basic structure. So for a source file in
./Programs/Source/, all MP-SPDZ scripts must be run from ./. Any
setup scripts such as setup-ssl.sh script must also be run from ./
to create the relevant data. For example:
MP-SPDZ$ cd ../
$ mkdir myprogs
$ cd myprogs
$ mkdir -p Programs/Source
$ vi Programs/Source/test.mpc
$ ../MP-SPDZ/compile.py test.mpc
$ ls Programs/
Bytecode Public-Input Schedules Source
$ ../MP-SPDZ/Scripts/setup-ssl.sh
$ ls
Player-Data Programs
$ ../MP-SPDZ/Scripts/rep-field.sh test
MP-SPDZ supports inference with selected TensorFlow graphs, in particular DenseNet, ResNet, and SqueezeNet as used in CrypTFlow. For example, you can run SqueezeNet inference for ImageNet as follows:
git clone https://github.com/mkskeller/EzPC
cd EzPC/Athos/Networks/SqueezeNetImgNet
axel -a -n 5 -c --output ./PreTrainedModel https://github.com/avoroshilov/tf-squeezenet/raw/master/sqz_full.mat
pip3 install numpy scipy pillow>=9.1 tensorflow
python3 squeezenet_main.py --in ./SampleImages/n02109961_36.JPEG --saveTFMetadata True
python3 squeezenet_main.py --in ./SampleImages/n02109961_36.JPEG --scalingFac 12 --saveImgAndWtData True
cd ../../../..
cp EzPC/Athos/Networks/SqueezeNetImgNet/SqNetImgNet_img_input.inp Player-Data/Input-Binary-P0-0
./compile.py -R 64 tf EzPC/Athos/Networks/SqueezeNetImgNet/graphDef.bin 1 trunc_pr split
Scripts/ring.sh tf-EzPC_Athos_Networks_SqueezeNetImgNet_graphDef.bin-1-trunc_pr-split
This requires TensorFlow and the axel command-line utility to be
installed. It runs inference with
three-party semi-honest computation, similar to CrypTFlow's
Porthos. Replace 1 by the desired number of thread in the last two
lines. If you run with some other protocols, you will need to remove
trunc_pr and/or split. Also note that you will need to use a
CrypTFlow repository that includes the patches in
https://github.com/mkskeller/EzPC.
The reference contains further documentation on available layers.
For arithmetic circuits modulo a power of two and binary circuits, you can emulate the computation as follows:
./emulate.x <program>
This runs the compiled bytecode in cleartext computation.
Some full implementations require oblivious transfer, which is implemented as OT extension based on https://github.com/mkskeller/SimpleOT or https://github.com/mkskeller/SimplestOT_C, depending on whether AVX is available.
The following table shows all programs for dishonest-majority computation using secret sharing:
| Program | Protocol | Domain | Security | Script |
|---|---|---|---|---|
mascot-party.x |
MASCOT | Mod prime | Malicious | mascot.sh |
mama-party.x |
MASCOT* | Mod prime | Malicious | mama.sh |
spdz2k-party.x |
SPDZ2k | Mod 2^k | Malicious | spdz2k.sh |
semi-party.x |
OT-based | Mod prime | Semi-honest | semi.sh |
semi2k-party.x |
OT-based | Mod 2^k | Semi-honest | semi2k.sh |
lowgear-party.x |
LowGear | Mod prime | Malicious | lowgear.sh |
highgear-party.x |
HighGear | Mod prime | Malicious | highgear.sh |
cowgear-party.x |
Adapted LowGear | Mod prime | Covert | cowgear.sh |
chaigear-party.x |
Adapted HighGear | Mod prime | Covert | chaigear.sh |
hemi-party.x |
Semi-homomorphic encryption | Mod prime | Semi-honest | hemi.sh |
temi-party.x |
Adapted CDN01 | Mod prime | Semi-honest | temi.sh |
soho-party.x |
Somewhat homomorphic encryption | Mod prime | Semi-honest | soho.sh |
semi-bin-party.x |
OT-based | Binary | Semi-honest | semi-bin.sh |
tiny-party.x |
Adapted SPDZ2k | Binary | Malicious | tiny.sh |
tinier-party.x |
FKOS15 | Binary | Malicious | tinier.sh |
Mama denotes MASCOT with several MACs to increase the security parameter to a multiple of the prime length.
