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PICCO
PICCO is a framework for secure computation with an arbitrary number of parties. It converts an extension of C to native C code, which is compiled and executed by n servers to run a secure computation. It's geared towards cloud computation and separates participants into three groups: input providers, computation servers, and output receivers.
Threshold: PICCO uses Shamir sharing by default. I'm not sure what the default threshold settings are, but it would only require an update to the I/O module, and no changes to the protocol itself, to support threshold outputs.
Compile setup isn't exactly correct. We had to remove boost dependency from picco/compute/objects.mk (see picco.patch).
Compiling is a multi-step affair, and I haven't found an end-to-end example with all then necessary config files. You need to generate public/private key pairs, and set several config files correctly.
- compile program to secure c++ program (2 inputs, 2 outputs)
picco <user program> <SMC config> <translated program> <utility config> - create executable (we include makefiles for our examples)
make <example> - generate inputs (automatic secret-sharing) (3 inputs + 1 flag, 1 output arg)
picco-utility -I <input party ID> <input fname> <utility config> <shares fname> - start compilation servers (run this for each server in reverse ID order) (6 inputs, 1 output list)
<example> <ID> <runtime config> <private key> <# input parties> <# output parties> <shares ...> <outputs ...> - start computations (2 inputs)
picco-seed <runtime config> <utility config> - process outputs (3 inputs + 1 flag, 1 output)
picco-utility -O <output party ID> <shares name> <utility config> <result fname>
We did some independent testing of floats (not rigorous and not included in this repository) and had were unable to successfully execute any operations between floating-point numbers.
Threshold value t must be small enough that 2*t+1 <= n where n is the number of parties (this is standard Shamir threshold sharing). This will segfault without comment in picco-utility.
We generated keys pairs which are required for secure communication. Our scripts generate 3 pairs by default but this number can be arbitrarily increased.
The extended moving around of files in install.sh is for my sanity when running through the multi-step compilation. Basically, shared stuff (generating the executable) is in the main example directory, and server-specific stuff (executing) is in the secure_server directory. These examples are all run locally from the same directory, but this could be extrapolated to a real distributed setup by copying the files in the server directory to each server (except for other people's private keys, of course).