Although, traditionally, can has meant “to be able” and may has meant “to be permitted” or to express possibility, both can and may are commonly used interchangeably in respect to permission.
For example; May/Can I go to the mall tonight?
Regardless of whether you choose can or may here, it is clear that permission is being requested.
In spoken English, a request for permission is generally answered with can, cannot, or can’t, rather than with may or may not, even if the question was formed using may.