# On the Differential Properties of the Power Mapping x^p^m+2

Let m be a positive integer and p a prime. In this paper, we investigate the differential properties of the power mapping x^p^m+2 over š½_p^n, where n=2m or n=2m-1. For the case n=2m, by transforming the derivative equation of x^p^m+2 and studying some related equations, we completely determine the differential spectrum of this power mapping. For the case n=2m-1, the derivative equation can be transformed to a polynomial of degree p+3. The problem is more difficult and we obtain partial results about the differential spectrum of x^p^m+2.

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