Low-Bandwidth Mixed Arithmetic in VOLE-Based ZK from Low-Degree PRGs

This is the implementation of our paper

"Low-Bandwidth Mixed Arithmetic in VOLE-Based ZK from Low-Degree PRGs"
by Amit Agarwal, Carsten Baum, Lennart Braun, and Peter Scholl.
Eurocrypt 2025.

The implementation is based on commit
ca5d6b7 of
the swanky framework (which was the HEAD of the dev branch on 2024-01-17).
The original README.md of swanky can be found here.

Our implementation is part of the diet-mac-and-cheese crate.
We give an overview of our additions and modifications in the here.

Build and Test

The implementation was developed and tested under Linux on an x86-64 CPU with AVX2 and Rust 1.81.
To run the benchmarks the tc utility is required to simulate
different network settings, and pandas is used to analyse the
benchmark results.

The software expects a Git repository to be present.
So if you download the software as .tar.gz/.zip archive instead of cloning the Git repository,
please initialize a Git repository and create a dummy commit:

git init
git commit -m dummy --allow-empty

To build and execute all tests of swanky run
(or first change into the diet-mac-and-cheese/ subdirectory to only run the
corresponding subset of tests):

cargo test

To build the benchmarking application, run:

cargo build --release --example=bench

Benchmarking and Analyzing the Data

The bench Program

The benchmarks are implemented
here
and you can run the benchmark program as follows:

cargo run --release --example=bench -- <subcommand> <options>
# or using the relative path to the binary (if already built)
./target/debug/examples/bench <subcommand> <options>

In the following examples, we will just write bench for brevity.

Use

bench help
# or
bench help <subcommand>

to get detailed usage information.
The two subcommands relevant for our benchmarks are conv and fpm for the conversion and
fixed-point multiplication benchmarks, respectively.
In the following we describe the most important options.

Common Options

• --party <...> which party to run
  • prover or verifier runs only the respective party and communicated to the other party via
    TCP/IP
  • both runs both parties in separate threads, communicating through a UNIX socket
• --repetitions how often the whole benchmark should be repeated
• --json if the output should be given in JSON instead of being human readable

• --protocol <...> select the protocol to use to verify the conversions/fixed-point multiplications

  • edabits: The protocol from BBMRS21 (CCS'21) our base line
  • cheddabits-v1-tspa: Our protocol with TSPA predicate and version 1 seed setup
  • cheddabits-v2-tspa: with TSPA predicate and version 2 seed setup
  • cheddabits-v1-xor4maj7: with Xor4Maj7 predicate and version 1 seed setup
  • cheddabits-v2-xor4maj7: with Xor4Maj7 predicate and version 2 seed setup

  (NB: version 1 and 2 does not make a difference for fixed-point multiplication)

Network Options

To connect to the other party (if not running both parties in the same process), use the following
set of options:
- --listen to listen for incoming connections
- --host <HOST> to set which address to listen on/to connect to (default: localhost)
- --port <PORT> to set which port to listen on/to connect to (default: 1337)
- --connect-timeout-seconds <SECONDS> to set how long to try connecting before aborting (default: 100)

conv Options

• --num <NUM> how many conversions to verify
• --bit-size <BITS> the size of each conversion

fpm Options

• --num <NUM> how many fixed-point multiplications to verify
• --integer-size <BITS> the bit-size of the integer part of a fixed-point number
• --fraction-size <BITS> the bit-size of the fractional part of a fixed-point number

Example Output

# run in first terminal
bench conv --party prover --listen --protocol cheddabits-v1-xor4maj7 --num 4096 --bit-size 16 --repetitions 3
# run in second terminal
bench conv --party verifier --protocol cheddabits-v1-xor4maj7 --num 4096 --bit-size 16 --repetitions 3 --json

Prover's output

``` Startup time: 172ns results: BenchmarkResult { repetitions: 3, party: "Prover", network_options: NetworkOptions { listen: true, host: "localhost", port: 1337, connect_timeout_seconds: 100, }, meta_data: BenchmarkMetaData { hostname: "machine", username: "user", timestamp: "2025-03-07T16:32:52+01:00", cmdline: [ "../target/release/examples/bench", "conv", "--party", "prover", "--listen", "--protocol", "cheddabits-v1-xor4maj7", "--num", "4096", "--bit-size", "16", "--repetitions", "3", ], pid: 94881, git_version: "1a564cc527be1949e70c04f821e26b27dc91f76e-dirty", }, protocol_stats: [ Conversion( ConversionStats { protocol: CheddabitsV1Xor4Maj7, num: 4096, bit_size: 16, time_stats: [ TimeStats { init_time: 578.553679ms, voles_time: 309.777587ms, commit_time: 1.965454ms, check_time: 775.238158ms, }, TimeStats { init_time: 555.850705ms, voles_time: 196.692759ms, commit_time: 1.950376ms, check_time: 775.358086ms, }, TimeStats { init_time: 506.32201ms, voles_time: 199.292973ms, commit_time: 1.929788ms, check_time: 763.061634ms, }, ], comm_stats: CommStats { init_kb_sent: 1044.5615234375, init_kb_received: 181.0361328125, voles_kb_sent: 515.8173828125, voles_kb_received: 1008.2080078125, voles_f2_stats: FComStats { num_voles_used: 0, num_vole_extensions_performed: 1, }, voles_fp_stats: FComStats { num_voles_used: 0, num_vole_extensions_performed: 1, }, commit_kb_sent: 32.0, commit_kb_received: 0.0, commit_f2_stats: FComStats { num_voles_used: 65536, num_vole_extensions_performed: 0, }, commit_fp_stats: FComStats { num_voles_used: 4096, num_vole_extensions_performed: 0, }, check_kb_sent: 16.8388671875, check_kb_received: 5.2705078125, check_f2_stats: FComStats { num_voles_used: 1186, num_vole_extensions_performed: 0, }, check_fp_stats: FComStats { num_voles_used: 1078, num_vole_extensions_performed: 0, }, }, }, ), ], } ```

Verifier's output in JSON

