In this paper, we construct the dual-complex Gauss transformation and propose novel algorithms for LU decomposition and partial pivoting LU decomposition of dual-complex matrices. In addition, the Cholesky and \(\textrm{LDL}^H\) decompositions of dual-complex matrices are also obtained as special cases. Strict authentication is designed to cater to applications that have a zero-tolerance policy for any modifications or alterations made to the protected object. To increase the feasibility, we first propose the dual-complex matrix representation of color images and design a scheme for strict color image authentication by means of the dual-complex LU decomposition. Numerical experiments are provided to demonstrate the efficiency of the algorithm.
