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<title>FHE Benchmarking: Zn-multiplication Workload</title>
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<div class="repository-link">
    <strong>Repository is found at</strong>
    <a href="https://github.com/fhe-benchmarking/Zn-multiplication">github.com/fhe-benchmarking/Zn-multiplication</a>
</div>

<h1>FHE Benchmarking: Zn-Multiplication Workload</h1>

<h2>Results</h2>
<ul>
<li>Single Multiplication:
    <a href="Single.html">Single</a>.
</li>
<li>Batch Multiplication:
    <a href="Small.html">Small</a>,
    <a href="Medium.html">Medium</a>,
    <a href="Large.html">Large</a>.
</li>
</ul>

<h2>Specification</h2>
<p>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.

</p>

<p>The workload includes two interfaces for benchmark submitters to implement: </p>

<ul type="disc">
 <li>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.</li>
 <li>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.</li>
</ul>

<table>
  <thead>
    <tr>
      <th>Size</th>
      <th>Records (N)</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>Small</td>
      <td>1000</td>
    </tr>
    <tr>
      <td>Medium</td>
      <td>100,000</td>
    </tr>
    <tr>
      <td>Large</td>
      <td>10,000,000</td>
    </tr>
  </tbody>
</table>

<p>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.</p>

<p>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. <a href="#BCC24">[BCC+24]</a>.)</p>

<p>All submissions must also ensure the correctness of their output with full precision.
</p>


<p>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.</p>

<div class="code-block">
<pre><code>
$ 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 <a href="https://github.com/fhe-benchmarking/Zn-multiplication/blob/main/harness/run_submission.py#L109" style="color: #63b3ed;">steps 4-9</a> (default: 1)
  --seed SEED          Random seed for dataset and query generation
</code></pre>
</div>
You can find more details on the <a href="https://github.com/fhe-benchmarking/Zn-multiplication">Zn-multiplication Github repository</a>.


<hr/>
<h3>Bibliography</h3>
<div class="bib-entry">
<p><span id="BCC24" style="font-weight: bold;">[BCC+24]</span>
<em>Security guidelines for implementing homomorphic encryption.</em>
Jean-Philippe Bossuat, Rosario Cammarota, Ilaria Chillotti, Benjamin R. Curtis,
Wei Dai, Huijing Gong, Erin Hales, Duhyeong Kim, Bryan Kumara, Changmin Lee,
Xianhui Lu, Carsten Maple, Alberto Pedrouzo-Ulloa, Rachel Player, Yuriy Polyakov,
Luis Antonio Ruiz Lopez, Yongsoo Song, and Donggeon Yhee.
<a href="https://doi.org/10.62056/anxra69p1">IACR Communications in Cryptology, 1(4):26, 2024</a>.
</p>
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