Abstract: Inner product encryption (IPE) is a concrete construction of predicate encryption, which represents a wide class of predicates that includes an equality test(for identity-based encryption and hidden vector encryption), disjunctions or conjunctions of equality tests (for attribute-based encryption). Hierarchical inner product encryption (HIPE) can provide the capacity of delegate for inner product encryption, and it can effectively reduce the workload of root node of the system. Aiming at the efficiency that exists in the hierarchical inner product encryption, we present a short ciphertexts IPE scheme with full security in asymmetric bilinear pairing. By making use of the IPE scheme as building blocks, we then present a new HIPE scheme with the new technique for dual system encryption. The new realization of dual system encryption does not use tags, which makes the compression of ciphertexts possible. The proposed HIPE scheme achieves constant-size ciphertexts and full security in the standard model. Security is proven under three static assumptions whose size does not depend on the number of queries. Furthermore, our scheme achieves lower computational cost because decryption only needs seven pairing operations. Compared with other existing schemes, our scheme is more compact to implement and can provide better efficiency in terms of the communication and computation cost.