XWiki + Tomcat + HTTPS login failure

XEM 4.1.4 + Tomcat 7 + Apache in front.
HTTP works fine.

Ingo Oellers reported:

Direct access on Tomcat-URL is OK.
But if go over Apache and try to login the message occurs:
"Unauthorized: This server could not verify that you are authorized
to access the document requested. Either you supplied the wrong
credentials (eg, bad password) or your browser doesn't understand how to
supply the credentials required.

The browser's URL is redirected to

https://mysub.mydomain.com/xwiki/bin/login/XWiki/XWikiLogin?xredirect=%2Fxwiki%2Fbin%2Fview%2FMain%2FWebHome

xwiki.cfg is configured with:
xwiki.home=https://mysub.mydomain.com/xwiki/
xwiki.url.protocol=https
xwiki.webapppath=xwiki/

I can add:

1. The Error in Firefox looks as following:
Not Found
The requested URL /xwiki/bin/loginsubmit/XWiki//xwiki/bin/admin/XWiki/XWikiPreferences?section=Groups&srid=kGBOvVJJ was not found on this server.

2. Chrome does not say anything: blank page only.

3. xwiki.url.protocol=https or empty parameter act the same.

4. Futher investigation showed, that until XWiki is Public it works fine. If set "Prevent viewing page for unregistered users" it fails to log in.