The default WordPress “shortlink” URLs look like this: <code>http://www.example.com/blog/?p=123</code>, where “<code>123</code>” is actually a 7+ digit decimal number. This plugin shrinks your shortlinks by encoding that number into only 4 characters, and using the abbreviated URL prefix of your choice.
On my site, the default shortlinks are 35 bytes long, even though I have a very short domain name. This plugin shrinks them to 21 total bytes, which is comparable to most public URL-shortener services, and better than many.
E.g., this: <code>http://www.jwz.org/blog/?p=13240780</code> 
becomes: <code>http://jwz.org/b/ygnM</code>
This doesn’t affect your (long) permalinks: those can still be in whatever format you like.

Base64 Shortlinks

This plugin makes your shortlinks shorter!

Jeremy Herve

Use shortlinks instead of permalinks in Jetpack sharing buttons
<ul>
<li>If you haven’t set up any shortlink plugin on your site, the sharing buttons will use the default numerical permalinks</li>
<li>If you have enabled WP.me Shortlinks in Jetpack, the sharing buttons will use them</li>
<li>If you’ve installed another plugin to create custom shortlinks, the sharing buttons will use them</li>
</ul>
Important: for this plugin to work, you must activate <a href="https://wordpress.org/extend/plugins/jetpack/" rel="ugc">Jetpack</a> first, and activate the Sharing module.
This plugin is a work in progress. You can report issues <a href="https://wordpress.org/support/plugin/jetpack-shortlinks-for-sharing-buttons/" rel="ugc">here</a>, or submit a pull request <a href="https://github.com/jeherve/jp-sd-custshortlink" rel="nofollow ugc">on GitHub</a>.

Shortlinks for Jetpack sharing buttons

Use shortlinks instead of permalinks in Jetpack sharing buttons

Base64 Shortlinks vs Shortlinks for Jetpack sharing buttons