Updatable public key encryption (UPKE) allows the senders to initiate a process to update the public key and generate a special ciphertext, such that the receiver can generate the corresponding secret key and decrypt the specially generated ciphertext. In this process, if the receiver needs to store the ciphertext, she/he must store a secret key (or key update information) corresponding to each received ciphertext, which inevitably increases the complexity of data management for the receiver. To address this limitation, we propose a novel concept called receiver-initiated public key encryption (), in which the receiver would update the key pair periodically. Additionally, after each round of key pair updates, the receiver can update the ciphertexts generated in the previous round, ensuring that these ciphertexts can be decrypted with the updated secret keys, thereby reducing the burden of key management. We also propose a generic construction of utilizing the Updatable Encryption (UE) scheme, and introduce two security models as and . We then prove the security of our construction under above security models respectively. Further, we propose applying scheme for time-limited data retention by controlling the ciphertext update process, thus regulating the decryptability of ciphertexts over a defined period.