You are probably right in the diagnosis of your SSL connection problem, but I had almost identical error messages, and my problem was a little different.
Originally Posted by greenoyster
I was trying to set up an e-mail account with fastmail, and was seeing the same errors that led me to this thread. The solution, after much digging around, was to get their SHA-256 SSL certificate by pointing a Web browser at an https server that was using the same certificate as the IMAP server. I was lucky in that my provider was using the same SSL cert both for IMAP SSL and for providing SSL for their carddav implementation.
I accesed the SSL certificate via my browser, saved it to my hard-drive, and e-mailed it to myself on my phone and touchpad. From there I installed it in my certificate manager as "trusted"
Then I was able to log in.
Just mentioning this because someone else might come here and conclude the issue must be the cipher support, but the issue could also be that you need to install the SSL certificate or root certificate of your e-mail provider and mark it as trusted.
The log/error message is virtually identical in both cases, so either the cipher or the lack of trusted cert could be an issue here.