Abstract
Let m be a positive integer and p a prime. In this paper, we investigate the differential properties of the power mapping xpm+2 over Fpn, where n=2m or n=2m−1. For the case n=2m, by transforming the derivative equation of xpm+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 higher degree p+3. The problem is more difficult and we only obtain partial results about the differential spectrum of xpm+2.
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