Improved One-Dimensional Piecewise Chaotic Maps for Information Security Ichraf Aouissaoui 1 , Toufik Bakir 2 , Anis Sakly 1 , and Smain Femmam 3 1 Laboratory LAESE, ENIM, University of Monastir, Monastir 5000, Tunisia 2 Laboratory ImVia, EA 7535, Dijon 21000, France 3 Haute-Alsace University, Strasbourg, France Email: ichraf.aouissaoui@enim.u-monastir.tn; Toufik.bakir@u-bourgogne.fr; anis.sakly@yahoo.fr; smain.femmam@uha.fr Abstract—Chaos represents interesting features that are suitable for the cryptography domain. One-dimensional chaotic maps are widely used for security issues due to their simplicity and chaotic behavior versus other multidimensional chaotic maps that can be complex for hardware implementation and hard to analyze. However, classical one-dimensional chaotic maps present a reduced range of chaotic behavior. In this paper, we propose two new piecewise compound one-dimensional chaotic maps; an Altered Sine-Logistic map based on Tent map (ASLT) and a combined Cubic-Tent map (CT). The proposed compound maps combine classical and simple one-dimensional chaotic maps to produce an extensive range of chaotic behavior. The ASLT system comprises a combined Sine-Tent map in the first piece of the function and a combined Logistic-Tent map in the second piece of the function. Then, the CT map is based on the nonlinear fusion operation between the Cubic map and the piecewise Tent map. Simulation results and chaotic behavior analysis are provided using the bifurcation diagram, Lyapunov exponent, initial sensitivity, and Shannon entropy measure. The evaluation results demonstrate the effectiveness of the proposed 1D maps with better chaotic performances, chaotic range, and complexity compared to their corresponding classical chaotic maps. The simple structure and effectiveness of the proposed systems make them suitable for chaos-based cryptography providing better security strength and more randomness. Index Terms—Chaotic map, chaotic range, Lyapunov exponent, bifurcation diagram, Initial sensitivity I. INTRODUCTION Nowadays, information security represents an important requirement with the advancement in communication and technology. In particular, the security of the transmitted images, which include personal information. Various image encryption schemes have been introduced in order to ensure real-time secure image transmission. In the past two decades, there has been a significant interest in the chaotic system and its use for image cryptography [1]–[5] among various encryption methods due to its interesting properties, such as initial sensitivity, pseudo-randomness, and unpredictability. In particular, standard 1D chaotic systems are widely used because of their simplicity and dynamic behavior. However, they are not secure and cannot resist many well-known attacks such as chosen-plaintext attack, known-plaintext attack, brute force attack because of their limited and interrupted chaotic range, low chaotic complexity, and higher dynamic behavior degradation rate [4]. Therefore, researchers aim to improve the chaotic properties of the 1D chaotic map by combining standard ones to provide better security strength and more randomness [4], [6]–[9]. Zhu et al. proposed a new compound chaotic system based on Sine and Tent chaotic maps (STS) to extend the chaotic range and increase the chaotic performance of 1D discrete chaotic maps [10]. The new 1D map is used to generate S-boxes then double S-boxes are used for image encryption purposes making the cryptosystem more secure and reducing the time cost. Wang et al. introduced a new and improved 1D sinusoidal chaotic map (I1DS) for image encryption. The proposed map combines standard and simple one-dimensional chaotic maps (Logistic and Sine) [6]. The chaotic behavior of the new chaotic map is improved, but it is still not chaotic at some points in the range [0,1]. Zhu et al. proposed a new combination of Logistic and Tent chaotic maps to produce chaotic sequences [11]. Then the combined map with a proposed fitness function is used to generate an efficient S-box, which will be used for image encryption. Farah et al. proposed a new hybrid chaotic map that exhibits an excellent randomness performance and sensitivity. The new chaotic map is composed of the Logistic map, Tent map, and Sine map [12]. It presents high values of Lyapunov exponents and Shannon entropy. Li et al. proposed Compressive Sensing (CS) based image compression, authentication, and encryption in the cloud [1]. For that, a new Logistic-Tent-Sine chaotic map (LTSS) is proposed; the proposed map has a more extensive chaotic range and better chaotic behavior than standard 1D chaotic maps. The LTSS is used to construct a Binary Data Cyclic Encryption algorithm (BDCE) chaotic stream cipher for encrypting the low-frequency part of images. This paper proposes new combined one-dimensional chaotic maps based on the standard 1D chaotic maps. The first map is based on altering the Sine and the Logistic map into the piecewise Tent map (ASLT). Furthermore, the second 1D proposed chaotic map is the Cubic-Tent map (CT), it is based on the Cubic and the Tent maps. The Journal of Communications Vol. 17, No. 1, January 2022 ©2022 Journal of Communications 11 Manuscript received July 7, 2021; revised December 21, 2021. Corresponding author email: ichraf.aouissaoui@enim.u-monastir.tn doi:10.12720/jcm.17.1.11-16