The quasi-period of odd order magic square transformation on digital image
Dongmei Wang · Journal of Zhejiang University of Technology · 2005
Abstrcat A transformation based on magic square has a periodicity, of which the period is n~2 while the transformed image's pixels are n×n. It is discovered that the encrypted images(P_(n× n)) based on odd order magic squares transformation (OOMS) are almost recovered at the iterative kn times, the quasi-periods, where k=1,2,…,n-1. The original images can be reconstructed via scissoring and splicing the quasi-periodic ones. It is analyzed theoretically the cause of the quasi-periodicity is due to the combination the algorithm of construction in odd magic square with the algorithm of magic square transformation. At the quasi-period of kn the row pixels are shifted down 2k rows as the column pixels are shifted to the left k columns as a whole which makes the transformed image to be recovered in four parts simultaneously. The experimental results on Matlab are convinced the quasi-period. With the quasi-periodicity of OOMS, the iterative OOMS algorithm complexity on encryption and decryption image is declined to O(n~7).