Discrete one-dimensional piecewise chaotic systems without fixed points

Acknowledgements The authors are thankful to the anonymous reviewers for their constructive feedback.Peer reviewe

Authenticated public key elliptic curve based on deep convolutional neural network for cybersecurity image encryption application

The demand for cybersecurity is growing to safeguard information flow and enhance data privacy. This essay suggests a novel authenticated public key elliptic curve based on a deep convolutional neural network (APK-EC-DCNN) for cybersecurity image encryption application. The public key elliptic curve discrete logarithmic problem (EC-DLP) is used for elliptic curve Diffie–Hellman key exchange (EC-DHKE) in order to generate a shared session key, which is used as the chaotic system’s beginning conditions and control parameters. In addition, the authenticity and confidentiality can be archived based on ECC to share the (Formula presented.) parameters between two parties by using the EC-DHKE algorithm. Moreover, the 3D Quantum Chaotic Logistic Map (3D QCLM) has an extremely chaotic behavior of the bifurcation diagram and high Lyapunov exponent, which can be used in high-level security. In addition, in order to achieve the authentication property, the secure hash function uses the output sequence of the DCNN and the output sequence of the 3D QCLM in the proposed authenticated expansion diffusion matrix (AEDM). Finally, partial frequency domain encryption (PFDE) technique is achieved by using the discrete wavelet transform in order to satisfy the robustness and fast encryption process. Simulation results and security analysis demonstrate that the proposed encryption algorithm achieved the performance of the state-of-the-art techniques in terms of quality, security, and robustness against noise- and signal-processing attacks

Analysis and Design Security Primitives Based on Chaotic Systems for eCommerce

Security is considered the most important requirement for the success of electronic commerce, which is built based on the security of hash functions, encryption algorithms and pseudorandom number generators. Chaotic systems and security algorithms have similar properties including sensitivity to any change or changes in the initial parameters, unpredictability, deterministic nature and random-like behaviour. Several security algorithms based on chaotic systems have been proposed; unfortunately some of them were found to be insecure and/or slow. In view of this, designing new secure and fast security algorithms based on chaotic systems which guarantee integrity, authentication and confidentiality is essential for electronic commerce development. In this thesis, we comprehensively explore the analysis and design of security primitives based on chaotic systems for electronic commerce: hash functions, encryption algorithms and pseudorandom number generators. Novel hash functions, encryption algorithms and pseudorandom number generators based on chaotic systems for electronic commerce are proposed. The securities of the proposed algorithms are analyzed based on some well-know statistical tests in this filed. In addition, a new one-dimensional triangle-chaotic map (TCM) with perfect chaotic behaviour is presented. We have compared the proposed chaos-based hash functions, block cipher and pseudorandom number generator with well-know algorithms. The comparison results show that the proposed algorithms are better than some other existing algorithms. Several analyses and computer simulations are performed on the proposed algorithms to verify their characteristics, confirming that these proposed algorithms satisfy the characteristics and conditions of security algorithms. The proposed algorithms in this thesis are high-potential for adoption in e-commerce applications and protocols

Image Encryption Algorithm Based on DNA Encoding and Chaotic Maps

We propose a new image encryption algorithm based on DNA sequences combined with chaotic maps. This algorithm has two innovations: (1) it diffuses the pixels by transforming the nucleotides into corresponding base pairs a random number of times and (2) it confuses the pixels by a chaotic index based on a chaotic map. For any size of the original grayscale image, the rows and columns are fist exchanged by the arrays generated by a logistic chaotic map. Secondly, each pixel that has been confused is encoded into four nucleotides according to the DNA coding. Thirdly, each nucleotide is transformed into the corresponding base pair a random number of time(s) by a series of iterative computations based on Chebyshev’s chaotic map. Experimental results indicate that the key account of this algorithm is 1.536 × 10127, the correlation coefficient of a 256 × 256 Lena image between, before, and after the encryption processes was 0.0028, and the information entropy of the encrypted image was 7.9854. These simulation results and security analysis show that the proposed algorithm not only has good encryption effect, but also has the ability to repel exhaustive, statistical, differential, and noise attacks

Pseudo-random bit generator based on multi-modal maps

"In this work we present a pseudo-random Bit Generator via unidimensional multi-modal discrete dynamical systems calledk-modal maps. These multi-modal maps are based on the logistic map and are useful to yield pseudo-random sequences with longer period, i.e., in order to attend the problem of periodicity. In addition the pseudo-random sequences generated via multi-modal maps are evaluated with the statistical suite of test from NIST and satisfactory results are obtained when they are used as key stream. Furthermore, we show the impact of using these sequences in a stream cipher resulting in a better encryption quality correlated with the number of modals of the chaotic map. Finally, a statistical security analysis applied to cipher images is given. The proposed algorithm to encrypt is able to resist the chosen-plaintext attack and differential attack because the same set of encryption keys generates a different cipher image every time it is used.