When you run Trillian 5.5.x, a message "systraySSLCertError" or "Trillian could not validate the SSL certificate for [an imap server]. The certificate may be self-signed or otherwise invalid. Use caution before proceeding." is showed according to the language you use.
Since its new version 5.5, trillian checks the validity of certificates. If these certificates appear invalid, it's simply because the anti-virus "Avast" (the free version and paid versions) rewrites the SSL certificates with certificates from their false certification authority : "avast Mail Scanner Root! ".
Certificates appear valid for Windows because SSL certificates generated by Avast are automatically added to the authorized certificates of the computer.
To solve this problem, there are two solutions :
1) Tell Trillian to use this certificate despite being considered invalid
To do this, simply click "Allow Anyway" on all warnings.
2) Disable the "analysis of incoming mail (POP3 / IMAP4)" in Avast
Warning : If you check your mails via a mail client such as the program "Outlook", "Thunerbird" ... we recommend using solution 1 because with solution 2, potential viruses in messages received will not be blocked.
To disable scanning of incoming mail by Avast, open Avast and go to Settings -> Active Protection. Then, click the gear facing Mail Agent.
Uncheck "Analyze incoming mail (POP3, IMAP4)" and click "OK".
Restart Trillian. Warnings have disappeared.