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Optics Express

A known-plaintext heuristic attack on the Fourier plane encryption algorithm

Unnikrishnan Gopinathan, David S. Monaghan, Thomas J. Naughton, John T. Sheridan

Published Jan 1, 2006• 231 citations
Publisher

Abstract

The Fourier plane encryption algorithm is subjected to a known-plaintext attack. The simulated annealing heuristic algorithm is used to estimate the key, using a known plaintext-ciphertext pair, which decrypts the ciphertext with arbitrarily low error. The strength of the algorithm is tested by using this estimated key to decrypt a different ciphertext which was also encrypted using the same original key. We assume that the plaintext is amplitude-encoded real-valued image, and analyze only the mathematical algorithm rather than a real optical system that can be more secure. The Fourier plane encryption algorithm is found to be susceptible to a known-plaintext heuristic attack.

DOI
10.1364/oe.14.003181

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The Fourier plane encryption algorithm is subjected to a known-plaintext attack. The simulated annealing heuristic algorithm is used to estimate the key, using a known plaintext-ciphertext pair, which decrypts the ciphertext with arbitrarily low error. The strength of the algorithm is tested by using this estimated key to decrypt a different ciphertext which was also encrypted using the same original key. We assume that the plaintext is amplitude-encoded real-valued image, and analyze only the mathematical algorithm rather than a real optical system that can be more secure. The Fourier plane encryption algorithm is found to be susceptible to a known-plaintext heuristic attack.
In conventional symmetric encryption, it is common for the encryption/decryption key to be reused for multiple plaintexts. This gives rise to the concept of a known-plaintext attack. In optical image encryption systems, such as double random phase encoding (DRPE), this is also the case; if one knows a plaintext-ciphertext pair, one can carry out a known-plaintext attack more efficiently than a brute-force attack, using heuristics based on phase retrieval or simulated annealing. However, we demonstrate that it is likely that an attacker will find an imperfect decryption key using such heuristics. Such an imperfect key will work for the known plaintext-ciphertext pair, but not an arbitrary unseen plaintext-ciphertext pair encrypted using the original key. In this paper, we illustrate the problem and attempt to characterise the increase in security it affords optical encryption.
In conventional symmetric encryption, it is common for the encryption/decryption key to be reused for multiple plaintexts. This gives rise to the concept of a known-plaintext attack. In optical image encryption systems, such as double random phase encoding (DRPE), this is also the case. With optical encryption, if one knows a plaintext-ciphertext pair, one can carry out a known-plaintext attack more efficiently than a bruteforce attack, using heuristics based on phase retrieval or simulated annealing. However, it is more likely that an attacker will find an imperfect encryption/decryption key using such heuristics. Such an imperfect key will work for the known plaintext-ciphertext pair, but not an arbitrary unseen plaintext-ciphertext pair using the original key. In this paper, we illustrate the problem and attempt to characterise the increase in security it affords optical encryption.
The modified iterative phase retrieval algorithms developed in Part I [Guo et al., Appl. Opt.54, 4698 (2015)] are applied to perform known plaintext and ciphertext attacks on amplitude encoding and phase encoding Fourier-transform-based double random phase encryption (DRPE) systems. It is shown that the new algorithms can retrieve the two random phase keys (RPKs) perfectly. The performances of the algorithms are tested by using the retrieved RPKs to decrypt a set of different ciphertexts encrypted using the same RPKs. Significantly, it is also shown that the DRPE system is, under certain conditions, vulnerable to ciphertext-only attack, i.e., in some cases an attacker can decrypt DRPE data successfully when only the ciphertext is intercepted.
The security of the encryption and verification techniques with significant output images is examined by a known-plaintext attack. We introduce an iterative phase-retrieval algorithm based on multiple intensity measurements to heuristically estimate the phase key in the Fourier domain by several plaintext-cyphertext pairs. We obtain correlation output images with very low error by correlating the estimated key with corresponding random phase masks. Our studies show that the convergence behavior of this algorithm sensitively depends on the starting point. We also demonstrate that this algorithm can be used to attack the double random phase encoding technique.
This paper analysis the security of the optical encryption scheme based on the classical double random phase encoding. We describe a known-plaintext attack which can be used to successfully access the encryption key with the pre-knowledge of only one arbiturary pair of known plaintext-ciphertext. A phase retrieval algorithm is employed in this attack. Computer simulations are made to demonstrate the effectiveness. The results show that even implementing only one round of iteration in the phase retrieval, an attacker can obtain a clear decoded plaintext (a gray-scale image) from an intercept ciphertext.
In the field of optical information security, the most attractive work is the so-called double-random-phase encoding encryption scheme proposed by Javidi. However, the security of this cryptosystem has not been analyzed thoroughly from the point of view of cryptoanalysis. In this article, the weakness of Javidi's optical security system is carefully analyzed with a known-plain text attack. It is shown that the double-random-phase encoding encryption scheme is a linear symmetric block cipher cryptosystem and its linearity opens avenues of attacks. Under the known-plaintext attack, attacker can obtain the phase key(s) in the input plane using the typical phase retrieval algorithms and subsequently deduce the phase key(s) in the Fourier domain easily. In addition, an optical implementation of known-plain text attack is also proposed.