利用有偏不动点简化帐篷地图的数字表示
Simplification of the digital representation of the tent map through biased fixed point
摘要：
混沌系统已经在工程的几个领域进行了研究。在控制理论中，这样的系统也促使了新技术的出现，被用作噪声产生的来源。混沌系统作为伪随机数在密码学中也得到了广泛的应用。在高性能情况下，这些应用程序的一个核心方面，例如涉及大量数据（大数据）的应用程序，是这些系统在短时间内的响应。尽管混沌系统在模拟电路中的设计取得了很大的进展，但在数字域中对这些系统的优化设计却关注较少。在这项工作中，极化固定点表示应用，以减少数字元素的数量。使用这种方法，可以显著减少减法运算中的逻辑门数量。当与文献中的其他作品相比时，帐篷地图的数字表示的每比特的元素数量减少了50%是可行的。通过计算李雅普诺夫指数证明了混沌性。利用直方图、熵和自相关检验对所代表系统的随机性进行了满意的评价。
英文摘要：
Chaotic systems have been investigated in several areas of engineering. In control theory, such systems have instigated the emergence of new techniques as well, have been used as a source of noise generation. The application of chaotic systems as pseudo-random numbers has also been widely employed in cryptography. One of the central aspects of these applications in high performance situations, such as those involving a large amount of data (Big Data), is the response of these systems in a short period of time. Despite the great advances in the design of chaotic systems in analog circuits, it is perceived less attention in the optimized design of these systems in the digital domain. In this work, the polarized fixed point representation is applied to reduce the number of digital elements. Using this approach, it was possible to significantly reduce the number of logic gates in the subtraction operation. When compared to other works in the literature, it has been viable to reduce by 50 \% the number of elements per bit of the digital representation of the tent map. The chaoticity was evidenced with the calculation of the Lyapunov exponent. Histogram, entropy and autocorrelation tests were used satisfactorily to evaluate the randomness of the represented system.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