Semi and Semi2k denote the result of stripping MASCOT/SPDZ2k of all steps required for malicious security, namely amplifying, sacrificing, MAC generation, and OT correlation checks. What remains is the generation of additively shared Beaver triples using OT.
Similarly, SemiBin denotes a protocol that generates bit-wise multiplication triples using OT without any element of malicious security.
Tiny denotes the adaption of SPDZ2k to the binary setting. In particular, the SPDZ2k sacrifice does not work for bits, so we replace it by cut-and-choose according to Furukawa et al.
The virtual machines for LowGear and HighGear run a key generation
similar to the one by Rotaru et
al.. The main difference is using
daBits to generate maBits. CowGear and ChaiGear denote covertly
secure versions of LowGear and HighGear. In all relevant programs,
option -T activates TopGear
zero-knowledge proofs in both.
Hemi and Soho denote the stripped version of LowGear and HighGear, respectively, for semi-honest security similar to Semi, that is, generating additively shared Beaver triples using semi-homomorphic encryption. Temi in turn denotes the adaption of Cramer et al. to LWE-based semi-homomorphic encryption. Both Hemi and Temi use the diagonal packing by Halevi and Shoup for matrix multiplication.
We will use MASCOT to demonstrate the use, but the other protocols work similarly.
First compile the virtual machine:
make -j8 mascot-party.x
and a high-level program, for example the tutorial (use -R 64 for
SPDZ2k and Semi2k and -B <precision> for SemiBin):
./compile.py -F 64 tutorial
To run the tutorial with two parties on one machine, run:
./mascot-party.x -N 2 -I -p 0 tutorial
./mascot-party.x -N 2 -I -p 1 tutorial (in a separate terminal)
Using -I activates interactive mode, which means that inputs are
solicited from standard input, and outputs are given to any
party. Omitting -I leads to inputs being read from
Player-Data/Input-P<party number>-0 in text format.
Or, you can use a script to do run two parties in non-interactive mode automatically:
Scripts/mascot.sh tutorial
To run a program on two different machines, mascot-party.x
needs to be passed the machine where the first party is running,
e.g. if this machine is name diffie on the local network:
./mascot-party.x -N 2 -h diffie 0 tutorial
./mascot-party.x -N 2 -h diffie 1 tutorial
The software uses TCP ports around 5000 by default, use the -pn
argument to change that.
We use half-gate garbling as described by Zahur et
al. and Guo et
al.. Alternatively, you can
activate the implementation optimized by Bellare et
al. by adding MY_CFLAGS += -DFULL_GATES to CONFIG.mine.
Compile the virtual machine:
make -j 8 yao
and the high-level program:
./compile.py -G -B <integer bit length> <program>
Then run as follows:
- Garbler:
./yao-party.x [-I] -p 0 <program> - Evaluator:
./yao-party.x [-I] -p 1 -h <garbler host> <program>
When running locally, you can omit the host argument. As above, -I
activates interactive input, otherwise inputs are read from
Player-Data/Input-P<playerno>-0.
By default, the circuit is garbled in chunks that are evaluated
whenever received.You can activate garbling all at once by adding
-O to the command line on both sides.
