A distributed environment using 4096 bit SSL keys

we have a serious problem after updating the SSL certificates of a CCM instance which is configured on a remote server.
CCM can interact with JTS but JTS can't interact with CCM.
Does anyone of you use 4096bit SSL certificates?
What experiences do you have with 4096bit certificates?
Thanks for the answers. ;-)
greetings georg.
P.S. We are working on the issue with IBM via PMR.
Accepted answer
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Some more informations about what happened and the symptoms:
server A: WebSphere with JTS and QM installed, having a 2048 bit certificate
server B: WebSphere with CCM installed, having a 4096 bit certificate, reverse proxy
JTS said
No access to rootservices scr *URL*
javax.net.ssl.SSLPeerUnverifiedException: peer not authenticated
CCM itself was available via any webbrowser, it could aquire licenses and user roles from JTS, using workitems was okay.
The DWH jobs of CCM couldn't be run.
So we thought it is a wrong configuration in the reverse proxy.
The access via rich client was depending on the version of Eclipse. The standard RTC client was not able to connect to CCM, newer Eclipse clients with RTC plugin were able to connect to CCM.
We reconfigured the reverse proxy, but the problem was still there.
Switching the certificate back to 2048 solved the complete issue.