The Markdown parser in Zulip server before 2.0.5 used a regular expression vulnerable to exponential backtracking. A user who is logged into the server could send a crafted message causing the server to spend an effectively arbitrary amount of CPU time and stall the processing of future messages.
In Zulip Server before 1.7.1, on a server with multiple realms, a vulnerability in the invitation system lets an authorized user of one realm on the server create a user account on any other realm.