Pseudo-random Image-Scrambling Patterns Generated By Direct Sequences
Hsin-Ya Chen, Hsiao-Chiu Chu · 2023
We present a new method for image scrambling that mitigates continuous data loss, or erasures during data transmission or storing/retrieving processes. In transmission or storing, the scrambling process disperses erasures randomly across the whole image. Even without further processing, the dispersion makes the image more readable than the unscrambled. The proposed method is a 2D mapping scrambling technique. We utilized n-bit linear-feedback shift register (LFSR) to generate pseudo-random sequences in 2D coordinates mappings. However, the mapping originates from the content of the n-bits LFSR. These n-bits contents of LFSRs form binary numbers ranging from 1 to $2^{n}-1$, inclusively. We researched LFSRs to generate the maximal-length sequence or m-sequence since m-sequences have the maximal period of $2^{n}-1$, where n is the length of LSFRs. As a result, contents from these LFSRs also have a non-repetitive pattern and a maximal period of $2^{n}-1$. To verify the method, we simulated and compared the performance of scrambling using m-sequences LSFRs and random mappings. Since it was difficult to quantify how comprehensible an image is, we used two metrics to roughly compare different scrambling methods. The minimum distance was defined as the 2D Euclidean distance from one erasure to another erasure closest to the former erasure. Then, we calculated the average of these distances for all dispersed erasures. The other was the percentage of dispersed erasures that were adjacent, or connected, to other erasures. We minimized this metric since continuous erasures after descrambling resulted in an image that was difficult to comprehend. We confined images with 2n pixels so the mapping was easy to establish. We used images of any size and modified the algorithm to perform scrambling and descrambling.