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Despite having many similar characteristics with cryptography, existing chaotic systems have many security issues that negatively affect the chaos-based cryptographic algorithms that utilize them. This paper proposes a new chaotification method that enhances the chaotic complexity of existing chaotic maps to surmount these issues. The proposed method uses a cosine function alongside a chaotic map in a cascade system. To depict its advantages, we apply it to enhance logistic and Henon maps before analyzing their chaotic properties. Results and comparisons indicate that the new chaotic maps have a wider chaotic range, elevated sensitivity, complex characteristics, high nonlinearity, and an extended cycle length as compared to the original (seed) maps as well as other chaotic maps. We then utilize the modified maps (and their corresponding seed maps) to design simple pseudorandom number generators to study their feasibility when used in cryptographic algorithms. We perform comparisons between the generators derived from both the original and seed maps. Results show that generators based on the new maps outperform their seed counterparts in nearly every aspect. This finding demonstrates the capability of the proposed method in improving the performance of chaos-based cryptographic algorithms.

Image watermarking schemes based on singular value decomposition (SVD) have become popular due to a good trade-off between robustness and imperceptibility. However, the false positive problem (FPP) is the main drawback of SVD-based watermarking schemes. The singular value is the main cause of FPP issues because it a fixed value that does not hold structural information of an image. In this paper, a new SVD-based image watermarking scheme that uses a chaotic map is proposed to overcome this issue. The secret key is first extracted from both the host and watermark image. This key is used to generate a new chaotic matrix and chaotic multiple scaling factors (CMSF) to increase the sensitivity of the proposed scheme. The watermark image is then transformed based on the chaotic matrix before being directly embedded into the singular value of the host image by using the CMSF. The extracted secret key is unique to the host and the watermark images, which improves security and overcomes FPP issues. Experimental results show that the proposed scheme fulfils all watermarking requirements in terms of robustness, imperceptibility, security, and payload. Furthermore, it achieves high robustness with different scaling factors, and outperforms several existing schemes.

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