We propose a Decentralized multi-authority Ciphertext-Policy Attribute-Based Encryption (DCP-ABE) scheme, where any party can become an authority by creating a public key and generating private keys for the users by utilizing their attributes. Any user can encrypt data in terms of any monotone access structure over attributes issued from any chosen set of authorities without requiring any central authority. DCP-ABE utilizes Learning With Errors over Rings (R-LWE) as its underlying hardness assumption. Our post-quantum protocol is secure under selective-set model where adversaries can corrupt authorities only statically with adaptive key queries.