Fast Finite Field Orthogonal Transform without length constraint

In this paper, we propose a new family orthogonal transforms defined over finite field called the Finite Field Orthogonal Transforms (FFOT). Unlike the traditional Number Theoretic Transform (NTT) that the relationship between the transform length and the field moduli has specific constraint in order to hold the orthogonality property, the FFOT has no such constraint so that the signal word length need not be limited by the transform length. In addition, the fast algorithm implementation like radix-2 Cooley-Tukey algorithm is also realizable for the FFOT and is suitable for fast data encryption.