Watermarking based on discrete wavelet transform and q-deformed chaotic map. (November 2017)

• Record Type: Journal Article
• Authors: Behnia, S.; Yahyavi, M.; Habibpourbisafar, R.
• Is Part Of: Chaos, solitons and fractals. Volume 104(2017)
• Page Start: 6
• Page End: 17
• Publication Date: 2017-11
• Subjects: q-deformed chaotic map -- Pseudo random sequence -- Ergodicity -- Digital image watermarking -- Key space -- Security,; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2017.07.020
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: We study the dynamics of one-dimensional ergodic chaotic maps with Tsallis type of q -deformation. Invariant measure and Kolmogorov–Sinai entropy for q -deformed maps are calculated analytically. This recent model can play an important role in increasing the randomness and one-way computation. Numerical simulations reveals a increasing the key space, encryption speed and level of security. This scheme have a high potential to be adopted for real-time secure watermarking applications. Abstract: Hierarchy of one-dimensional ergodic chaotic maps with Tsallis type of q -deformation are studied. We find that in the chaotic region, these maps with q -deformation are ergodic as the Birkhoff ergodic theorem predicts. q -deformed maps are defined as ratios of polynomials of degree N . Hence, by using the Stieltjes transform approach (STA), invariant measure is proposed. In addition, considering Sinai-Ruelle-Bowen (SRB) measure, Kolmogorov-Sinai (KS) entropy for q -deformed maps is calculated analytically. The new q -deformed scheme have ability to keep previous significant properties such as ergodicity, sensitivity to initial condition. By adding q -parameter to the hierarchy in order increase the randomness and one-way computation, we present a new scheme for watermarking. The introduced algorithm tries to improve the problem of failure of encryption such as small key space, encryption speed and level of security. To illustrate the effectiveness of the proposed scheme, some security analyses are presented. By considering the obtained results, it can be concluded that, this scheme have a high potential to be adopted for watermarking. It can be concluded that, the proposed novel watermarking scheme for image authentication can be applied for practical applications.