In the previous construction of attributed-based encryption for circuits on lattices, the secret key size was exponential to the number of AND gates of the circuit. Therefore, it was suitable for the shallow circuits whose depth is bounded. For decreasing the key size of previous scheme, combining the techniques of Two-to-One Recoding (TOR), and sampling on lattices, we propose a new Key-Policy Attribute-Based Encryption (KP-ABE) scheme for circuits of any arbitrary polynomial on lattices, and prove that the scheme is secure against chosen plaintext attack in the selective model under the Learning With Errors (LWE) assumptions. In our scheme, the key size is proportional to the number of gates or wires in the circuits.