Some clients unable to connect after migration to 3.10.2

I recently moved our Openfire installation from a 32-bit 3.9.1 to a 64-bit 3.10.2.

Afterwards, I found that some clients (pidgin and Thunderbird) were unable to connect. The error was something along the line of “Unable to find a suitable encryption method” Researching I found that this might be a Java SSL problem. And knowing I had a problem on the 32-bit box using the built in Java rather then the supplied JRE I tried using OpenJRE and Oracle Sun Java. Neither has worked so far.

Has anyone else seen this problem and how to correct it?