Selective encryption (SE) methods for images often encrypt the sign bits, i.e., the most significant bits (MSBs) of the codewords corresponding to key syntax elements (in compressed images) or to pixel intensities (for uncompressed images). Our work is motivated by the key observation that the binary code (BC) used for these representations has an impact on the quality of the reconstruction at the eavesdropper (Eve), which can be regarded as a measure of the degree of security of the encryption (the lower the quality, the higher the level of security). Therefore, we address the design of BCs that enhance the security of MSB-based SE by increasing the degradation at Eve’s side when she uses a simple replacement attack (replacing all MSBs either by 0s or by 1s). We first consider the scenario of fixed-length BCs, i.e., where all the codewords have the same length. We formulate the design problem as an optimization problem with the objective of maximizing the distortion at Eve’s without any constraint or with a constraint on the entropy of the MSBs in order to shorten the size of the MSB stream to reduce the computational overhead of encryption. We show that the problem can be cast as a binary integer linear program equivalent to a weighted non-bipartite graph matching problem, for which polynomial-time solution algorithms exist. We empirically assess the performance of the optimized BCs on a Mixed Gaussian source, as well as on Gaussian and Laplacian sources, the
latter two being commonly used to model the distribution of transform coefficients and prediction residuals. Our experiments lead to the conclusion that MSB-based SE schemes could benefit from the proposed BC designs. For the case of uncompressed images, we also propose a family of structured BCs for the pixel intensity values. These BCs are constructed such that intensity values that are close have reconstructions that are far apart. As a result, the reconstruction with the replacement attack significantly destroys the smooth areas and blurs the edges, therefore increasing the degree of security. Next, we focus on the construction of variable-length BCs for the non-zero quantized AC coefficients in JPEG compressed images. For this, we first formulate the BC design problem as the problem of maximizing the distortion at Eve’s side with a constraint on the entropy. This problem can also be cast as a weighted non-bipartite graph matching problem and, therefore, can be solved efficiently. Furthermore, by gaining insights from the optimization results, a simpler and faster method for BC design is devised, which consists of only swapping a few codewords in the original code used in JPEG. We assess the practical performance of the proposed BCs for the SE method of JPEG images that encrypts only the MSBs of the non-zero quantized AC coefficients, along with the full encryption of the DC coefficients. Our experimental results show that high visual security can be achieved with only a small sacrifice in compression efficiency. In addition, the proposed BCs can be tuned to achieve various levels of degradation at Eve’s side, a property that is convenient for certain applications. / Thesis / Doctor of Philosophy (PhD)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/28145 |
| Date | January 2022 |
| Creators | Kafi, Mehrshad |
| Contributors | Dumitrescu, Sorina, Electrical and Computer Engineering |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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