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The Statuses of Lacking Distances of Exponential Transformation on Z_p-1

In this paper, we propose an exponential transformation on Zp-1 which is an extension of the exponential transformation in SAFER. We proof this kind transformation is permutation, discuss the statuses of permutation distances about this kind permutation and analyze orderliness of the lacking distances. We discover an interesting thing that is each exponential transformation lacks one distance. Ulteriorly we discuss the relation between lacking distances and the primitive in an exponential transformation on Zp-1. The lacking distances about these exponential transformations present either entirely odd or entirely even through all different generators in an exponential transformation. The lacking distance about an arbitrary primitive of Zp plus the lacking distance about the inverse of this primitive is equal to p-1 in an exponential transformation.