How to set default privacy by "Unique Key"

I've a custom field (Text Box) which is used for a user to enter his mobile number, i've set a unique key for this field as "MOBILENUMBER".

There is a privacy tab in profile types which has an option for set privacy for "TEXT BOX", but i rekon that this will be universal for all text boxes used in custom fields (e.g education, College...)

Now how can i set a default privacy to "Only Me" for Mobile number which has a unique key "MOBILENUMBER"

As i want the user to opt for showing his mobile number publicly by editing his privacy after registration, and not have our site showing his mobile number publicly by default.