  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.
