Improving Efficiency on BFV-based Encrypted Watermarking using Hadamard Product Decomposition

Fully homomorphic encryption (FHE) enables arithmetic computation over encrypted data to preserve data privacy in the untrusted computing domain. Nevertheless, the BFV-based FHE computation is memory expensive that does not scale for high-resolution image computation such as image watermarking. This paper proposed a vector decomposition approach based on the Hadamard product to enable memory-efficient encrypted watermarking on huge-size images. The method uses singular value decomposition (SVD)-based watermarking by splitting the watermark embedding into row-wise of Hadamard products. The evaluation shows that the proposed method reduces the memory requirements to N times, where N refers to the image dimension in pixels. In addition, the proposed method allows parallel computation for faster computation, from 4-times up to 24-times faster, by utilizing the available memory.