Secure distributed linear regression

A protocol for secure distributed linear regression. For a detailed description of the protocol and evaluation results, please have a look at the Paper.

Dependencies

The following libraries need to be installed for a successful build:

• Obliv-C must be cloned from Github and installed in a directory of your choice, to which the OBLIVC_PATH environment variable should point.
• Protocol Buffers and Protobuf-C can be either built from source or installed using your favorite package manager. If built from source, libraries and binaries need to be installed in a directory where they are found by compilers and linkers.
• OpenSSL headers. On Ubuntu based systems, these come with the package libssl-dev.

Compilation

In order to download submodules and compile, simply run make.
By default, computations are performed using 64 bit fixed-point arithmetic.

One can change the bit width for phase 1 of the protocol to 32 bit by setting the flag BIT_WIDTH_32_P1=1 at compile time.
(either by passing it to make or setting it directly in the Makefile).

One can change the bit width for phase 2 of the protocol to 32 bit by setting the flag BIT_WIDTH_32_P2=1 at compile time.
(either by passing it to make or setting it directly in the Makefile).

Currently only the following combinations of bitwidths for both phases are supported:

bit width phase 1	bit width phase 2
32	32
64	64
64	32

Using smaller bit widths will increase computation speed at the cost of accuracy.

Running experiments

The protocol consists of two phases. bin/linreg is used to run both phases at once.

Usage: bin/linreg [Input_file] [Precision] [Party] [Algorithm] [Num. iterations CGD] [Lambda] [Options]
Options: --use_ot: Enables the OT-based phase 1 protocol
         --prec_phase2=<Precision phase 2>: Use different precision for phase 2 of the protocol

[Precision] specifies the number of bits used for the fractional part of fixed-point encoded numbers.
The role of the process is given by [Party].
Values of 1 and 2 denote the CSP and Evaluator, respectively.
Higher values denote data providers.
[Algorithm] is the algorithm used for phase 2 of the protocol and can be either cholesky, ldlt, or cgd.
In the case of CGD, [Num. iterations CGD] gives the number of iterations used before terminating.
[Lambda] specifies the regularization parameter, and the --use-ot flag enables the aggregation phase protocol based on Oblivious Transfers.
When using different bit widths for phase 1 and 2 (see above) one can use --prec_phase2<=Precision phase 2> to set a different precision for the second
phase of the protocol.

An example input file can be found in examples/readme_example.in:

10 5 3
localhost:1234
localhost:1235
localhost:1236 0
localhost:1237 1
localhost:1238 2
10 5
-0.49490189906 0.204027068031 1.0 -0.0048744428595 0.101856000869
0.49217428514 0.233090721372 -0.0370213771185 0.657720359628 0.525310770733
0.39721227919 -0.470002959473 0.277398798616 0.726013362994 0.498046786861
-0.595183792269 -0.0827269428691 -0.227611333929 0.80744916955 0.543968791627
-0.419150270985 0.292994257369 -0.0232190555386 -0.108185527543 0.238913650953
-0.247990663017 -1.0 -0.0241769053355 -0.842345696475 -1.0
-1.0 0.437037219652 -0.140750839011 1.0 -0.0679355153937
0.777015345458 0.981488358907 0.2870338525 0.579832272908 -0.262265338898
-0.0431656936622 0.0910166551363 -0.0724090181375 -0.144008713528 0.202706144381
-0.470188350902 -0.261201944989 -0.0468243599479 0.944605903172 0.455480894023
10
0.463624257142 1.03914869701 0.641866385451 -0.289962112725 -0.328203220996 -1.64668349374 -0.205128259075 2.13151959591 -0.129983842519 -0.0766970254399

It contains the number of samples, features and parties, followed by a network endpoint for each party.
The special roles CSP and Evaluator are defined by the first two lines.
Then, the data providers follow (3 in this example), each with a network endpoint and the starting index of its partition.
Afterwards, the dimensions of X are specified, followed by X itself.
Finally, the length and values of y are given.

Running this example locally with

for party in {1..5}; do bin/linreg examples/readme_example.in 56 $party cgd 10 0.001 & done

yields the following result, in addition to some debug outputs:

Time elapsed: 5.673679
Number of gates: 18569664
Result:    0.984331027786964    0.792399824970372    0.754117840176144    0.592849130685193    0.057351715952213