You have installed GPG, then tried to commit and suddenly you see this error message after it:

error: gpg failed to sign the data
fatal: failed to write commit object

For understanding what's going on, first check what git is doing, so add GIT_TRACE=1 at the beginning of the command you used before (git commit or git rebase):

GIT_TRACE=1 git commit

With that you can see what the problem can be. And what GPG is doing: Probably you will see something like this

10:37:22.346480 run-command.c:637       trace: run_command: gpg --status-fd=2 -bsau <your GPG key>

(Check if your GPG key is correct)

Execute that gpg command again in the command line:

gpg --status-fd=2 -bsau <your GPG key>

Now you could see what happened in detail!

We can have many problems, but I list what I found:

1. It could be that the GPG key was expired: https://stackoverflow.com/a/47561300/532912
2. Another thing could be that the secret key was not set (In my case the message said gpg: signing failed: No secret key as it can be see in the image below). It means that is not finding the key that was set.
3. You can see in the thread of this gist other ways to find the solution to other problems. I recommend to read the Github guide for signing commits with GPG.

Hope it helps!