An Equivalent Representation of Generalized Differentials
By: Valentin Suder
Potential Business Impact:
Finds math patterns for secret codes.
We propose an equivalent formula for the higher-order derivatives used in the study of Generalized Almost Perfect Nonlinear functions over an arbitrary finite field of characteristic $p$. The result is obtained by counting the number of subsets of the prime field with a fixed cardinality for which the sum of their elements is constant. We then ask related questions regarding the diversity of higher-order derivatives.
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