# A Novel Fractional Sine Chaotic Map and Its Application to Image Encryption and Watermarking
###### Abstract  
This article addresses the telecommunications industry's priority of ensuring information security during the transition to next-generation networks. It proposes an image encryption system that combines watermarking techniques and a discrete fractional sine chaotic map. The authors also incorporate the principles of blockchain to enhance the security of transmitted and received image data. The proposed system utilizes a newly developed sine chaotic map with a fractional difference operator, exhibiting long-term chaotic dynamics. The complexity of this map is demonstrated by comparing it with three other fractional chaotic maps from existing literature, using bifurcation diagrams and the largest Lyapunov exponent. The authors also show the map's sensitivity to changes in initial conditions through time-series diagrams. To encrypt images, the authors suggest a method involving watermarking of two secret images and encryption based on blockchain technology. The cover image is watermarked with the two hidden images using discrete wavelet transformations. Then, the image pixels undergo diffusion using a chaotic matrix generated from the discrete fractional sine chaotic map. This encryption process aims to protect the image data and make it resistant to unauthorized access. To evaluate the algorithm, the authors perform statistical analysis and critical sensitivity analysis to examine its characteristics. They also analyse different attacks to assess the algorithm's ability to resist such threats and maintain image quality after decryption. The results demonstrate that the proposed algorithm effectively defends against attacks and ensures image security. discretized calculus; chaotic map; bifurcation; image encryption; blockchain 2023  
security is blockchain. Industries are exploring blockchain for secure record-keeping, as it replaces centralized systems with decentralized ones involving only the relevant parties in a transaction. Blockchain technology is not limited to financial transactions; it is used for energy transfers between neighbours, copyright verifications in the media industry, and supply chain management. Many industries are embracing blockchain technology due to its advantages. The working process of blockchain can be explained in simple terms. Transaction data, including details of the parties, conditions, and assets exchanged, are recorded. Consensus is reached among the participants, and the information is securely stored as a block, forming a chain. A final ledger copy is shared with all participants. Emerging technologies have encouraged industries to explore new methods for enhancing security and overcoming limitations. Blockchain technology offers high security, making it difficult for unauthorized changes to be made to transaction records. It also improves efficiency, transparency, and allows for quick data auditing. Researchers have explored the application of blockchain in secure image sharing [1] and its integration with the Internet of Things (IoT) [2]. Image encryption is a vast field with contributions from researchers across various disciplines. In simple terms, image encryption involves converting an image into an encrypted form using a secret key. The encrypted image is then decrypted by the receiver using the same secret key, but in reverse order. The key used in encryption is of utmost importance. Typically, there are two types of keys: private and public. A private key is a unique key used for both encryption and decryption processes, while public keys consist of separate keys for encryption and decryption. The literature on image encryption encompasses a wide range of algorithms developed to address security requirements. These algorithms aim to protect the confidentiality and integrity of images during transmission and storage. Some methods include the techniques of watermarking [3], steganography [4] and scrambling of images [5]. Over the past few decades, there has been a growing interest in utilizing chaotic systems for cryptography.