How do I change the login background for Mavericks?

Then give Mavericks a favorite login background! It's not really difficult, you just have to make (or find) the right size background map and replace the relevant resource file in the Mavericks system.

The only thing to note is that if you want to get the best results, you need to prepare a 8095 scale picture of your screen resolution (click here), and a 160190 scale image to replace it for full screen replacement. For example, your MAC screen resolution is 1280800, so you need to prepare a 12801520-resolution background image (1280/80=16,1695=1520) and a 25603040-resolution picture, all of which need to be saved in PNG format.

Copy each of the two images to get 4 pictures. The two small resolution images are named Apple.png and Apple_s1.png respectively, and two large resolution images are named Apple@2x.png and Apple_s1@2x.png respectively.

Then press the shortcut key command+shift+g in the Finder to enter the following path:

/system/library/privateframeworks/loginuikit.framework/versions/a/frameworks/loginuicore.framework/resources/

Locate the Apple.png, Apple_s1.png, Apple@2x.png, apple_s1@2x.png four pictures in the folder, back them up to a secure location, and replace them with the 4 pictures you received earlier (you need to enter the Administrator password Authentication).

After you log out of your current account, you can see that the new background is already in effect on the login screen.