Attribute-based Encryption (ABE) as a relatively new extension of public-key cryptography, introduces a new scheme of one to many encryption, compared to one to one scheme in the traditional public-key cryptography. It defines the users based on their attributes and provides fine-grained access control based on those attributes. As an improved version of ABE, decentralized ABE (DABE) aimed to remove the dependency between attribute authorities and any centralized entity in the system. Due to its heavy operations, DABE includes resource extensive computations based on the used attributes in the access policies and is not efficient in executing its different algorithms. This prevents its implementations or results in execution with significant delay on some resource-constrained devices. In this paper, we proposed a model to securely distribute the heavy computations of DABE in the encryption algorithm using secret sharing and let the user only perform some multiplications based on the received results. When the bottleneck is the exponentiation, our model can perform better. We defined and proved the correctness and security of our model. Additionally, our performance analysis showed notable improvements in terms of efficiency.