A number of optical encryption techniques have been developed for information security [1-20]. One of the most well-known optical encryption techniques is double random phase encryption (DRPE), which adopts random phase encoding in the input and the Fourier planes [1]. In DRPE, two physical phase masks are used for random phase encoding and are keys for correct decryption. Since the physical phase masks are not modifiable, DRPE can be insecure [2]. Thus, various techniques for enhancement of security with DRPE have been developed, including the following: DRPE in the Fresnel domain [3], photon-counting DRPE [4,5], DRPE using fractional Fourier transformation [6-8], DRPE using orthogonal encoding [9], and DRPE using accumulation encoding [10].
In order to improve the security of DRPE, photon-counting DRPE generates a sparse encrypted image with a limited number of photons, while DRPE using the Fresnel domain or fractional Fourier transformation employs more complex keys than the original DRPE, and DRPE using orthogonal encoding or accumulation encoding performs additional encoding for encrypted images from the original DRPE. However, the fundamental security problem of using fixed phase masks may be effectively solved by updating the phase masks, rather than using additional schemes for the DRPE. Therefore, in this paper, we propose a key phase mask updating scheme for DRPE, in which a spatial light modulator (SLM) is used to implement key phase mask updating. In the proposed scheme, only the second phase mask is updated with the SLM, and the input data of the SLM (i.e., the updated key data) are the amplitudes of the data that are obtained by Fourier transform after multiplying previous image data by the first phase mask. Thus, the proposed scheme requires only information from a previous image and the first phase mask to update the key phase mask, and hence it can be considered a simple key updating scheme. In this paper, we provide a detailed method for encryption and decryption of a DRPE system with the proposed key updating scheme, and also report simulation results to verify the security of DRPE with the proposed scheme.
The paper is organized as follows: in Section II, the original DRPE concept is introduced. In Section III, the key phase mask updating scheme for a DRPE system is described. In Section IV, simulation results for the proposed key updating scheme are provided to verify its security. In Section V, we conclude the paper.
Encryption and decryption for the original DRPE proposed in [1] are described in Fig. 1(a) and (b), respectively. Without loss of generality, we assume one-dimensional data only. For encryption of DRPE, the primary data
where ℑ^{-1}{‧} is the inverse Fourier transform.
For decryption of DRPE, the encrypted data
Fig. 2(a) depicts the encryption of the key phase mask updating scheme for a DRPE system. We assume that for encryption the initial key
Fig. 2(b) shows the decryption of the key phase mask updating scheme for a DRPE system. We assume that complete initial key data are known for decryption. As seen in Fig. 2(b), the complex-conjugate phase mask exp{-
As shown in Fig. 2, the proposed scheme requires only information on the previous image and the first phase mask to update the key phase mask in both encryption and decryption. Therefore, it can be considered a simple key updating scheme. In addition, the proposed scheme fully utilizes two phase masks in both encryption and decryption unlike the original DRPE, in which the first phase mask is not used in decryption. In this paper, in order to focus on security performance evaluation of the proposed scheme, we only consider that the previous image is perfectly decrypted by assuming perfect initial key data in decryption. We also assume that there is no modulation error in SLM, and the size of the phase mask and SLM is the same because a DRPE system with a unity magnification ratio is considered.
For simulation of a DRPE system with the key phase mask updating scheme, we consider two primary images with 500(H)×500(V) pixels, as shown in Fig. 3. The first primary image in Fig. 3(a) is encrypted through DRPE using the initial key in Fig. 4(a), and then the second primary image in Fig. 3(b) is encrypted through DRPE using the updated key in Fig. 4(b). The initial key data in Fig. 4(a) are randomly generated with uniform distribution over [0,1] and correspond to
Fig. 5(a) and (b) show correctly decrypted images by DRPE with the key phase mask updating scheme. By assuming that the initial key is perfectly known for decryption, the first encrypted image in Fig. 4(c) is completely decrypted, as seen in Fig. 5(a). The updated key data are then obtained by using the first decrypted image and the known first phase mask as in Fig. 2(b), which are the same as Fig. 4(b). With the updated key, the second encrypted image is correctly decrypted, and the second primary image is clearly obtained, as shown in Fig. 5(b).
Fig. 6(a) and (b) show simulation results of decryption for a DRPE system with the key phase mask updating scheme when only the initial key is used for decryption. The first decrypted image in Fig. 6(a) is correct because the known initial key is used for decryption of DRPE. However, the second decrypted image in Fig. 6(b) is incorrect and entirely unrecognizable since the key is not updated and the initial key is used to decrypt the second encrypted image, i.e., = in Fig. 2(b).
Fig. 7(a) shows the second decrypted image by DRPE with the key phase mask updating scheme when the first decrypted image is correct but the key is updated with an incorrect first phase mask in decryption. The wrong phase mask is randomly generated, and it does not match the first phase mask used in encryption. Fig. 7(b) shows the updated key data that are obtained by using the wrong phase mask. As seen in Fig. 7(a), although the first encrypted image is perfectly decrypted, the decryption of the second encrypted image fails if the first phase mask is wrong. From the simulation results in Figs. 6(b) and 7(a), we verify that the proposed key phase mask updating scheme can improve the security of the original DRPE.
We propose a key phase mask updating scheme to enhance the security of a DRPE system, where SLM is used to update a key phase mask. In fact, we present the method of encryption and decryption in detail for a DRPE system using the proposed key updating scheme. From the simulation results, we also verify that the updated key data by the proposed scheme include randomness such as noise, and DRPE using the updated key is able to achieve the security enhancement. Moreover, as the proposed scheme only requires the information of a previous image and the first phase mask to update the key phase mask, it can be considered a simple and effective key updating scheme for DRPE systems.