FHE Benchmarking: Zn-Multiplication Workload

Results

• Single Multiplication: Single.
• Batch Multiplication: Small, Medium, Large.

Specification

The Zn-multiplication workload implements an encrypted multiplication functionality. The input is a collection of integer pairs modulo 2^n. The goal is to perform multiplication of these integers using homomorphic encryption. Currently we support n=64, and we may expand to other values of n in the future. Such 64-bit encrypted integer multiplications are essential to blockchain applications.

The workload includes two interfaces for benchmark submitters to implement:

• Single Multiplication: On a single pair of integers, submitters are expected to implement the multiplication functionality for a single input pair and return a single integer.
• Batched Multiplication: On a batch of input integer pairs, the submitters are expected to implement the multiplication functionality for a batch of input pairs and return a vector of integers of the batch size. This can be more efficient than single multiplication for large datasets leveraging parallelism.

Hence, there are a total of four variants of this workload: single multiplication and batch multiplication for each one of the three sizes. Submitters need not implement all four, instead each submitter can implement and report the results of any subset.

Submission to the benchmarking suite must set the implementation parameters so as to achieve security level of at least 128 bits (against a semi-honest server). Submitters must document their choice of parameters and explain why they believe that it meets the 128-bit security mandate. (For example, for LWE-based schemes without a sparse key, they can rely on Table 5.2 or Table 5.3 in the HE-security-guidelines document of Bossuat et al. [BCC+24].)

All submissions must also ensure the correctness of their output with full precision.

The Zn-multiplication harness contains a script that can be called to run the implementation of submitters, that script accepts command-line arguments to specify which interface of what instance size to run.

$ python3 harness/run_submission.py -h
usage: run_submission.py [-h] [--num_runs NUM_RUNS] [--seed SEED] [--count_only] [--remote]
                         {0,1,2,3}

Run the Zn-multiplication FHE benchmark.

positional arguments:
  {0,1,2,3}            Instance size (0-single/1-small/2-medium/3-large)

options:
  -h, --help           show this help message and exit
  --num_runs NUM_RUNS  Number of times to run steps 4-9 (default: 1)
  --seed SEED          Random seed for dataset and query generation

Bibliography