A Note on Linear Transformations in Cryptography

Based on the definition of linear transformations, the Walsh linear spectrum and cyclic spectrum and their inverse transformations are discussed; the dual property of Bent functions is also proved; the Chrestenson linear spectrum and cyclic spectrum and their inverse transformations are discussed. Finally, it is proved that the relationship between Chrestenson linear spectrum and Chrestenson cyclic spectrum is a linear transformation; and simple proofs of the expressions in which Chrestenson linear spectrum and cyclic spectrum are linearly represented by each other are given.