A Novel Image-Encryption Scheme Based on a Non-Linear Cross-Coupled Hyperchaotic System with the Dynamic Correlation of Plaintext Pixels

Abstract

Based on a logistic map and Feigenbaum map, we proposed a logistic Feigenbaum non-linear cross-coupled hyperchaotic map (LF-NCHM) model. Experimental verification showed that the system is a hyperchaotic system. Compared with the existing cross-coupled mapping, LF-NCHM demonstrated a wider hyperchaotic range, better ergodicity and richer dynamic behavior. A hyperchaotic sequence with the same number of image pixels was generated by LF-NCHM, and a novel image-encryption algorithm with permutation that is dynamically related to plaintext pixels was proposed. In the scrambling stage, the position of the first scrambled pixel was related to the sum of the plaintext pixel values, and the positions of the remaining scrambled pixels were related to the pixel values after the previous scrambling. The scrambling operation also had a certain diffusion effect. In the diffusion phase, using the same chaotic sequence as in the scrambling stage increased the usage rate of the hyperchaotic sequence and improved the calculation efficiency of the algorithm. A large number of experimental simulations and cryptanalyses were performed, and the results proved that the algorithm had outstanding security and extremely high encryption efficiency. In addition, LF-NCHM could effectively resist statistical analysis attacks, differential attacks and chosen-plaintext attacks.

A Novel Asymmetric Hyperchaotic Image Encryption Scheme Based on Elliptic Curve Cryptography

“…Moreover, Table 4 displays the results of the number of pixel change rate (NPCR) and unified average changing intensity (UACI) values in this paper and other references. It is evident to see that from the comparison result, the NPCR results performs better than [20,34,37,38], and inferior to [1,33], but for the UACI results, the value in our algorithm is closer to the theoretical value than for any other algorithms. Considering all these three implications, the algorithm proposed here performs well in resisting the differential attacks.…”

“…From the table we can see that the algorithm we proposed performs with better time efficiency and consumes fewer machine cycles. Compared with the block-based scheme in [38], our scheme improved the security with the exchange of the speed, while the time efficiency is enhanced from the comparison with the pixel-level algorithm in [33] and the bit-level algorithms in [21,37]. Considering the results from the comparison, our algorithm performed excellently in both time efficiency and security aspects.…”

“…For the encryption schemes based on chaotic systems, the corresponding chaotic systems play an important role in generating the pseudorandom sequences for permutation and diffusion. Due to the better pseudo-randomness and higher unpredictability, the logistic Feigenbaum non-linear cross-coupled hyperchaotic map (LF-NCHM) proposed by the authors of [33] is used here. The mathematical expression is shown in (1), where the parameter µ ∈ (0, 4].…”

“…In the whole operation, the spread process is from the botom to the top, and from the right to the left, which means after the present pixel is relevant to its lower and right neighbors. The details of the operation based on [33] are as follows:…”

“…Table 6 shows the encryption time of our algorithm and some other algorithms in [33,37,38], and the comparison of the EF and the number of cycles is revealed in Table 7.…”