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- W2149336598 abstract "This paper mainly focuses on permutation polynomials over the residue class ring Z N , where N > 3 is composite. We have proved that for the polynomial f ( x ) = a 1 x + a 2 x 2 + ⋯ + a k x k with integral coefficients, f ( x ) mod N permutes Z N if and only if f ( x ) mod N permutes S μ for all μ ∣ N , where S μ = { 0 < t < N : gcd ( N , t ) = μ } for μ ≠ N and S N = { 0 } . Based on it, we give a lower bound of the differential uniformities for such permutation polynomials, that is, δ ( f ) ≥ N # S a , where a is the biggest nontrivial divisor of N . Especially, f ( x ) cannot be APN permutations over the residue class ring Z N . It is also proved that f ( x ) mod N and ( f ( x ) + x ) mod N cannot permute Z N at the same time when N is even." @default.
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- W2149336598 date "2013-12-01" @default.
- W2149336598 modified "2023-09-29" @default.
- W2149336598 title "Permutation polynomials and their differential properties over residue class rings" @default.
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- W2149336598 doi "https://doi.org/10.1016/j.dam.2013.06.020" @default.
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