On full differential uniformity of permutations on the ring of integers modulo n
Applicable Algebra in Engineering, Communication and Computing, 2023•Springer
In this paper, we report some interesting results on permutations on Z _ n Z n, the ring of
integers modulo n, having full differential uniformity. By full differential uniformity of a
permutation f on Z _ n Z n, we mean that the cardinality of the set {x ∈ Z _ n: f (x+ a)-f (x)= b\}
x∈ Z n: f (x+ a)-f (x)= b is exactly n for some a, b ∈ Z _ n ∖ {0\} a, b∈ Z n {0. We give a
sufficient condition for an arbitrary map on Z _ n Z n to have full differential uniformity. A
necessary and sufficient condition for a permutation to have full differential uniformity over …
integers modulo n, having full differential uniformity. By full differential uniformity of a
permutation f on Z _ n Z n, we mean that the cardinality of the set {x ∈ Z _ n: f (x+ a)-f (x)= b\}
x∈ Z n: f (x+ a)-f (x)= b is exactly n for some a, b ∈ Z _ n ∖ {0\} a, b∈ Z n {0. We give a
sufficient condition for an arbitrary map on Z _ n Z n to have full differential uniformity. A
necessary and sufficient condition for a permutation to have full differential uniformity over …
Abstract
In this paper, we report some interesting results on permutations on , the ring of integers modulo n, having full differential uniformity. By full differential uniformity of a permutation f on , we mean that the cardinality of the set is exactly n for some . We give a sufficient condition for an arbitrary map on to have full differential uniformity. A necessary and sufficient condition for a permutation to have full differential uniformity over the ring of integers modulo n is also given. Further, we propose an upper bound and two lower bounds on permutations with full differential uniformity on . We prove that these bounds are non-trivial bounds and give the exact number of permutations with full differential uniformity for a certain class of moduli.
Springer
以上显示的是最相近的搜索结果。 查看全部搜索结果