Correlation-immune and resilient functions over a finite alphabet and their applications in cryptography
Correlation-immune functions and resilient functions are known to be important concepts for some applications in cryptography. In the paper the notions of correlation-immune functions and resilient functions are extended to functions over any finite alphabet; also some other results are given as well. First, three characterizations of correlation-immune functions over a finite alphabet are given. An orthogonal array characterization, a characterization by means of characters and a matrix characterization are presented. Then the properties of the algebraic normal form of correlation-immune functions over a finite field are investigated and construction of \(t\)-resilient functions with optimal nonlinearity order over any finite field is given. The next section is devoted to the construction of new correlation-immune functions by composition of correlation-immune functions of smaller order. Finally links between correlation-immune functions and several other cryptographic notions like perfect local randomizers or multipermutations are explored.
scientific article; zbMATH DE number 1332720