^{1}

^{*}

^{2}

A color information encryption method using phase-truncated gyrator transform domain is proposed. In this technique, the color image is decomposed into R, G and B channels. The decomposed three RBG channels evade the interference of crosstalks efficiently. Each channel is separately modulated to the first random phase mask and then gyrator transformed. The transformed image is phase-truncated to get first encoded image and amplitude-truncated to produce first asymmetric phase key. The obtained image is modulated to the second random phase mask and then again gyrator transformed. The resulted image is phase-truncated to obtain second encoded image and amplitude-truncated to generate second asymmetric phase key. The proposed system includes transformation angles of GT and asymmetric phase keys as decryption keys. The proposed system can be implemented digitally or optically. The optical setup is free from optical misalignment problem. The theoretical analysis and numerical simulation results both validate the proposed technique.

Optical cryptography techniques have emerged as one of the next generation technologies, in which optical image encryption techniques have been widely studied because of their inherent advantages of high-speed and paralleloptical signal processing. Refregier and Javidi first proposed a double random phase encoding (DRPE) based on the 4-f optical correlator to encode an input image into stationary white noise [

In this paper, for the first time, to our knowledge, a new asymmetric color image cryptosystem based on gyrator transform (GT) domain is proposed. In this method, the color image is divided into R, G and B channels. Each of these channels is independently attached to the first RPM placed at the image plane and then gyrator transformed. The transformed image is phase-truncated to get first encoded image and amplitude-truncated to produce first decryption phase key. The transformed image is attached to the second RPM placed at the gyrator transform plane and then again gyrator transformed. The resulted image is phase-truncated to get second encoded image and amplitude-truncated to generate second decryption phase key. The proposed system provides transformation angles of GT as additional keys and decryption phase keys as asymmetric keys. Consequently, a high robustness against existing attacks can be achieved. Numerical simulations show the validity and viability of the proposed technique.

The gyrator transform (GT) is defined as a linear canonical transform which produces the twisted rotation in position-spatial frequency planes of phase space. Thus, the GT operation of a two-dimensional function

where

In this method, an original color image is segregated into R, G and B color components. For simplicity, only red component is considered for the proposed cryptosystem. Let

The operator

where

The decryption process is straightforward and much simpler compared with encryption process.

The blue and green channels are encrypted and decrypted by the same procedure.

The encryption process is performed digitally whereas the decryption process can be implemented using optoelectronic device. The GT can be implemented by using three generalized lenses (indicated as

The optical setup is shown in

Numerical simulations have been carried out on a Matlab 7.11.0 (R2010b) platform to test the feasibility and security of the new proposal. The original color image having size

To evaluate the reliability of the proposed algorithm quantitatively, the mean square error (MSE) is introduced and defined as

where

In

In attack analysis, first the known plaintext attack is considered, in which an attacker knows all the transformation angles and attempts to produce decryption keys from a fake color image of size

Second, the robustness of the proposed technique against occlusion attacks on the encrypted data has been examined. The 50%- and 70%- occluded encrypted images are shown in

Third, the robustness of the proposed method against noise attacks on the encrypted data has also been checked. The Gaussian and speckle noised encrypted images with variance 0.1 are displayed in

From above results, it can be concluded that if the encrypted data is destroyed by occlusion or degraded by noise in storage and transmission process, the decrypted image with all right keys is recognizable. Therefore, the proposed method has certain robustness against occlusion and noise attacks.

The sensitive degree of the transformation angle is analyzed and then calculated. The sampling interval is fixed at the range

A new information encryption system based phase-truncated gyrator transform domain is presented. The original color image is separated into