The increasing popularity of remote Cloud File Sharing (CFS) has become a major concern for privacy breach of sensitive data. Aiming at this concern, we present a new resource sharing framework by integrating enterprise-side Attribute-Based Access Control/eXtensible Access Control Markup Language (ABAC/XACML) model, client-side Ciphertext-Policy Attribute-Based Encryption (CP-ABE) scheme, and cloud-side CFS service. Moreover, the framework workflow is provided to support the encrypted-file writing and reading algorithms in accordance with ABAC/XACML-based access policy and attribute credentials. However, an actual problem of realizing this framework is that policy matrix, derived from access policy, seriously affects the performance of existing CP-ABE from Lattice (CP-ABE-L) schemes. To end it, we present an optimal generation algorithm of Small Policy Matrix (SPM), which only consists of small elements, and generates an all-one reconstruction vector. Based on such a matrix, the improved CP-ABE-L scheme is proposed to reduce the cumulative errors to the minimum and prevent the enlargement of error bounds. Furthermore, we give the optimal estimation of system parameters to implement a valid Error Proportion Allocation (EPA). Our experimental results indicate that our scheme has short size of parameters and enjoys efficient computation and storage overloads. Thus, our new framework with optimization methods is conducive to enhancing the security and efficiency of remote work on CFS.