Investigation and Improvement of the Assessment Metrics for Image Encryption

Abstract

The increasing interest in data security has led to the emergence of the security assessment metrics. These metrics work generally with stream data; they give a proper indication about the security level of their encryption process. However, it was concluded that these metrics failed and performed poorly when they have been used in images; that contributed to the fact that the images represented by two dimensions, and they contain a large number of pixels, which in turn leads to high information redundancy. This failure has motivated researchers to seek provides metrics that are more suitable for evaluating the security level of images. We attempt in this thesis to address the common assessment, as well as the, recent methodologies that employed to some of these metrics to make them more suitable for testing the image encryption process. These methodologies used the ideal encrypted image definition to generate the statistical randomness test. This idea first used to derive the statistical test for the Number of Pixel Changing Rate (NPCR) parameter, the Unified Averaged Change Intensity (UACI) parameter and the Local Shannon Entropy (LSE). In this thesis, we aim to address the weakness of Avalanche Effect (AE), LSE, Encryption Quality (EQ) and Chi-square. Moreover, derive the solution for some of these weaknesses. In detailed, we improve the performance of the AE by deriving its statistical test, and the modifi- cation of the local Shannon entropy (MLSE) is proposed to solve the issues of using the LSE in testing the performance of the image’s encryption process. The performance of the AE statistical test is examined by the empirical significance level test. It is shown that the AE is an exact test (the empirical significance level coincides with viii the nominal significance level). Moreover, the modification of the local Shannon entropy is examined by the empirical significance level and the statistical power. It is shown that the modification of the local Shannon entropy is of level alpha (the empirical significance level is less than the nominal significance level) and the maximum statistical power is attained at the block size 64 × 64 and an 8000 number of blocks as result of the numerical analysis