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Optics Letters

Vulnerability to chosen-plaintext attack of a general optical encryption model with the architecture of scrambling-then-double random phase encoding

Yushu Zhang, Di Xiao, Wenying Wen, Hong Liu

Published Oct 31, 2013• 75 citations
Publisher

Abstract

We demonstrate a new approach to chosen-plaintext attack on a general encryption model based on scrambling preprocessing operation and double random phase encoding (DRPE). With this attack, an opponent can access both the scrambling key and two random phase keys. We hope that our work motivates further security analysis of the optical encryption scheme combining the scrambling techniques and DRPE.

DOI
10.1364/ol.38.004506

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We demonstrate a new approach to chosen-plaintext attack on a general encryption model based on scrambling preprocessing operation and double random phase encoding (DRPE). With this attack, an opponent can access both the scrambling key and two random phase keys. We hope that our work motivates further security analysis of the optical encryption scheme combining the scrambling techniques and DRPE.
We demonstrate a method of chosen-plaintext attack on lensless double-random phase encoding (L-DRPE) in the Fresnel domain. With this attack an opponent can access two encryption keys with help of the impulse functions as chosen plaintexts. This shows that a lensless optical encryption scheme based on DRPE is vulnerable to chosen-plaintext attack. Cryptoanalysis also indicates that the security worry originates from the linearity of the encryption and decryption mechanism of the L-DRPE scheme. One of the interesting features of the proposed attack is that the decryption process is lossless. Numerical simulations show good agreement with theoretical analysis.
In this paper, we analyze the security of the classical double random phase encoding (DRPE) technique in Fourier domain, as well as its extended schemes in Fresnel and fractional Fourier domains. These schemes are resistant to bruteforce attacks, for their large key spaces. However, due to the linearity property of their encryption transformations, they are vulnerable to other attacks, such as chosen-plaintext attack and known-plaintext attack. We successfully break each of the three encryption schemes with the help of a certain quantity of plaintext-ciphertext pairs. Each attack is validated by computer simulations. The cryptanalysis indicates that, to minimize the risks, it is recommendable to introduce nonlinear operations to optical encryption systems.
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.
From the perspective of optical information security, we demonstrate that conventional phase retrieval algorithms, such as the Gerchberg–Saxton algorithm, can be still valid when extended from the Fourier transform domain into the fractional Fourier transform (FRFT) domain. Based on this extension, we propose a method of known-plaintext attack (KPA) on double random phase encoding in the fractional Fourier transform domain (DRPE-FRFT). With this attack, an opponent can access two encryption phase keys with the help of the phase retrieval algorithm in the FRFT domain, and meanwhile obtain the two FRFT order keys by using an exhaustive search. This indicates that the optical encryption scheme based on the DRPE-FRFT scheme is vulnerable to KPA due to the nature of the linearity of FRFT. The validity of this attack is verified by numerical simulations.