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Applied Optics

New method of attack and security enhancement on an asymmetric cryptosystem based on equal modulus decomposition

Yong Wang, Chenggen Quan, Cho Jui Tay

Published Jan 19, 2016• 74 citations
Publisher

Abstract

A recently proposed asymmetric cryptosystem based on coherent superposition and equal modulus decomposition has shown to be robust against a specific attack. In this paper, we have shown that it is vulnerable to a newly designed attack. With this attack, an intruder is able to access the exact private key and obtain precise attack results using a phase retrieval algorithm. In addition, we have also proposed a security-enhanced asymmetric cryptosystem using a random decomposition technique and a 4f optical system. In the proposed system, random decomposition is employed to create an effective trapdoor one-way function. As a result, it is able to avoid various types of attacks and maintain the asymmetric characteristics of the cryptosystem. Numerical simulations are presented to demonstrate the feasibility and robustness of the proposed method.

DOI
10.1364/ao.55.000679

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Asymmetric optical cryptosystem based on coherent superposition and equal modulus decomposition: comment

Xiaopeng Deng

I comment on the recent Letter by Cai et al. [Opt. Lett.40, 475 (2015).], in which the authors claimed that the method can resist the special attack. However, I think their attack analysis and algorithm are ill-considered and worth discussing.

Optics Letters•Aug 12, 2015•45 citations
A recently proposed asymmetric cryptosystem based on coherent superposition and equal modulus decomposition has shown to be robust against a specific attack. In this paper, we have shown that it is vulnerable to a newly designed attack. With this attack, an intruder is able to access the exact private key and obtain precise attack results using a phase retrieval algorithm. In addition, we have also proposed a security-enhanced asymmetric cryptosystem using a random decomposition technique and a 4f optical system. In the proposed system, random decomposition is employed to create an effective trapdoor one-way function. As a result, it is able to avoid various types of attacks and maintain the asymmetric characteristics of the cryptosystem. Numerical simulations are presented to demonstrate the feasibility and robustness of the proposed method.
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.
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.
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.
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.
We propose an improved method of attack on an asymmetric cryptosystem based on a phase-truncated Fourier transform. With the proposed method of attack, an attacker is able to access the exact decryption keys and obtain precise attack results. The method is based on a novel median-filtering phase-retrieval algorithm. Compared with existing attacks, the proposed attack has the following advantages: (1) exact information of the original image can be obtained in gray-scale and binary forms; (2) better computing efficiency; (3) more robust against noise and occlusion contaminations. Numerical simulation results show the effectiveness and robustness of the proposed method. Based on the proposed method of attack, we further propose a new cryptosystem, which not only enhances the security of the system but also does not require truncated phases.