多项式复杂度下判定一般一维线性元胞自动机可逆性的有效方法
Efficient methods to determine the reversibility of general 1D linear cellular automata in polynomial complexity
摘要：
本文研究了一维线性元胞自动机（LCA）在零边界条件下的可逆性问题，其核心问题分为可逆周期的计算和周期内可逆性的验证两大部分。在现有的方法中，这两部分的时间和空间复杂度仍然太昂贵而不能使用。因此，该过程很快变得完全不可计算，尺寸稍大，这极大地限制了其应用。在本文中，我们着手解决这两个问题，使用两个有效的算法，这使得有可能解决可逆的LCA非常大的尺寸。此外，我们提供了一个有趣的视角，从一个给定的可逆性周期反向生成1D LCA。由于我们的方法的效率，我们可以计算出可逆的LCA的大规模，这是很大的潜力，以提高密码系统的安全性。
英文摘要：
In this paper, we study reversibility of one-dimensional(1D) linear cellular automata(LCA) under null boundary condition, whose core problems have been divided into two main parts: calculating the period of reversibility and verifying the reversibility in a period. With existing methods, the time and space complexity of these two parts are still too expensive to be employed. So the process soon becomes totally incalculable with a slightly big size, which greatly limits its application. In this paper, we set out to solve these two problems using two efficient algorithms, which make it possible to solve reversible LCA of very large size. Furthermore, we provide an interesting perspective to conversely generate 1D LCA from a given period of reversibility. Due to our methods' efficiency, we can calculate the reversible LCA with large size, which has much potential to enhance security in cryptography system.
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