The spurious rings, denoted by SR(q), are an algebraic structure similar to the finite rings of q elements but they do not satisfy certain axioms of the rings. The sequences generated over SR(q) can be applied as cryptographic keys. Finding such a key is more difficult than the key generated over GF(q). In this paper, the properties of keys generated over SR(q) are presented. The advantages of the keys using the sequences over SR(q) for applications in stream cipher have been discussed.