This document proposes a new scheme called Key-Policy Time-Specified Attribute-Based Encryption (KP-TSABE) for secure self-destructing of sensitive data shared in clouds. KP-TSABE aims to provide fine-grained access control over user-defined authorization periods and ensure data is automatically destroyed after expiration. It encrypts data with attributes and time constraints, so that ciphertext can only be decrypted if the time period is valid and attributes match the key's access structure. The scheme is proven secure under the decisional l-bilinear Diffie-Hellman inversion assumption. KP-TSABE addresses limitations of prior work and provides stronger security and privacy for sensitive data lifecycles in