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Applied Optics

Cryptanalysis of an “asymmetric optical cryptosystem based on coherent superposition and equal modulus decomposition”

Jingjing Wu, Wei Liu, Zhengjun Liu, Shutian Liu

Published Oct 14, 2015• 46 citations
Publisher

Abstract

We analyze and present an attack scheme of the asymmetric optical cryptosystem proposed recently based on coherent superposition and equal modulus decomposition [Opt. Lett.40, 475 (2015)OPLEDP0146-959210.1364/OL.40.000475]. We prove that the attacker can recover the original image with the ciphertext and public keys through the amplitude-phase retrieval algorithm by using two constraints. One constraint of the amplitude-phase retrieval algorithm is the public key and the other is obtained through the analysis of the cryptosystem. The simulation results demonstrate the feasibility of the attack method.

DOI
10.1364/ao.54.008921

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We analyze and present an attack scheme of the asymmetric optical cryptosystem proposed recently based on coherent superposition and equal modulus decomposition [Opt. Lett.40, 475 (2015)OPLEDP0146-959210.1364/OL.40.000475]. We prove that the attacker can recover the original image with the ciphertext and public keys through the amplitude-phase retrieval algorithm by using two constraints. One constraint of the amplitude-phase retrieval algorithm is the public key and the other is obtained through the analysis of the cryptosystem. The simulation results demonstrate the feasibility of the attack method.
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We propose an asymmetric optical image encryption scheme with silhouette removal by using interference and equal modulus decomposition (EMD). Plaintext is first separated into two complex value masks with the same modulus using EMD in the Fresnel transform domain. The two masks are encoded into four phase-only masks (POMs), two of which are treated as ciphertexts and other two as plaintext-dependent private keys by using the inverse Fresnel transform with different diffraction distances and interference-based encryption. Any information about the plaintext, including its silhouette, cannot be retrieved using one, two, or even three of the four POMs. Our scheme also avoids the constraint of the same modulus in EMD and eliminates the vulnerability against the iterative amplitude-phase attack and advanced iterative amplitude-phase attack. Numerical simulations were used to verify the validity and security of our proposed method.
Amplitude-phase retrieval attack (APRA) imposes serious threat upon the asymmetric security system cryptosystems based on equal modulus decomposition (EMD). To resolve that security threat, an APRA free asymmetric cryptosystem based on EMD is proposed by using one random amplitude mask AM and one random phase mask PM, where AM is treated as the private key and PM is treated as the public key. First, AM and PM are input into an optical interference architecture to generate two phase masks. Then, encrypting the plaintext results in one complex-valued cyphertext via EMD with the two-phase masks generated in the first step. This proposed cryptosystem is asymmetric, in which the encryption process is conducted digitally without iteration computation and the decryption procedure are simply accomplished using digital or optical methods. Moreover, constraints are decreased so that APRA does not work for this cryptosystem. Results of the simulation are displayed to verify the suggested cryptosystem's security and feasibility.
A novel asymmetric cryptosystem based on coherent superposition, which is free from silhouette problem, is proposed. Being different from the phase-truncated Fourier transform-based cryptosystem, the encryption process uses equal modulus decomposition (EMD) to create an effective trapdoor one-way function. As a result, the proposed method achieves high robustness against the special attack based on iterative Fourier transform. Simulation results are presented to prove the validity of the proposed system.
Abstract The equal modulus decomposition (EMD) is a novel asymmetric cryptosystem based on coherent superposition which was proposed to resist the specific attack. In a subsequent work, the scheme was shown to be vulnerable to specific attack. In this paper, we counter the vulnerability through an encoding technique which uses multiple diffraction intensity pattern recordings as the input to the EMD setup in the gyrator domain. This allows suppression of the random phase mask in the EMD path. As a result, the proposed scheme achieves resistance to specific attack. The simulation results and the security analysis demonstrate that EMD based on multiple intensity pattern recording is an effective optical asymmetric cryptosystem suitable for securing data and images.