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Applied Optics

Improved method of attack on an asymmetric cryptosystem based on phase-truncated Fourier transform

Yong Wang, Chenggen Quan, Cho Jui Tay

Published Jul 28, 2015• 67 citations
Publisher

Abstract

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.

DOI
10.1364/ao.54.006874

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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.
This paper presents two different aspects of cryptanalysis of the optical phase-truncated Fourier transform (PTFT)-based cryptosystem. In the first part, a comparative study is carried out for a specific attack on the PTFT-based scheme in different optical transformation domains. In the second part, a new attack algorithm is proposed. The existing attack algorithms devised for the PTFT-based cryptosystem require knowledge of both the encryption keys for successful retrieval of phase through phase-retrieval algorithms to extract information about the plaintext. The proposed new attack method eliminates the requirement of one of the encryption keys to carry out the attack on the PTFT-based scheme. The numerical results support the proposed method.
We propose an asymmetric cryptosystem based on a phase-truncated Fourier transform. With phase truncation in Fourier transform, one is able to produce an asymmetric ciphertext as real-valued and stationary white noise by using two random phase keys as public keys, while a legal user can retrieve the plaintext using another two different private phase keys in the decryption process. Owing to the nonlinear operation of phase truncation, high robustness against existing attacks could be achieved. A set of simulation results shows the validity of proposed asymmetric cryptosystem.
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.
In this paper, the security of a cryptosystem based on phase truncation and a designed amplitude modulator (AM) is evaluated. In the cryptosystem, an undercover AM used as an additional key is added to modulate the amplitude information of the spectrum in the Fourier plane. Compared to the conventional phase-truncated Fourier transform (PTFT)-based cryptosystem, the security of the cryptosystem is improved by increasing the number of unknown keys. However, it is found that the designed AM is irrelative to the plaintext, and one of the parameters in the designed AM contributes less to the security enhancement of the cryptosystem due to low key sensitivity. Based on the analysis, a special attack containing two iterative processes is proposed to crack the cryptosystem, in which the known-plaintext-attack-based iterative process I with a specific normalization operator is used to retrieve the designed AM and the amplitude-phase-retrieval-technique-based iterative process II is used to retrieve the corresponding plaintext from the arbitrarily given ciphertext with the help of the retrieved AM. In addition, an inherent drawback widely existing in PTFT-based cryptosystems is reported for the first time: most information of the original image could be retrieved using two correct phase keys (or only the first phase key) generated in the encryption process, even without the corresponding ciphertext in PTFT-based cryptosystems. To address this issue, a security-enhanced cryptosystem is proposed in this paper. Numerical simulation is carried out to demonstrate the effectiveness and feasibility of the proposed attack and cryptosystem.
We propose an improvement method for an asymmetric cryptosystem based on spherical wave illumination. Compared with the phase-truncated Fourier transform-based cryptosystem and the reported improving methods, the encryption process uses a spherical wave to illuminate the encryption system, rather than a uniform plane wave. As a result, the proposed method can avoid various types of the currently existing attacks and maintain the asymmetric characteristic of the cryptosystem. Moreover, due to only changing the illuminating mode, the proposed method can be easily implemented in optics compared with the reported improving methods. Simulation results are presented to demonstrate the feasibility and the security performance of the proposed method.
We propose a simple amplitude-phase retrieval attack free cryptosystem based on direct attack to phase-truncated Fourier-transform-based encryption using a random amplitude mask (RAM). The RAM that is not saved during the encryption provides extremely high security for the two private keys, and no iterative calculations are involved in the nonlinear encryption process. Lack of enough constraints makes the specific attack based on iterative amplitude-phase retrieval algorithms unusable. Numerical simulation results are given for testing the validity and security of the proposed approach.