The following table shows all programs for honest-majority computation:
| Program | Sharing | Domain | Malicious | # parties | Script |
|---|---|---|---|---|---|
replicated-ring-party.x |
Replicated | Mod 2^k | N | 3 | ring.sh |
brain-party.x |
Replicated | Mod 2^k | Y | 3 | brain.sh |
ps-rep-ring-party.x |
Replicated | Mod 2^k | Y | 3 | ps-rep-ring.sh |
malicious-rep-ring-party.x |
Replicated | Mod 2^k | Y | 3 | mal-rep-ring.sh |
sy-rep-ring-party.x |
SPDZ-wise replicated | Mod 2^k | Y | 3 | sy-rep-ring.sh |
rep4-ring-party.x |
Replicated | Mod 2^k | Y | 4 | rep4-ring.sh |
replicated-bin-party.x |
Replicated | Binary | N | 3 | replicated.sh |
malicious-rep-bin-party.x |
Replicated | Binary | Y | 3 | mal-rep-bin.sh |
ps-rep-bin-party.x |
Replicated | Binary | Y | 3 | ps-rep-bin.sh |
replicated-field-party.x |
Replicated | Mod prime | N | 3 | rep-field.sh |
ps-rep-field-party.x |
Replicated | Mod prime | Y | 3 | ps-rep-field.sh |
sy-rep-field-party.x |
SPDZ-wise replicated | Mod prime | Y | 3 | sy-rep-field.sh |
malicious-rep-field-party.x |
Replicated | Mod prime | Y | 3 | mal-rep-field.sh |
atlas-party.x |
ATLAS | Mod prime | N | 3 or more | atlas.sh |
shamir-party.x |
Shamir | Mod prime | N | 3 or more | shamir.sh |
malicious-shamir-party.x |
Shamir | Mod prime | Y | 3 or more | mal-shamir.sh |
sy-shamir-party.x |
SPDZ-wise Shamir | Mod prime | Y | 3 or more | sy-shamir.sh |
ccd-party.x |
CCD/Shamir | Binary | N | 3 or more | ccd.sh |
malicious-cdd-party.x |
CCD/Shamir | Binary | Y | 3 or more | mal-ccd.sh |
We use the "generate random triple optimistically/sacrifice/Beaver"
methodology described by Lindell and
Nof to achieve malicious
security with plain arithmetic replicated secret sharing,
except for the "PS" (post-sacrifice) protocols where the
actual multiplication is executed optimistically and checked later as
also described by Lindell and Nof.
The implementations used by brain-party.x,
malicious-rep-ring-party.x -S, malicious-rep-ring-party.x,
and ps-rep-ring-party.x correspond to the protocols called DOS18
preprocessing (single), ABF+17 preprocessing, CDE+18 preprocessing,
and postprocessing, respectively,
by Eerikson et al.
We use resharing by Cramer et
al. for Shamir's secret sharing and
the optimized approach by Araki et
al. for replicated secret sharing.
The CCD protocols are named after the historic
paper by Chaum, Crépeau, and
Damgård, which introduced binary computation using Shamir secret
sharing over extension fields of characteristic two.
SY/SPDZ-wise refers to the line of work started by Chida et
al. for computation modulo a prime
and furthered by Abspoel et al.
for computation modulo a power of two. It involves sharing both a
secret value and information-theoretic tag similar to SPDZ but not
with additive secret sharing, hence the name.
Rep4 refers to the four-party protocol by Dalskov et
al.
malicious-rep-bin-party.x is based on cut-and-choose triple
generation by Furukawa et al. but
using Beaver multiplication instead of their post-sacrifice
approach. ps-rep-bin-party.x is based on the post-sacrifice approach
by Araki et
al. but
without using their cache optimization.
All protocols in this section require encrypted channels because the information received by the honest majority suffices the reconstruct all secrets. Therefore, an eavesdropper on the network could learn all information.
MP-SPDZ uses OpenSSL for secure channels. You can generate the necessary certificates and keys as follows:
Scripts/setup-ssl.sh [<number of parties> <ssl_dir>]
The programs expect the keys and certificates to be in
SSL_DIR/P<i>.key and SSL_DIR/P<i>.pem, respectively, and
the certificates to have the common name P<i> for player
<i>. Furthermore, the relevant root certificates have to be in
SSL_DIR such that OpenSSL can find them (run c_rehash <ssl_dir>). The script above takes care of all this by generating
self-signed certificates. Therefore, if you are running the programs
on different hosts you will need to copy the certificate files.
