A Method for Derivating an Algorithm of Power Computation of Cyclic Permutation

Permutation algorithm is widely used in numerous information technology domains such as cryptology. Any permutation can be viewed as a combination of several cyclic permutations which have no shared element. This article continues the work discussed in existing documents, reforms its part of formal derivation using dynamic programming in order to reveal essence of this algorithm. On the basisof ring representation for cyclic permutation, this article uses dynamic programming to get a bottom-up recurrence relation through a series of formal derivations. And then gets a concise middle algorithm. After that, through correlation between ring and abstract array containing a cyclic permutation, it uses an equally simple coordinate transformation to yield the final algorithm for computing positive power of cyclic permutation stored as a function in an abstract array.