An S-box is the most important part of a symmetric encryption algorithm. Various schemes are put forward by using chaos theory. In this paper, a construction method of S-boxes with good cryptographic properties is proposed. The output of an S-box can be regarded as a group of Boolean functions. Therefore, we can use the different properties of chaos and Bent functions to generate a random Bent function with a high nonlinearity. By constructing a set of Bent functions as the output of an S-box, we can create an S-box with good cryptological properties. The nonlinearity, differential uniformity, strict avalanche criterion and the independence criterion of output bits are then analyzed and tested. A security analysis shows that the proposed S-box has excellent cryptographic properties.
We propose an adaptive radial basis (RBF) neural network controller based on Lyapunov stability theory for uncertain fractional-order time-delay chaotic systems (FOTDCSs) with different time delays. The controller does not depend on the system model and can achieve synchronous control under the condition that nonlinear uncertainties and external disturbances are completely unknown. Stability analysis showed that the error system asymptotically tended to zero in combination with the relevant lemma. Numerical simulation results show the effectiveness of the controller.
In recent years, side-channel analysis technology has been one of the greatest threats to information security. SCA decrypts the key information in the encryption device by establishing an appropriate leakage model. As one of many leakage models, the XOR operation leakage proposed by linear regression has typical representative significance in side-channel analysis. However, linear regression may have the problem of irreversibility of a singular matrix in the modeling stage of template analysis and the problem of poor data fit in the template analysis after the cryptographic algorithm is masked. Therefore, this paper proposes a second-order template analysis method based on orthogonal transformation nonlinear regression. The irreversibility of a singular matrix and the inaccuracy of the model are solved by orthogonal transformation and adding a negative direction to the calculation of the regression coefficient matrix. In order to verify the data fitting effect of the constructed template, a comparative experiment of template analysis based on regression, Gaussian, and clustering was carried out on SAKURA-G. The experimental results show that the second-order template analysis based on orthogonal transformation nonlinear regression can complete key recovery without sacrificing the performance of regression estimation. Under the condition of high noise and high order template analysis, the established template has good universality.
Chaos is considered as a natural candidate for encryption systems owing to its sensitivity to initial values and unpredictability of its orbit. However, some encryption schemes based on low-dimensional chaotic systems exhibit various security defects due to their relatively simple dynamic characteristics. In order to enhance the dynamic behaviors of chaotic maps, a novel 3D infinite collapse map (3D-ICM) is proposed, and the performance of the chaotic system is analyzed from three aspects: a phase diagram, the Lyapunov exponent, and Sample Entropy. The results show that the chaotic system has complex chaotic behavior and high complexity. Furthermore, an image encryption scheme based on 3D-ICM is presented, whose security analysis indicates that the proposed image encryption scheme can resist violent attacks, correlation analysis, and differential attacks, so it has a higher security level.
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