Construction Method and Performance Analysis of Chaotic S-Box Based on a Memorable Simulated Annealing Algorithm

The substitution box (S-box) is the only nonlinear components in the symmetric block cipher. Its performance directly determines the security strength of the block cipher. With the dynamic characteristics degradation and the local periodic phenomenon of digital chaos, and the security problems caused by them becoming more and more prominent, how to efficiently generate an S-box with security guarantee based on chaos has gradually attracted the attention of cryptographers. In this paper, a chaotic S-box construction method is proposed based on a memorable simulated annealing algorithm (MSAA). The chaotic S-box set is produced by using the nonlinearity and randomness of the dynamic iteration of digital cascaded chaotic mapping. The composite objective function is constructed based on the analysis of the performance indexes of S-box. The MSAA is used to efficiently optimize the S-box set. The matrix segmentation and scrambling operations are carried out on the optimized S-box. The cryptographic performance of chaotic S-box is tested and analyzed, and compared with the mainstream chaotic S-box of the same kind. The results show that the S-box constructed in this paper can not only stably and efficiently generate chaotic S-box with better performance, but also make an effective exploration of the construction of chaotic S-boxes based on intelligent algorithms.

Novel Models of Image Permutation and Diffusion Based on Perturbed Digital Chaos

Most of chaos-based cryptosystems utilize stationary dynamics of chaos for the permutation and diffusion, and many of those are successfully attacked. In this paper, novel models of the image permutation and diffusion are proposed, in which chaotic map is perturbed at bit level on state variables, on control parameters or on both. Amounts of perturbation are initially the coordinate of pixels in the permutation, the value of ciphered word in the diffusion, and then a value extracted from state variables in every iteration. Under the persistent perturbation, dynamics of chaotic map is nonstationary and dependent on the image content. The simulation results and analyses demonstrate the effectiveness of the proposed models by means of the good statistical properties of transformed image obtained after just only a single round.

Suggested Integral Analysis for Chaos-Based Image Cryptosystems

Currently, chaos-based cryptosystems are being proposed in the literature to provide confidentiality for digital images, since the diffusion effect in the Advance Encryption Standard (AES) algorithm is weak. Security is the most important challenge to assess in cryptosystems according to the National Institute of Standard and Technology (NIST), then cost and performance, and finally algorithm and implementation. Recent chaos-based image encryption algorithms present basic security analysis, which could make them insecure for some applications. In this paper, we suggest an integral analysis framework related to comprehensive security analysis, cost and performance, and the algorithm and implementation for chaos-based image cryptosystems. The proposed guideline based on 20 analysis points can assist new cryptographic designers to present an integral analysis of new algorithms. Future comparisons of new schemes can be more consistent in terms of security and efficiency. In addition, we present aspects regarding digital chaos implementation, chaos validation, and key definition to improve the security of the overall cryptosystem. The suggested guideline does not guarantee security, and it does not intend to limit the liberty to implement new analysis. However, it provides for the first time in the literature a solid basis about integral analysis for chaos-based image cryptosystems as an effective approach to improve security.

Counteracting the Dynamical Degradation of Digital Chaos by Applying Stochastic Jump of Chaotic Orbits

The performance of digital chaotic systems in secure communications and cryptographic applications is significantly degraded due to the limited precision of digital computational devices that are used to implement digital chaotic systems. However, regardless of the initial value, the digital chaotic map employed in these applications converges to several periodic orbits. Thus, a periodic orbit search algorithm (POSA) can be designed to accurately locate fixed points and limit cycles. In addition, an effective method based on stochastic jumps of chaotic orbits is proposed to counteract the performance degradation of digital chaos. Numerical simulations were performed to assess the effectiveness and feasibility of the proposed method in terms of autocorrelation, phase space inspection, approximate entropy and periodicity analysis. Furthermore, comparison with other existing methods is presented to show the competitiveness of the proposed scheme. Finally, a pseudorandom bit generator (PRBG), with desirable statistical properties, is constructed for chaos cryptography and other applications.