Motivated by today’s huge volume of data that needs to be handled in secrecy, there is a wish to develop not only fast and light but also reliably secure cryptosystems. Chaos allows for the creation of pseudo-random numbers (PRNs) by low-dimensional transformations that need to be applied only a small number of times. These two properties may translate into a chaos-based cryptosystem that is both fast (short running time) and light (little computational effort). What we propose here is an approach to generate PRNs—and consequently digital secret keys—that can serve as a seed for an enhanced chaos-based cryptosystem. We use low-dimensional chaotic maps to quickly generate PRNs that have little correlation, and then, we quickly (“fast”) enhance secrecy by several orders (“reliability”) with very little computational cost (“light”) by simply looking at the less significant digits of the initial chaotic trajectory. This paper demonstrates this idea with rigor, by showing that a transformation applied a small number of times to chaotic trajectories significantly increases its entropy and Lyapunov exponents, as a consequence of the smoothing out of the probability density towards a uniform distribution.

受当今需要保密处理的大量数据的影响，人们希望不仅开发快速，轻便而且可靠的安全密码系统。混沌允许通过低维变换创建伪随机数（PRN），只需将其应用几次即可。这两个属性可能会转换为基于混沌的密码系统，该系统既快速（运行时间短）又轻巧（计算量小）。我们在这里提出的是一种生成PRN的方法，从而生成数字秘密密钥，可以用作增强型基于混沌的密码系统的种子。我们使用低维混沌图来快速生成几乎没有相关性的PRN，然后，我们只需简单地查看初始混沌轨迹的较低有效数字，就可以以很少的计算成本（“轻”）快速（“快速”）将保密性提高几个数量级（“可靠性”）。本文通过严格地证明这一思想，表明通过对混沌轨迹应用少量变换可以显着增加其熵和Lyapunov指数，这是由于将概率密度平滑化为均匀分布的结果。