Browsing by Subject "3D watermarks"
  • Publication
    New families of 3D watermarks
    ( 2020-07) Bustillo-Zárate, Alcibíades De Asís ; Bollman, Dorothy ; College of Engineering ; Rivera-Gallego, Wilson ; Schütz-Schmuck, Marko ; Ortiz-Ubarri, José ; Mégret, Rémi ; Department of Computer Science and Engineering ; Colón-Reyes, Omar
    In recent years researchers have developed families of 3D watermarks that are built by composition, using a base array and a periodic sequence of shifts. Multidimensional arrays that are constructed by composition of a base array and a suitably chosen sequence of shifts preserve the correlation properties of the base array. If the base array has good auto-correlation properties, the multidimensional array and appropriately defined family members will preserve the same properties. This motivates us to see what happens if we build 3D watermarks by composition using as a base array 2D Legendre arrays and as a sequence of row-column shifts derived from a cyclic group of elements in Fp × Fp. We use scalar multiples of these shifts to generate families of 3D watermarks. For the shifts we consider two types of cyclic groups, the multiplicative group of Fp2 and a cyclic group of points on an elliptic curve over Fp. The 3D watermarks constructed in this work have good correlation values with peak values considerably larger than non-peak values, only two nonpeak values for constructions that use shifts derived from Fp2 and a maximum of 4 non-peak values using shifts derived from points on an elliptic curve. In the case of constructions using shifts derived from points on an elliptic curve, the number of correlation values is determined by the number of repeated differences between certain pairs of shifts, which in turn is determined by the number of solutions of systems of equations generated by the formulas for point additions. We compute the values of linear complexity for some 3D watermarks constructed by our methods and we show that these values compare favorably with the linear complexity values for other known arrays constructed by composition. Finally, we show an example of how to use this type of 3D watermarks in video watermarking.