BGN Encryption Based Lossless Data Hiding by Random Number Replacement and Partitioning

For security enhancement and privacy preservation, homomorphic encryption is deployed to facilitate computations among cipher texts. To transmit extra data over a cipher text without affecting its usage, lossless data hiding in encrypted domain (LDH-CT) has been developed by exploiting randomness introduced in homomorphic encryption such as Paillier, BGN and NTRU schemes. As data extraction without decrypting the cipher text has been accomplished with BGN, how to retrieve the hidden data after decryption remains unexplored. In this article, an LDH-CT scheme named random number replacement and partitioning (RNRP) is proposed to achieve the versatility of data embedding by designing two algorithms, namely the random number replacement algorithm to embed data to be extracted after decryption and the cipher value selection algorithm to embed data to be extracted without decryption. For the first time, confidential information to be extracted after decryption can be hidden into a cipher text by a third party without knowing its plain text. For convenience in performance evaluation, the proposed algorithms and the RNRP scheme are applied to a set of test images. Experimental results and comparisons with the state-of-the-art schemes demonstrate the better applicability of the proposed scheme, such as in saving bandwidth.