Note that <ssl_dir> must match SSL_DIR set in CONFIG or CONFIG.mine.
Just like SSL_DIR, <ssl_dir> defaults to Player-Data.
In the following, we will walk through running the tutorial modulo 2^k with three parties. The other programs work similarly.
First, compile the virtual machine:
make -j 8 replicated-ring-party.x
In order to compile a high-level program, use ./compile.py -R 64:
./compile.py -R 64 tutorial
If using another computation domain, use -F or -B as described in
the relevant section above.
Finally, run the three parties as follows:
./replicated-ring-party.x -I 0 tutorial
./replicated-ring-party.x -I 1 tutorial (in a separate terminal)
./replicated-ring-party.x -I 2 tutorial (in a separate terminal)
or
Scripts/ring.sh tutorial
The -I argument enables interactive inputs, and in the tutorial party 0 and 1
will be asked to provide three numbers. Otherwise, and when using the
script, the inputs are read from Player-Data/Input-P<playerno>-0.
When using programs based on Shamir's secret sharing, you can specify
the number of parties with -N and the maximum number of corrupted
parties with -T. The latter can be at most half the number of
parties.
This security model defines a special party that generates correlated randomness such as multiplication triples, which is then used by all other parties. MP-SPDZ implements the canonical protocol where the other parties run the online phase of the semi-honest protocol in Semi(2k/Bin) and the dealer provides all preprocessing. The security assumption is that dealer doesn't collude with any other party, but all but one of the other parties are allowed to collude. In our implementation, the dealer is the party with the highest number, so with three parties overall, Party 0 and 1 run the online phase.
| Program | Sharing | Domain | Malicious | # parties | Script |
|---|---|---|---|---|---|
dealer-ring-party.x |
Additive | Mod 2^k | N | 3+ | dealer-ring.sh |
BMR (Beaver-Micali-Rogaway) is a method of generating a garbled circuit using another secure computation protocol. We have implemented BMR based on all available implementations using GF(2^128) because the nature of this field particularly suits the Free-XOR optimization for garbled circuits. Our implementation is based on the SPDZ-BMR-ORAM construction. The following table lists the available schemes.
| Program | Protocol | Dishonest Maj. | Malicious | # parties | Script |
|---|---|---|---|---|---|
real-bmr-party.x |
MASCOT | Y | Y | 2 or more | real-bmr.sh |
semi-bmr-party.x |
Semi | Y | N | 2 or more | semi-bmr.sh |
shamir-bmr-party.x |
Shamir | N | N | 3 or more | shamir-bmr.sh |
mal-shamir-bmr-party.x |
Shamir | N | Y | 3 or more | mal-shamir-bmr.sh |
rep-bmr-party.x |
Replicated | N | N | 3 | rep-bmr.sh |
mal-rep-bmr-party.x |
Replicated | N | Y | 3 | mal-rep-bmr.sh |
In the following, we will walk through running the tutorial with BMR based on MASCOT and two parties. The other programs work similarly.
First, compile the virtual machine. In order to run with more than
three parties, change the definition of MAX_N_PARTIES in
BMR/config.h accordingly.
make -j 8 real-bmr-party.x
In order to compile a high-level program, use ./compile.py -B:
./compile.py -G -B 32 tutorial
Finally, run the two parties as follows:
./real-bmr-party.x -I 0 tutorial
./real-bmr-party.x -I 1 tutorial (in a separate terminal)
or
Scripts/real-bmr.sh tutorial
The -I enable interactive inputs, and in the tutorial party 0 and 1
will be asked to provide three numbers. Otherwise, and when using the
script, the inputs are read from Player-Data/Input-P<playerno>-0.
