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params.html
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---
layout: page
permalink: /params-times/
title: params and times
tags: menu
usemathjax: true
---
<div>
<br>
<h3>Parameters: </h3>
<br>
<p>Our current parameters are (note that this might change):</p>
<br>
<p>We select and implement four parameter sets: For <strong>NIST security level 1</strong>, we select two parameter sets: <code>MAYO_one</code> and <code>MAYO_two</code>, where <code>MAYO_one</code> has smaller public keys but larger signatures and conversely <code>MAYO_two</code> has smaller signatures but larger public keys. For <strong>NIST security level 3</strong> and <strong>NIST security level 5</strong>, we select one parameter set each, which we refer to as <code>MAYO_three</code> and <code>MAYO_five</code>, respectively. The parameter sets and the corresponding key and signature sizes are displayed below. All sizes are reported in bytes -B-.</p>
<br>
<center>
<table class="param-table">
<tr>
<th>Parameter set</th>
<td><code>MAYO_one</code></td>
<td><code>MAYO_two</code></td>
<td><code>MAYO_three</code></td>
<td><code>MAYO_five</code></td>
</tr>
<tr>
<th>security level</th>
<td>1</td>
<td>1</td>
<td>3</td>
<td>5</td>
</tr>
<tr>
<th>secret key size</th>
<td>24 B</td>
<td>24 B</td>
<td>32 B</td>
<td>40 B</td>
</tr>
<tr>
<th>public key size</th>
<td>1168 B</td>
<td>5488 B</td>
<td>2656 B</td>
<td>5008 B</td>
</tr>
<tr>
<th>signature size</th>
<td>321 B</td>
<td>180 B</td>
<td>577 B</td>
<td>838 B</td>
</tr>
</table>
</center>
<br>
<h3>Cycle counts for our AVX2 optimized implementation:</h3>
<br>
<p>The fastest results on the 2.0 GHz Ice Lake platform perform KeyGen in 55 μs, Signing (+ExpandSK) in 246 μs, and Verifying (+ExpandPK) in 77 μs with <code>MAYO_one</code>. Batch signing (without expandSK) is fastest with 126 μs and <code>MAYO_two</code>. Batch verification (without expandPK) is fastest with 30 μs and <code>MAYO_two</code>.</p>
<br>
<p>All builds use <code>-O3</code> compiler optimization level and <code>-march=native</code> build architecture. Turbo Boost was deactivated to achieve consistent timings. We report the CPU cycles using AES-NI. More results can be found in our specification.</p>
<br>
<p>On Intel Xeon Gold 6338 CPU (Ice Lake) with 2.0 GHz for the AVX2 optimized implementation:</p>
<br>
<center>
<table>
<tr>
<td>Scheme</td>
<td>KeyGen</td>
<td>ExpandSK + Sign</td>
<td>ExpandPK + Verify</td>
</tr>
<tr>
<td><code>MAYO_one</td>
<td>110,112</td>
<td>460,978</td>
<td>175,158</td>
</tr>
<tr>
<td><code>MAYO_two</td>
<td>309,422</td>
<td>563,900</td>
<td>91,512</td>
</tr>
<tr>
<td><code>MAYO_three</td>
<td>508,608</td>
<td>1,663,666</td>
<td>610,010</td>
</tr>
<tr>
<td><code>MAYO_five</td>
<td>1,210,154</td>
<td>4,149,954</td>
<td>1,186,132</td>
</tr>
</table>
</center>
<br>
<p>The library was compiled on Ubuntu with clang version 12.0.1-19ubuntu3. Results are the median of 1000 benchmark runs.</p>
<br>
<br>
<p>On Intel Xeon E3-1225 v3 CPU (Haswell) at 3.20GHz for the AVX2 optimized implementation:</p>
<br>
<center>
<table>
<tr>
<td>Scheme</td>
<td>KeyGen</td>
<td>ExpandSK + Sign</td>
<td>ExpandPK + Verify</td>
</tr>
<tr>
<td><code>MAYO_one</td>
<td>184,116</td>
<td>652,052</td>
<td>283,228</td>
</tr>
<tr>
<td><code>MAYO_two</td>
<td>487,032</td>
<td>789,020</td>
<td>178,276</td>
</tr>
<tr>
<td><code>MAYO_three</td>
<td>956,696</td>
<td>3,249,120</td>
<td>1,160,552</td>
</tr>
<tr>
<td><code>MAYO_five</td>
<td>2,153,280</td>
<td>6,606,208</td>
<td>1,984,424</td>
</tr>
</table>
</center>
<br>
<p>The library was compiled on Ubuntu with clang version 12.0.0-3ubuntu1 20.04.5. Results are the median of 1000 benchmark runs.</p>
<br>
<p>On Intel Xeon E3-1260L v5 CPU (Skylake) at 2.90GHz for the optimized implementation:</p>
<br>
<center>
<table>
<tr>
