We propose a key-policy attribute-based encryption (KP-ABE) scheme with constant-size ciphertexts, whose almost tightly semi-adaptive security is proven under the decisional linear (DLIN) assumption in the standard model. The access structure is expressive, that is given by non-monotone span programs. It also has fast decryption, i.e., a decryption includes only a constant number of pairing operations. As an application of our KP-ABE construction, we also propose an efficient, fully secure attribute-based signatures with constant-size secret (signing) keys from the DLIN. For achieving the above results, we extend the sparse matrix technique on dual pairing vector spaces. In particular, several algebraic properties of an elaborately chosen sparse matrix group are applied to the dual system security proofs.