3 research outputs found
On isotopisms of commutative presemifields and CCZ-equivalence of functions
A function from \textbf{F} to itself is planar if for any \textbf{F} the function is a permutation. CCZ-equivalence is the most general known equivalence relation of functions preserving planar property. This paper considers two possible extensions of CCZ-equivalence for functions over fields of odd characteristics, one proposed by Coulter and Henderson and the other by Budaghyan and Carlet. We show that the second one in fact coincides with CCZ-equivalence, while using the first one we generalize one of the known families of PN functions. In particular, we prove that, for any odd prime and any positive integers and , the indicators of the graphs of functions and from \textbf{F} to \textbf{F} are CCZ-equivalent if and only if and are CCZ-equivalent.
We also prove that, for any odd prime , CCZ-equivalence of functions from \textbf{F} to \textbf{F}, is strictly more general than EA-equivalence when and is greater or equal to the smallest positive divisor of different from 1
cc-differential uniformity, (almost) perfect cc-nonlinearity, and equivalences
In this article, we introduce new notions -differential uniformity,
-differential spectrum, PccN functions and APccN functions, and investigate
their properties. We also introduce -CCZ equivalence, -EA equivalence,
and -equivalence. We show that -differential uniformity is invariant
under -equivalence, and -differential uniformity and -differential
spectrum are preserved under -CCZ equivalence. We characterize
-differential uniformity of vectorial Boolean functions in terms of the
Walsh transformation. We investigate -differential uniformity of power
functions . We also illustrate examples to prove that -CCZ
equivalence is strictly more general than -EA equivalence.Comment: 18 pages. Comments welcom