1. To know the format of cookies used for the web site you are targetting. Specifically, whatever cookie contains authentication.
2. The ability to injection a request to the target web server while someone is connected (such as with JavaScript, an XSS, or plug-in).
3. Ability to monitor the SSL connection is it is transported across TCP.
Would have been fun if they called this the CPE1704TKS attack instead of CRIME: http://www.youtube.com/watch?v=NHWjlCaIrQo