Run offline phase as a service for input masks

[sbellem]

Using spdz2-offline.x as per the recommendations in https://gitter.im/MP-SPDZ/community?at=5f7fa55c24a20801a8d564aa.

To figure out:

• Where are the elements written to (e.g.: Player-Data/2-p-256/Triples-p-P0)?
• How to retrieve elements, suitable for input masks, to be sent to clients, requesting input masks.
• How to access input masks, given an id/index.
• Set a different prime than the one currently being generated.
• Why does ./check-passive.x fails on the triples generated with spdz2-offline.x? The product a*b does not equal c. -- It's for ot-offline.cpp (see https://gitter.im/MP-SPDZ/community?at=5fb35593d5a5a635f2c6ccd0)
• Use MaliciousShamirShare instead of ShamirShare for the input mask generation.

[sbellem]

Code is on branch https://github.com/initc3/MP-SPDZ/tree/hbswap_demo-updates

To try the preprocessing for random shares (e.g. for input masks), with docker:

docker-compose build
docker-compose run --rm mpspdz bash
./random-shamir.x -i 0 & ./random-shamir.x -i 1 & ./random-shamir.x -i 2 & ./random-shamir.x -i 3

The shares should be In Player-Data/4-MSp-255/Randoms-MSp-P*

With nix:

Must first generate keys:

./Scripts/setup-ssl.sh 4

Build the application (random-shamir.x) with nix:

nix-build random-shamir.nix

Run it:

./result/random-shamir.x -i 0 & ./result/random-shamir.x -i 1 & ./result/random-shamir.x -i 2 & ./result/random-shamir.x -i 3

The shares will also be In Player-Data/4-MSp-255/Randoms-MSp-P*

[sbellem]

UPDATES

• Some fixes have been updated to work with a more recent version of MP-SPDZ (almost the most recent - just before last commit).
• The option to pass the threshold has been added, as it was missing.

Regarding the threshold, it needs to be verified whether it is set and used correctly. For instance, if t servers are not responsive, i.e. not running at all, should the preprocessing work as expected? I assume that yes, the preprocessing must still work as expected. This must be checked.