Aside from the obvious fact that the set everyday numbers (both rationals and reals) are fields, most crypto heavily relies on finite fields.
[edit] and come to think of it, I might be mistaken I don't think the notion of vector space and therefore the whole of linear algebra would work without a field for the underlying coordinates.
[edit] and come to think of it, I might be mistaken I don't think the notion of vector space and therefore the whole of linear algebra would work without a field for the underlying coordinates.