<td>Scheme</td>
<td>KeyGen</td>
<td>ExpandSK + Sign</td>
<td>ExpandPK + Verify</td>
</tr>
<tr>
<td><code>MAYO_one</td>
<td>155,568</td>
<td>584,906</td>
<td>208,973</td>
</tr>
<tr>
<td><code>MAYO_two</td>
<td>419,778</td>
<td>697,946</td>
<td>129,863</td>
</tr>
<tr>
<td><code>MAYO_three</td>
<td>831,339</td>
<td>2,804,104</td>
<td>904,918</td>
</tr>
<tr>
<td><code>MAYO_five</td>
<td>1,727,943</td>
<td>5,148,078</td>
<td>1,478,483</td>
</tr>
</table>
</center>
<br>
<p>The library was compiled on Ubuntu with clang version 14.0.0-1ubuntu1 20.04.5. Results are the median of 1000 benchmark runs.</p>
<br>
<br>
<h3>Cycle counts for our optimized implementation:</h3>
<br>
<p>All builds use <code>-O3</code> compiler optimization level and <code>-march=native</code> build architecture. Turbo Boost was deactivated to achieve consistent timings. We report the CPU cycles using AES-NI. More results can be found in our specification.</p>
<br>
<p>On Intel Xeon Gold 6338 CPU (Ice Lake) with 2.0 GHz for the optimized implementation:</p>
<br>
<center>
<table>
<tr>
<td>Scheme</td>
<td>KeyGen</td>
<td>ExpandSK + Sign</td>
<td>ExpandPK + Verify</td>
</tr>
<tr>
<td><code>MAYO_one</td>
<td>222,666</td>
<td>1,087,794</td>
<td>205,692</td>
</tr>
<tr>
<td><code>MAYO_two</td>
<td>613,636</td>
<td>1,269,250</td>
<td>118,534</td>
</tr>
<tr>
<td><code>MAYO_three</td>
<td>2,917,294</td>
<td>8,839,058</td>
<td>1,470,684</td>
</tr>
<tr>
<td><code>MAYO_five</td>
<td>4,263,490</td>
<td>13,928,986</td>
<td>1,783,626</td>
</tr>
</table>
</center>
<br>
<p>The library was compiled on Ubuntu with clang version 12.0.1-19ubuntu3. Results are the median of 1000 benchmark runs.</p>
<br>
<br>
<p>On Intel Xeon E3-1225 v3 CPU (Haswell) at 3.20GHz for the optimized implementation:</p>
<br>
<center>
<table>
<tr>
<td>Scheme</td>
<td>KeyGen</td>
<td>ExpandSK + Sign</td>
<td>ExpandPK + Verify</td>
</tr>
<tr>
<td><code>MAYO_one</td>
<td>515,168</td>
<td>1,947,392</td>
<td>397,464</td>
</tr>
<tr>
<td><code>MAYO_two</td>
<td>1,444,244</td>
<td>2,505,584</td>
<td>212,264</td>
</tr>
<tr>
<td><code>MAYO_three</td>
<td>4,314,644</td>
<td>13,179,744</td>
<td>1,982,160</td>
</tr>
<tr>
<td><code>MAYO_five</td>
<td>6,096,148</td>
<td>19,609,280</td>
<td>2,705,800</td>
</tr>
</table>
</center>
<br>
<p>The library was compiled on Ubuntu with clang version 12.0.0-3ubuntu1 20.04.5. Results are the median of 1000 benchmark runs.</p>
<br>
<p>On Intel Xeon E3-1260L v5 CPU (Skylake) at 2.90GHz for the optimized implementation:</p>
<br>
<center>
<table>
<tr>
<td>Scheme</td>
<td>KeyGen</td>
<td>ExpandSK + Sign</td>
<td>ExpandPK + Verify</td>
</tr>
<tr>
<td><code>MAYO_one</td>
<td>313,438</td>
<td>1,496,786</td>
<td>283,366</td>
</tr>
<tr>
<td><code>MAYO_two</td>
<td>921,052</td>
<td>1,826,460</td>
<td>159,714</td>
</tr>
<tr>
<td><code>MAYO_three</td>
<td>4,016,744</td>
<td>12,324,612</td>
<td>1,637,394</td>
</tr>
<tr>
<td><code>MAYO_five</td>
<td>4,465,717</td>
<td>16,203,574</td>
<td>2,244,080</td>
</tr>
</table>
</center>
<br>
<p>The library was compiled on Ubuntu with clang version 14.0.0-1ubuntu1 20.04.5. Results are the median of 1000 benchmark runs.</p>
<br>
<h3>Arm Cortex-M4 implementation:</h3>
<br>
<p>We are working on an Arm Cortex-M4 implementation. Preliminary results are shown below.</p>
<p>We use the ST NUCLEO-L4R5ZI development board which comes with a STM32L4R5ZI Cortex-M4 CPU with 2MBof flash memory and 640KB of SRAM.</p>
<br>
<p>All builds use <code>-O3</code> compiler optimization level using the Arm GNU toolchain.</p>
<br>
<center>
<table>
<tr>
<td>Scheme</td>
<td>KeyGen</td>
<td>ExpandSK + Sign</td>
<td>ExpandPK + Verify</td>
</tr>
<tr>
<td><code>MAYO_one</td>
<td>5,245,606</td>
<td>9,183,088</td>
<td>4,886,583</td>
</tr>
<tr>
<td><code>MAYO_two</td>
<td>11,925,130</td>
<td>12,033,879</td>
<td>5,103,238</td>
</tr>
</table>
</center>
<br>
</div>