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Optics Letters

Information encryption in phase space

Jun Liu, Xiaobin Xu, Quanying Wu, John T. Sheridan, Guohai Situ

Published Feb 27, 2015• 29 citations
Publisher

Abstract

In this Letter, we propose an information encryption technique based on the theory of phase-space optics. We show that encoding the plaintext in phase space provides a higher level of security: first, the key-space is significantly enlarged. Second, it is immune to various known-plaintext (cyphertext) attacks to which the double-random phase encryption (DRPE) is vulnerable. Third, the bilinearity of phase-space distributions offers additional security. Theoretical analysis and numerical calculation results show that the proposed technique has significantly different responses to errors added to the cypheretext and the two phase keys in comparison to the classical DRPE.

DOI
10.1364/ol.40.000859

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In this Letter, we propose an information encryption technique based on the theory of phase-space optics. We show that encoding the plaintext in phase space provides a higher level of security: first, the key-space is significantly enlarged. Second, it is immune to various known-plaintext (cyphertext) attacks to which the double-random phase encryption (DRPE) is vulnerable. Third, the bilinearity of phase-space distributions offers additional security. Theoretical analysis and numerical calculation results show that the proposed technique has significantly different responses to errors added to the cypheretext and the two phase keys in comparison to the classical DRPE.
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This Letter proposes an optical encryption technique that disguises the information with modular arithmetic concepts and time-varying noise components that are unknown to the receiver. Optical encryption systems that use these techniques produce a nondeterministic system response, as well as noise like image data that can easily be generated with ordinary spatial light modulators. The principle of this technique is demonstrated for the double random phase encoding (DRPE) method. The conventional DRPE method has major vulnerabilities for Dirac signal and plain signal attacks, making them impractical for secure encryption. It is shown that the proposed encryption technique provides a robustness against these types of attacks, allowing optical DRPE to be employed in secure encryptions. Moreover, applications of this Letter are not limited to DRPE alone but can also be adopted by other optical encryption techniques such as fractional Fourier transform and Fresnel-transform-based techniques.
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.
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.
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.