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SPIE Three-Dimensional Imaging, Visualization, and Display

Secret key sharing schemes in optical cryptosystems based on double random phase encoding

Inkyu Moon, You-Hyun Kim

Published Apr 22, 2020• 0 citations
Publisher

Abstract

This paper overviews new secret key sharing schemes which can be useful in optical cryptosystems based on double random phase encoding. These key sharing schemes, which are complex waveform versions of the Diffie-Hellman (DH) key exchange, allow us to establish the shared secret key in the Fourier optics-based cryptosystems. We show that the presented schemes can also be applied to cryptosystems in which multiple users can share a secret key securely.

DOI
10.1117/12.2557027

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This paper overviews new secret key sharing schemes which can be useful in optical cryptosystems based on double random phase encoding. These key sharing schemes, which are complex waveform versions of the Diffie-Hellman (DH) key exchange, allow us to establish the shared secret key in the Fourier optics-based cryptosystems. We show that the presented schemes can also be applied to cryptosystems in which multiple users can share a secret key securely.
We propose novel random phase key exchange schemes for image cryptography, which are complex sinusoidal waveform versions of the Diffie-Hellman (DH) key exchange algorithm. We demonstrate that the proposed schemes can be particularly helpful to establish a shared secret key in Fourier optics-based image cryptosystems since the problem of symmetric secret key establishment is one of the fundamental difficulties in Fourier optics-based image cryptography. We also propose a ring-type key exchange system in which multiple users can securely share a secret key, which is an extension of the key exchange scheme for two users. The schemes are verified by numerical simulations.
Digital cryptosystems can provide perfect forward secrecy (PFS) for key exchange protocols based on the Diffie–Hellman (DH) scheme. However, key exchange algorithms are optimally designed only to encode small datasets, such as text and voice sets, which makes rapidly processing large-scale datasets difficult. In this paper, we propose new schemes that can efficiently and securely provide PFS in double random phase encoding (DRPE) schemes for robust image cryptography. We demonstrate that the proposed complex sinusoidal waveform versions of the DH algorithm with fusion of a random phase mask (RPM) and ephemeral secret exponents can guarantee PFS. Different experimental results reveal that the proposed schemes can enhance the security of DRPE-based image cryptosystems using a one-time RPM and PFS. We also propose a ring-type PFS scheme in which an unlimited number of users can securely share a temporary session key, which is an extension of PFS for only two users. We provide formal proof for the schemes and prove feasibility through numerical simulations.
In this paper, we propose a new optical secret key sharing method based on the Diffie-Hellman key exchange protocol required in cipher system. The proposed method is optically implemented by using a free-space interconnected optical logic gate technique in order to process XOR logic operations in parallel. Also, we present a compact type of optical module which can perform the modified Diffie-Hellman key exchange for a cryptographic system. Schematically, the proposed optical configuration has an advantage of producing an open public key and a shared secret key simultaneously. Another advantage is that our proposed key exchange system uses a similarity to double key encryption techniques to enhance security strength. This can provide a higher security cryptosystem than the conventional Diffie-Hellman key exchange protocol due to the complexity of the shared secret key. Results of numerical simulation are presented to verify the proposed method and show the effectiveness in the modified Diffie-Hellman key exchange system.
Recently several optical encryption techniques have been proposed for two-dimensional data. These techniques use random phase masks, jigsaw transforms, digital signatures, and linear transforms like the Fourier transforms, the fractional Fourier transform and the Fresnel transform. The strength of these encryption techniques is dependent on the size of the key but is strongly limited by the security linked with the exchange of the secret key. We propose a new technique, based on the Diffie-Hellman protocol, in which the key can be exchanged with high security. The Diffie-Hellman protocol allows two users to exchange a secret key over an insecure channel without any prior secrets. Fractional Fourier transforms have been used for the secure key transfer. Results of computer simulation are presented to verify the proposed idea and analyse the robustness of the proposed technique.
A secret sharing scheme is an important cryptographic procedure that enables the secure distribution of secret information, such as private images, in an untrusted network. However, in all secret sharing schemes, the sizes of the shares increase in proportion to the size of the secret information, because they involve computationally expensive polynomials of degreen−1n-1n−1(n is total number of shares) and increasingly large modulus of modulo operations for security. Moreover, with large share sizes, it is not easy in practice to encrypt them quickly using block cipher algorithms. Therefore, ensuring the security of secret sharing for large-scale visual data with a reasonable share length and efficiently encrypting n shares properly represents formidable challenges. To overcome these challenges in secret sharing schemes, we propose new multiparty random phase wrapping secret sharing systems for visual datasets. Computational optical imaging enables the acquisition of wrapped phase information, ranging from –$\pi tototo\pi $, to be expressed in the form of a complex sinusoidal waveform. The proposed scheme allows for large-scale secret data—such as confidential digital images and visual data, including optical images—to be securely and efficiently shared and distributed to multiple parties or agencies utilizing a digital representation of a complex sinusoidal waveform of the secret information. The proposed scheme can be useful in cryptographic key escrow systems and in use with large-scale secret data.
Recently several optical encryption techniques have been proposed for two-dimensional data. These techniques use random phase masks, jigsaw transforms, digital signatures, and linear transforms like the Fourier transforms, the fractional Fourier transform and the Fresnel transform. The strength of these encryption techniques is dependent on the size of the key but is strongly limited by the security linked with the exchange of the secret key. We propose a new technique, based on the Diffie-Hellman protocol, in which the key can be exchanged with high security. Fractional Fourier transforms have been used for the secure key transfer. Results of computer simulation are presented to verify the proposed idea and analyse the robustness of the proposed technique.