Permission to see hidden fields There is a node type with hidden fields. Anyone can find nodes of that content type from the search form, and see open information. To see all the fields, users must make a request to the node owner, who decides the users who can see, or not those fields.

Is there any module with this purpose? Is there any other way?
I think you can accomplish this with the field permissions module. You can then specify that users without permission cannot view the field. 

Secondly, create a new user role for the people who can see the field. When a user makes a request to see the field, you can set the field permission to view the field by assigning the new role to that user.