After installing SUPEE-8788 on Magento 1.8, a file is created in app/code/local/Mage/Core/functions.php. Why Mage file is here instead of app/code/core ?
This is your custom file. Patch changes only
app/code/core/Mage/Core/function.php file. You could leave your local function file in case you have PHP >= 5.6 otherwise copy method
hash_equal into your local