Google Play Game Services And Sha1 Certificate

In google play game services, you have to link your apps to your Game service campaign. Whenever you link an app you have to authorize it by providing the package and then the SHA1

Solution 1:

My question is if you generate the app's apk on a different computer, the SHA1 certificate will be different

Why would the certificate be different? You must use the same keystore and provide the keystore password every time you generate the APK for a release. See the documentation about this.

Warning: Keep your keystore and private key in a safe and secure place, and ensure that you have secure backups of them. If you publish an app to Google Play and then lose the key with which you signed your app, you will not be able to publish any updates to your app, since you must always sign all versions of your app with the same key.