Choppr ins an extension for Opera and that adds a short flic.kr-url to the right hand column on a Flickr™ photo page.
This short url is calculated from the photo's unique id (actually, the calculation is ”bijective“, thus could be inverted) – there is no web service contacted during that process.
You find the short url behind a little ☆-icon below the photo's license statement and above its privacy information in the right hand info column.
