Cryptanalyzing two image encryption algorithms based on a first-order time-delay system

Security is a key problem for the transmission, interchange and storage process of multimedia systems and applications. In 2018, M. Li et al. proposed in-depth security analysis on an image encryption algorithm based on a first-order time-delay system (IEATD) and gave a specific chosen-plaintext attack on it. Moreover, an enhanced version called as IEACD was designed to fix the reported security defects. This paper analyzes the essential structures of the two algorithms and evaluates their real security performances: 1) no efficient nonlinear operations are adopted to assure the sensibility of keystream; 2) the equivalent secret key of IEATD can be efficiently recovered from one known plain-image and the corresponding cipher-image; 3) IEACD can still be efficiently cracked with a chosen-plaintext attack. Both rigorous theoretical analyses and detailed experimental results are provided to demonstrate effectiveness of the advanced cryptanalytic methods.