CCZ-equivalence of bent vectorial functions and related constructions
Lilya Budaghyan, Claude Carlet · Designs Codes and Cryptography · 2011
We observe that the CCZ-equivalence of bent vectorial functions over $${{\bf F}_2^n}$$ (n even) reduces to their EA-equivalence. Then we show that in spite of this fact, CCZ-equivalence can be used for constructing bent functions which are new up to EA-equivalence and therefore to CCZ-equivalence: applying CCZ-equivalence to a non-bent vectorial function F which has some bent components, we get a function F′ which also has some bent components and whose bent components are CCZ-inequivalent to the components of the original function F. Using this approach we construct classes of nonquadratic bent Boolean and bent vectorial functions.