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Journal of Modern Optics

Optical asymmetric cryptosystem based on photon counting and phase-truncated Fresnel transforms

Sudheesh K. Rajput, Naveen Kumar Nishchal

Published Dec 12, 2016• 13 citations
Publisher

Abstract

We propose a novel optical asymmetric cryptosystem combining the photon counting imaging with phase-truncated Fresnel transform, which can be used for complete information retrieval and authentication verification. The proposed combination overcomes the weakness of photon counting-based double random phase-encoding scheme. For retrieval of original image for authentication, the reverse process of phase truncation approach is followed and a nonlinear correlation filter is used. The complete information retrieval and authentication verification are possible provided sufficient number of photons is available. To check the robustness of the proposed scheme, attack analysis has been carried out. The simulation results are presented to demonstrate the proposed idea.

DOI
10.1080/09500340.2016.1265677

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We propose a novel optical asymmetric cryptosystem combining the photon counting imaging with phase-truncated Fresnel transform, which can be used for complete information retrieval and authentication verification. The proposed combination overcomes the weakness of photon counting-based double random phase-encoding scheme. For retrieval of original image for authentication, the reverse process of phase truncation approach is followed and a nonlinear correlation filter is used. The complete information retrieval and authentication verification are possible provided sufficient number of photons is available. To check the robustness of the proposed scheme, attack analysis has been carried out. The simulation results are presented to demonstrate the proposed idea.
We propose a novel optical information encryption and authentication scheme that uses asymmetric keys generated by the phase-truncation approach and the phase-retrieval algorithm. Multiple images bonded with random phase masks are Fourier transformed, and obtained spectra are amplitude- and phase-truncated. The phase-truncated spectra are encoded into a single random intensity image using the phase-retrieval algorithm. Unlike most of the authentication schemes, in this study, only one encrypted reference image is required for verification of multiple secured images. The conventional double random phase encoding and correlation techniques are employed for authentication verification. Computer simulation results and theoretical explanation prove the effectiveness of the proposed scheme.
Recently, double random phase encoding (DRPE) has been integrated with the photon counting (PC) imaging technique for the purpose of secure image authentication. In this scheme, the same key should be securely distributed and shared between the sender and receiver, but this is one of the most vexing problems of symmetric cryptosystems. In this study, we propose an efficient asymmetric image authentication scheme by combining the PC-DRPE and RSA algorithms, which solves key management and distribution problems. The retrieved image from the proposed authentication method contains photon-limited encrypted data obtained by means of PC-DRPE. Therefore, the original image can be protected while the retrieved image can be efficiently verified using a statistical nonlinear correlation approach. Experimental results demonstrate the feasibility of our proposed asymmetric image authentication method.
Collision is a phenomenon in which two distinct inputs produce an identical output, so if an attacker finds the encryption keys in such a way that when it is applied to an encrypted image, it produces an arbitrary image instead of original one. We propose collision in an asymmetric cryptosystem based on a phase-truncated Fresnel transform. For encryption, instead of using conventional random-phase masks, structured phase masks with desired construction parameters are used. The decryption keys are generated using the amplitude and phase truncation. An attacker generates an arbitrary (collision) image from the encrypted image using a modified Gerchberg-Saxton phase retrieval algorithm. Two different users, authorized and unauthorized user (attacker), can claim the retrieved image as the original data. The authorized user uses the correct decryption keys and retrieves the original image, while an unauthorized user uses the generated keys and retrieves the collision image. In order to verify the authenticity of the retrieved data, a joint transform correlator is used. A sharp auto-correlation peak is obtained when an image retrieved by authorized user is matched with the encrypted image. However, cross-correlation is obtained when an encrypted image is matched with the collision image. Results of computer simulation support the idea of the proposed collision.
The integration of photon-counting imaging techniques and optical encryption systems can improve information authentication robustness against intruder attacks.Photon-counting imaging generates distributions with far fewer photons than conventional imaging, and provides substantial bandwidth reduction by generating a sparse encrypted data.We show that photon-limited encrypted distributions have sufficient information for successful decryption, authentication and signal retrieval.Additional compression of the encrypted distribution is applied by limiting the number of phase values used to reproduce the phase information of the complex-valued encrypted data.The validity of this technique -with and without phase compression -is probed through simulated experiments for two types of input images: alphanumerical signs and dithered natural scenes.
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Photon-counting imaging is integrated with optical encryption for information authentication. An image is double-random-phase encrypted, and a photon-limited encrypted image is obtained. The photon-counting encrypted image is generated with few photons and appears sparse; however, we show that it has sufficient information for decryption and authentication. The decrypted image cannot be easily visualized so that an additional layer of information protection is achieved. The authentication is carried out by recognition algorithms. This approach may make the verification process more robust against attacks. To the best of our knowledge, this is the first report on integrating photon-counting imaging and encryption for authentication.