In this section we show how to benchmark purely the data-dependent (often called online) phase of some protocols. This requires to generate the output of a previous phase. There are two options to do that:
- For select protocols, you can run preprocessing as required.
- You can run insecure preprocessing. For this, you will have to
(re)compile the software after adding
MY_CFLAGS = -DINSECUREtoCONFIG.minein order to run this insecure generation. Make sure to runmake cleanbefore recompiling any binaries. Then, you need to runmake Fake-Offline.x <protocol>-party.x.
Note that you can as well run the full protocol with option -v to
see the cost split by preprocessing and online phase.
The SPDZ protocol uses preprocessing, that is, in a first (sometimes called offline) phase correlated randomness is generated independent of the actual inputs of the computation. Only the second ("online") phase combines this randomness with the actual inputs in order to produce the desired results. The preprocessed data can only be used once, thus more computation requires more preprocessing. MASCOT and Overdrive are the names for two alternative preprocessing phases to go with the SPDZ online phase.
All programs required in this section can be compiled with the target online:
make -j 8 online
This requires the INSECURE flag to be set before compilation as explained above. For a secure offline phase, see the section on SPDZ-2 below.
Run the command below. If you haven't added MY_CFLAGS = -DINSECURE to CONFIG.mine before compiling, it will fail.
Scripts/setup-online.sh
This sets up parameters for the online phase for 2 parties with a 128-bit prime field and 128-bit binary field, and creates fake offline data (multiplication triples etc.) for these parameters.
Parameters can be customised by running
Scripts/setup-online.sh <nparties> <nbitsp> [<nbits2>]
To compile for example the program in ./Programs/Source/tutorial.mpc, run:
./compile.py tutorial
This creates the bytecode and schedule files in Programs/Bytecode/ and Programs/Schedules/
To run the above program with two parties on one machine, run:
./mascot-party.x -F -N 2 0 tutorial
./mascot-party.x -F -N 2 1 tutorial (in a separate terminal)
Or, you can use a script to do the above automatically:
Scripts/mascot.sh -F tutorial
MASCOT is one of the protocols that use SPDZ for the online phase, and
-F causes the programs to read preprocessing material from files.
To run a program on two different machines, firstly the preprocessing
data must be copied across to the second machine (or shared using
sshfs), and secondly, mascot-party.x needs to be passed the machine
where the first party is running. E.g., if this machine is named
diffie on the local network:
./mascot-party.x -F -N 2 -h diffie 0 test_all
./mascot-party.x -F -N 2 -h diffie 1 test_all
The software uses TCP ports around 5000 by default, use the -pn
argument to change that.
Creating fake offline data for SPDZ2k requires to call
Fake-Offline.x directly instead of via setup-online.sh:
./Fake-Offline.x <nparties> -Z <bit length k for SPDZ2k> -S <security parameter>
You will need to run spdz2k-party.x -F in order to use the data from storage.
Preprocessing data for the default parameters of most other protocols can be produced as follows:
./Fake-Offline.x <nparties> -e <edaBit length,...>
The -e command-line parameters accepts a list of integers separated
by commas.
You can then run the protocol with argument -F. Note that when
running on several hosts, you will need to distribute the data in
Player-Data. The preprocessing files contain -P<party number>
indicating which party will access it.
This part has been developed to benchmark ORAM for the Eurocrypt 2018 paper by Marcel Keller and Avishay Yanay. It only allows to benchmark the data-dependent phase. The data-independent and function-independent phases are emulated insecurely.
By default, the implementations is optimized for two parties. You can
change this by defining N_PARTIES accordingly in BMR/config.h. If
you entirely delete the definition, it will be able to run for any
number of parties albeit slower.
Compile the virtual machine:
make -j 8 bmr
After compiling the mpc file:
- Run everything locally:
Scripts/bmr-program-run.sh <program> <number of parties>. - Run on different hosts:
Scripts/bmr-program-run-remote.sh <program> <host1> <host2> [...]
