Increasing Degree of Ternary Bent Functions

Binary bent functions are often used as a basis for deriving cryptographically interesting sequences. For instance, such sequences are used to secure safe communication among unsafe channels. Ternary bent functions are a mathematically interesting object defined as a direct extension of the concept by referring to definition of binary bent functions in terms of Walsh spectral coefficients. The degree of ternary bent functions is defined as the largest sum of powers of variables in a term in their Generalized Positive-polarity Reed-Muller expressions for ternary functions. In cryptography, the corresponding expression for the binary case is also called the Algebraic Normal Form (ANF). It is supposed that bent functions with larger degrees are more suitable for practical applications. We present a way to increase the degree of ternary bent functions by using a particular class of FFT-like permutation matrices implementing certain well suited substitutions of variables.