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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantitative analysis on key estimation by known-plaintext attacks to DRPE

Kazuya Nakano, Hiroyuki Suzuki, Masahiro Yamaguchi, Takashi Obi, Nagaaki Ohyama

Published Aug 10, 2011• 2 citations

Abstract

Double Random Phase Encoding (DRPE), which is a typical optical encryption technique, has been reported to be vulnerable to Known Plaintext-Attacks (KPAs) using a Phase Retrieval Algorithm (PRA). But the reported case in which the encryption key is successfully estimated was that the plain image was rather simple such as the image of a character. In addition, although Phase Only DRPE (PO-DRPE) was proposed to achieve more resistance to the KPA than Complex DRPE (C-DRPE) in which both amplitude and phase components are used as an encrypted image, no quantitative results about the relationship between the vulnerability and the plaintext image. In this paper, we show the result of quantitative analysis on KPA by PRA to C-DRPE and PO-DRPE, for the plaintext images of different characteristics. As a result of experiment, KPA to C-DRPE succeeded to estimate the correct key while the probability of success became lower when the number of non-zero pixel increases in the plaintext image. However, KPA to PO-DRPE enabled to estimate only "singular" keys, which are effective for no more than given plaintext/ciphertext image pair and far different from the correct encryption key. We also conducted KPA using two plaintext-ciphertext image pairs for KPA. In the case when two plaintext-ciphertext image pairs were given to KPA, the cryptanalysis succeeded with higher probability than the case of one. Moreover, the probability of success in the KPA was high even in PO-DRPE.

DOI: 10.1117/12.903356

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Classical double-random phase encoding (C-DRPE) is an optical symmetric-key encryption technique. C-DRPE is reported to be vulnerable to a known-plaintext attack (KPA) that uses a phase retrieval algorithm. However, although phase-only DRPE (PO-DRPE) is reported to be more resistant to KPAs than C-DRPE, it is not obvious yet that PO-DRPE is sufficiently resistant to a KPA under any condition, because the vulnerability to KPA varies depending on various factors, such as the number of the known plaintext-ciphertext pairs that are given for the KPA, or the gray level of the known-plaintext image (i.e., binary or multivalued image). In this paper, we investigate the resistance of C-DRPE and PO-DRPE to KPA under various conditions related to the number of known plaintext-ciphertext pairs and to the gray level of the known-plaintext image.

Double random phase encoding (DRPE) is vulnerable to known-plaintext attacks (KPAs) based on phase retrieval algorithms. We previously analyzed DRPE resistance to KPA cryptanalysis with multiple known plaintext-ciphertext image pairs and obtained secret keys at a higher probability rate than when performing KPA cryptanalysis using one known image pair. However, the robustness of KPA in the presence of noise or occlusion in DRPE is unclear. We analyzed KPA properties in relation to DRPE when white Gaussian noise was gradually added to the Fourier amplitude or phase of a known ciphertext complex amplitude image. Additionally, we analyzed KPA properties when the Fourier phase of the known ciphertext image was gradually occluded by zero-valued pixels. The results showed that KPAs performed using multiple known plaintext-ciphertext image pairs were largely affected by noise added to the Fourier phase and thus are not always a strong tool for DRPE cryptanalysis.

Although initial research shows that double-random phase encoding (DRPE) is vulnerable to known-plaintext attacks that use phase retrieval algorithms, subsequent research has shown that phase-only DRPE, in which the Fourier amplitude component of an image encrypted with classical DRPE remains constant, is resistant to attacks that apply phase retrieval algorithms. Herein, we numerically analyze the key-space of DRPE and investigate the distribution property of decryption keys for classical and phase-only DRPE. We determine the difference in the distribution property of successful decryption keys for these DRPE techniques from the numerical analysis results and then discuss the security offered by them.

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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.