You can benchmark the ORAM implementation as follows:
- Edit
Program/Source/gc_oram.mpcto change size and to choose Circuit ORAM or linear scan without ORAM. - Run
./compile.py -G -D gc_oram. The-Dargument instructs the compiler to remove dead code. This is useful for more complex programs such as this one. - Run
gc_oramin the virtual machines as explained above.
For select protocols, you can run all required preprocessing but not the actual computation. First, compile the binary:
make <protocol>-offline.x
At the time of writing the supported protocols are mascot,
cowgear, mal-shamir, semi, semi2k, and hemi.
If you have not done so already, then compile your high-level program:
./compile.py <program>
Finally, run the parties as follows:
./<protocol>-offline.x -p 0 & ./<protocol>-offline.x -p 1 & ...
The options for the network setup are the same as for the complete computation above.
If you run the preprocessing on different hosts, make sure to use the same player number in the preprocessing and the online phase.
This implementation is suitable to generate the preprocessed data used in the online phase.
You need to compile with USE_NTL = 1 in CONFIG.mine to run this.
For quick run on one machine, you can call the following:
./spdz2-offline.x -p 0 & ./spdz2-offline.x -p 1
More generally, run the following on every machine:
./spdz2-offline.x -p <number of party> -N <total number of parties> -h <hostname of party 0> -c <covert security parameter>
The number of parties are counted from 0. As seen in the quick example, you can omit the total number of parties if it is 2 and the hostname if all parties run on the same machine. Invoke ./spdz2-offline.x for more explanation on the options.
./spdz2-offline.x provides covert security according to some parameter c (at least 2). A malicious adversary will get caught with probability 1-1/c. There is a linear correlation between c and the running time, that is, running with 2c takes twice as long as running with c. The default for c is 10.
The program will generate every kind of randomness required by the online phase except input tuples until you stop it. You can shut it down gracefully pressing Ctrl-c (or sending the interrupt signal SIGINT), but only after an initial phase, the end of which is marked by the output Starting to produce gf2n. Note that the initial phase has been reported to take up to an hour. Furthermore, 3 GB of RAM are required per party.
These implementations are not suitable to generate the preprocessed data for the online phase because they can only generate either multiplication triples or bits.
MASCOT can be run as follows:
host1:$ ./ot-offline.x -p 0 -c
host2:$ ./ot-offline.x -p 1 -c
For SPDZ2k, use -Z <k> to set the computation domain to Z_{2^k}, and
-S to set the security parameter. The latter defaults to k. At the
time of writing, the following combinations are available: 32/32,
64/64, 64/48, and 66/48.
Running ./ot-offline.x without parameters give the full menu of
options such as how many items to generate in how many threads and
loops.
We have implemented several protocols to measure the maximal throughput for the Overdrive paper. As for MASCOT, these implementations are not suited to generate data for the online phase because they only generate one type at a time.
| Binary | Protocol |
|---|---|
simple-offline.x |
SPDZ-1 and High Gear (with command-line argument -g) |
pairwise-offline.x |
Low Gear |
cnc-offline.x |
SPDZ-2 with malicious security (covert security with command-line argument -c) |
These programs can be run similarly to spdz2-offline.x, for example:
host1:$ ./simple-offline.x -p 0 -h host1
host2:$ ./simple-offline.x -p 1 -h host1
Running any program without arguments describes all command-line arguments.
Lattice-based ciphertexts are relatively large (in the order of megabytes), and the zero-knowledge proofs we use require storing some hundred of them. You must therefore expect to use at least some hundred megabytes of memory per thread. The memory usage is linear in MAX_MOD_SZ (determining the maximum integer size for computations in steps of 64 bits), so you can try to reduce it (see the compilation section for how set it). For some choices of parameters, 4 is enough while others require up to 8. The programs above indicate the minimum MAX_MOD_SZ required, and they fail during the parameter generation if it is too low.