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In this paper, we present several new constructions of differentially4-uniform permutations over $\F_{2^{2m}}$ by modifying the values of theinverse function on some subsets of $\F_{2^{2m}}$. The resulted differentially4-uniform permutations have high nonlinearities and algebraic degrees, whichprovide more choices for the design of cryptographic substitution boxes.

Further results on differentially 4-uniform permutations over $\F_{2^{2m}}$