Broadcast proxy reencryption (BPRE), which combines broadcast encryption (BE) and proxy reencryption (PRE), is a technology used for the redistribution of data uploaded on the cloud to multiple users. BPRE reencrypts data encrypted by the distributor and then uploads it to the cloud into a ciphertext that at a later stage targets multiple recipients. As a result of this, flexible data sharing is possible for multiple recipients. However, various inefficiencies and vulnerabilities of the BE, such as the recipient anonymity problem and the key escrow problem, also creep into BPRE. Our aim in this study was to address this problem of the existing BPRE technology. The partial key verification problem that appeared in the process of solving the key escrow problem was solved, and the computational efficiency was improved by not using bilinear pairing, which requires a lot of computation time.