Title :
Classes of Quadratic APN Trinomials and Hexanomials and Related Structures
Author :
Budaghyan, Lilya ; Carlet, Claude
Author_Institution :
Univ. of Bergen, Bergen
fDate :
5/1/2008 12:00:00 AM
Abstract :
A method for constructing differentially 4-uniform quadratic hexanomials has been recently introduced by J. Dillon. We give various generalizations of this method and we deduce the constructions of new infinite classes of almost perfect nonlinear quadratic trinomials and hexanomials from F22m to F22m. We check for m = 3 that some of these functions are CCZ-inequivalent to power functions.
Keywords :
cryptography; functions; polynomials; almost perfect nonlinear trinomials; cryptanalysis; differentially 4-uniform quadratic hexanomials; infinite classes; polynomials; power functions; quadratic APN trinomials; Boolean functions; Differential equations; Gold; Informatics; Mathematics; Nonlinear equations; Polynomials; Affine equivalence; CCZ-equivalence; S-box; almost bent; almost perfect nonlinear; differential uniformity; nonlinearity; vectorial Boolean function;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2008.920246
