In this paper, we propose a new real one-dimensional cosine fractional (1-DCF) chaotic map. Several chaos-theory analysis tests demonstrate that the proposed map has many good cryptography properties, such as a highly chaotic behavior, a large chaotic range, an infinite number of unstable fixed points, and a widely superior sensitivity to the initial conditions than most of the low-dimensional chaotic maps. Regarding these attractive features, we use the 1-DCF map to design a novel fast image encryption scheme for real-time image processing. Unlike most of the existing encryption schemes, we adopt a permutation-less architecture to increase the encryption speed. Regardless of the permutation phase absence, a high-security level is obtained by using a substitution process with a high sensitivity to the plain image. Moreover, we replace the natural row-order encryption with a more secure random-like encryption order generated from the secret key. Experimentation and simulations show that the new scheme is better than many recently proposed encryption schemes in both security and rapidity.

中文翻译：

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一种新的一维混沌映射及其在新的无排列图像加密方案中的应用

在本文中，我们提出了一种新的实一维余弦分数 (1-DCF) 混沌映射。一些混沌理论分析测试表明，所提出的映射具有许多良好的密码学特性，例如高度混沌行为、大混沌范围、无限数量的不稳定不动点以及对初始条件的敏感性远优于大多数算法。低维混沌图。针对这些吸引人的特征，我们使用 1-DCF 映射设计了一种新颖的快速图像加密方案，用于实时图像处理。与大多数现有加密方案不同，我们采用无排列架构来提高加密速度。不管置换阶段是否存在，通过使用对普通图像具有高敏感性的替代过程来获得高安全级别。而且，我们用从密钥生成的更安全的类似随机的加密顺序替换了自然的行顺序加密。实验和模拟表明，新方案在安全性和快速性方面都优于最近提出的许多加密方案。