Quaternion gyrator transform and its application to color image encryption

The gyrator transform has been proposed in optics a few years ago. By using the theory of quaternion numbers, this paper presents the quaternion gyrator transform (QGT). It is shown that the QGT can be computed via the left-side type of quaternion Fourier transforms. The new transform is applied to color image encryption for validation, where the rotation angles are used as encryption keys making it more secure compared to a recent method using discrete quaternion Fourier transforms (DQFTs). Experimental results show that the proposed encryption algorithm for color image performs as well as the DQFTs method in terms of noise robustness, so that it could be a useful tool for color image encryption.