Everyday, a vast amount of information is created and shared on the internet. Security steps and methods are needed to ensure the data is sent and stored safely. Random numbers are essential to cryptography because they are crucial to securing data. In recent years, the use of chaos theory has become increasingly important in producing pseudo-random number sequences in the field of cryptography. But the majority of fundamental chaotic maps have a variety of limitations, such as constrained chaotic regions, a low Lyapunov Exponent (LE), chaotic annulling conditions, and high computational cost. In this research, we construct a new chaotic map based on the skew tent map (STM) in order to find a better solution to these problems. The proposed chaotic map includes significantly enhanced chaotic behaviour and has a more comprehensive chaotic range and higher LE. Furthermore, two novels Pseudo-random Number Generators (PRNGs) based on a new M-STM chaotic map, have been built to investigate its application in security-related fields. The performance evaluations of these generators demonstrate their ability to generate pseudo-random number sequences that exhibit improved statistical properties efficiently.

每天，大量信息在互联网上创建和共享。需要安全步骤和方法来确保数据的安全发送和存储。随机数对于密码学至关重要，因为它们对于保护数据至关重要。近年来，混沌理论的使用在密码学领域产生伪随机数序列方面变得越来越重要。但大多数基本混沌映射都存在各种局限性，例如混沌区域受限、李雅普诺夫指数 (LE) 较低、混沌无效条件以及计算成本较高。在本研究中，我们基于倾斜帐篷图（STM）构建了一种新的混沌图，以找到更好的解决这些问题的方法。所提出的混沌图包括显着增强的混沌行为，并且具有更全面的混沌范围和更高的LE。此外，还构建了两种基于新的 M-STM 混沌图的新型伪随机数生成器（PRNG），以研究其在安全相关领域的应用。这些生成器的性能评估证明了它们生成伪随机数序列的能力，这些序列有效地表现出改进的统计特性。