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In this paper, we study reversibility of one-dimensional(1D) linear cellularautomata(LCA) under null boundary condition, whose core problems have beendivided into two main parts: calculating the period of reversibility andverifying the reversibility in a period. With existing methods, the time andspace complexity of these two parts are still too expensive to be employed. Sothe process soon becomes totally incalculable with a slightly big size, whichgreatly limits its application. In this paper, we set out to solve these twoproblems using two efficient algorithms, which make it possible to solvereversible LCA of very large size. Furthermore, we provide an interestingperspective to conversely generate 1D LCA from a given period of reversibility.Due to our methods' efficiency, we can calculate the reversible LCA with largesize, which has much potential to enhance security in cryptography system.

Efficient methods to determine the reversibility of general 1D linear cellular automata in polynomial complexity