# Hybrid Chaotic-Based PRNG for Secure Cryptography Applications
###### Abstract  
This paper suggests a novel one-dimensional (ID) map to address the limitations of traditional chaotic 1D maps. In contrast to traditional 1D maps, the proposed map has three control parameters \(a\), \(\mu\), and \(c\), allowing it to exhibit chaotic behavior over a wide range of values. The dynamic behavior of the new 1D map was analyzed using well-known numerical methods, including the bifurcation diagram and Lyapunov exponent. Both tests showed their complex and diverse behavior. In addition, a novel image encryption scheme was devised using the new function as its pseudorandom number generator. Rigorous statistical testing was applied to the proposed encryption algorithm. The mean square error (MSE) and peak signal-to-noise ratio (PSNR) results, in addition to subjecting 28 images to number of pixels change rate (NPCR) and unified average changing intensity (UACI) tests demonstrated the robustness of the system. The results of this study demonstrate the effectiveness of the new 1D map for use in secure image cryptography applications, providing a more robust and secure alternative to traditional chaotic 1D maps. c 2023 13 7768 2023 13 77  
is a more complex method that allows computations to be performed on encrypted data without the need for decryption [7], which is primarily meant for noncryptographers. The process of encryption is commonly judged by how strong the proposed method is in terms of protection against different types of attacks [8; 9]. It involves the use of an encryption mechanism using an encryption key, a communication channel for data transmission, a decryption system, and a key to decrypt the encrypted data. The strength of an encryption system is determined by the attributes of the key, such as its secrecy, difficulty to guess, and ability to withstand against an exhaustive search [10]. Each of these methods has its own benefits and limitations, and the appropriate method depends on the specific requirements and circumstances of each application [11; 12]. The security of an encryption scheme is closely linked to the characteristics of the key the scheme uses. For an unbreakable scheme, the key should be truly random, suitable for one use only, and should be of the same length as the message, also called a one-time pad (OTP). However, these properties also have drawbacks. For instance, transmitting a key that is too long over a secure channel may not be practical, and it may make more sense to send the message itself through it. Furthermore, if the same key is utilized twice, the adversary may use XOR or frequency analysis to obtain information about the messages, and create a straightforward running key cipher in disguise. Despite the importance of the strength of the key, other critically essential factors should be taken into account, including a novel chaotic oscillator for the overall performance of a novel encryption system [13] covering potential perspectives of the proposed PRNG. The results are produced in the form of the cipher versions of images. These include the computational complexity of the mathematics representation, the size of the generated key, and the unpredictable nature of the generated sequencing. In addition, the efficiency and practicality of an encryption algorithm should also be considered, as should the availability of the necessary computational resources and the ease of key management. In particular, under the exceptional circumstances of COVID-19 [14], the tokens shuffling approach (TSA) was introduced for better reliability during the pandemic. Cryptologists use chaotic functions due to their simple mathematical representation and randomness [15] by applying the proposed algorithm to some original images to be reconstructed subsequently, achieving remarkable results in screening colonoscopy images through neural networks (NN) [16].