Do I have to release the patch for a GPL software under GPL?

[Dancefire]

Hi, all,

I am confusing on GPL now, I need someone to clear me.

Do I have to release the patch under GPL if the patch is for a GPL software?
As my understanding, for example, If I modified Linux kernel, I do not have
to release it under GPL if I use it privately, unless I make it public. But
how about the patch for the kernel? That is, if I generate the patch of my
modification for the Linux Kernel, and never release the modified Linux
kernel to public, however, I want to sell the kernel patch of the Linux to
customers as whatever license as I want, but I don’t want the patch under
GPL for some reason. Can I?

Dancefire
 
--
CCNA
I am expecting to do research on Operating System, Embedded System and
Network Security.