```json { "repetitions": 3, "party": "Verifier", "network_options": { "listen": false, "host": "localhost", "port": 1337, "connect_timeout_seconds": 100 }, "meta_data": { "hostname": "machine", "username": "user", "timestamp": "2025-03-07T16:32:54+01:00", "cmdline": [ "../target/release/examples/bench", "conv", "--party", "verifier", "--protocol", "cheddabits-v1-xor4maj7", "--num", "4096", "--bit-size", "16", "--repetitions", "3", "--json" ], "pid": 94884, "git_version": "1a564cc527be1949e70c04f821e26b27dc91f76e-dirty" }, "protocol_stats": [ { "Conversion": { "protocol": "CheddabitsV1Xor4Maj7", "num": 4096, "bit_size": 16, "time_stats": [ { "init_time": { "secs": 0, "nanos": 578151899 }, "voles_time": { "secs": 0, "nanos": 302861015 }, "commit_time": { "secs": 0, "nanos": 41021430 }, "check_time": { "secs": 0, "nanos": 814705993 } }, { "init_time": { "secs": 0, "nanos": 555155599 }, "voles_time": { "secs": 0, "nanos": 195929395 }, "commit_time": { "secs": 0, "nanos": 41273196 }, "check_time": { "secs": 0, "nanos": 815317857 } }, { "init_time": { "secs": 0, "nanos": 505466672 }, "voles_time": { "secs": 0, "nanos": 198314748 }, "commit_time": { "secs": 0, "nanos": 40481408 }, "check_time": { "secs": 0, "nanos": 803548037 } } ], "comm_stats": { "init_kb_sent": 181.0361328125, "init_kb_received": 1044.5615234375, "voles_kb_sent": 1008.2080078125, "voles_kb_received": 515.8173828125, "voles_f2_stats": { "num_voles_used": 0, "num_vole_extensions_performed": 1 }, "voles_fp_stats": { "num_voles_used": 0, "num_vole_extensions_performed": 1 }, "commit_kb_sent": 0.0, "commit_kb_received": 32.0, "commit_f2_stats": { "num_voles_used": 65536, "num_vole_extensions_performed": 0 }, "commit_fp_stats": { "num_voles_used": 4096, "num_vole_extensions_performed": 0 }, "check_kb_sent": 5.2705078125, "check_kb_received": 16.8388671875, "check_f2_stats": { "num_voles_used": 1186, "num_vole_extensions_performed": 0 }, "check_fp_stats": { "num_voles_used": 1078, "num_vole_extensions_performed": 0 } } } } ] } ```

Running Benchmarks

All scripts mentioned in this section are located in the scripts/ directory.
To run benchmarks for a large set of parameters, we provide run_conv.sh and
run_fpm.sh.
In our case, we execute the benchmarks on the same physical server using the tc (traffic
control) utility to simulate different network settings.

The benchmark scripts use tc.sh to switch between the LAN/WAN settings.
Note that the parameters and the RTT and throughput measured with ping and iperf3 can differ
slightly.
We used the latter to find the right tc parameters.
To use tc you need additional permissions, so make sure you are allowed to use sudo.
The scripts will ask you for your password.

To run the benchmarks, please make sure the bench binary is build (using --release mode as described above).
Then open two terminals, change into the scripts/ directory, and run:

./run_conv.sh prover    # in the first terminal
./run_conv.sh verifier  # in the second terminal

and similarly for run_fpm.sh.
The benchmark results will be printed to the screen and also saved in the
scripts/results/ subdirectory:

ls results/
conv__party=prover_protocol=cheddabits-v1-tspa__bit-size=16__num=1024__network=lan__time=2025-03-07T13:18:04,692669286+01:00.json
conv__party=prover_protocol=cheddabits-v1-tspa__bit-size=16__num=1024__network=wan__time=2025-03-07T15:40:01,233233066+01:00.json
conv__party=prover_protocol=cheddabits-v1-tspa__bit-size=16__num=256__network=lan__time=2025-03-07T13:17:42,070965340+01:00.json
...

Analyzing Benchmark Results

Again we have two scripts analyze_conv.py and anaylze_fpm.py which use a somewhat recent version
of pandas (tested with v2.2.3) which aggregate the JSON files into pandas dataframes and print to
the terminal:

./analyze_conv.py results/
./analyze_fpm.py results/

Both scripts display a pandas dataframe to the terminal and store corresponding CSV files
(res_conv.csv and res_fpm.csv) in the passed directory.

License

The swanky framework and our modifications are licensed under an MIT license.