JPEG Decompression in the Homomorphic Encryption Domain

Privacy-preserving processing is desirable for cloud computing to relieve users' concern of loss of control of their uploaded data. This may be fulfilled with homomorphic encryption. With widely used JPEG, it is desirable to enable JPEG decompression in the homomorphic encryption domain. This is a great challenge since JPEG decoding needs to determine a matched codeword, which then extracts a codeword-dependent number of coefficients. With no access to the information of encrypted content, a decoder does not know which codeword is matched, and thus cannot tell how many coefficients to extract, not to mention to compute their values. In this paper, we propose a novel scheme that enables JPEG decompression in the homomorphic encryption domain. The scheme applies a statically controlled iterative procedure to decode one coefficient per iteration. In one iteration, each codeword is compared with the bitstream to compute an encrypted Boolean that represents if the codeword is a match or not. Each codeword would produce an output coefficient and generate a new bitstream by dropping consumed bits as if it were a match. If a codeword is associated with more than one coefficient, the codeword is replaced with the codeword representing the remaining undecoded coefficients for the next decoding iteration. The summation of each codeword's output multiplied by its matching Boolean is the output of the current iteration. This is equivalent to selecting the output of a matched codeword. A side benefit of our statically controlled decoding procedure is that paralleled Single-Instruction Multiple-Data (SIMD) is fully supported, wherein multiple plaintexts are encrypted into a single plaintext, and decoding a ciphertext block corresponds to decoding all corresponding plaintext blocks. SIMD also reduces the total size of ciphertexts of an image. Experimental results are reported to show the performance of our proposed scheme.