Advanced Search by Keyword--Possible to limit by custom fields?

I’m building a site for a large-ish art collection, where each individual piece of art will have an entry with a lot of custom fields for data about the piece (artist name, medium of work, subject matter).

The site needs an advanced search form where the user will be able to search by keyword or dropdown within these custom fields. So for instance, the ability to search the keyword “picasso” within a custom field called “artist_name” in a channel called “art_collection.” Or the ability to select “etching” from a “Media” dropdown, where the dropdown would be populated by values from a “medium” custom field.

Does anyone know if this is doable? This seems like it would be a common need for an advanced search form, but I’m not seeing anything obvious in the example. I might be thinking about this the wrong way.

Thanks for any assistance!

Erik