We propose an optical architecture that encodes a primary image to stationary white noise by using two statistically independent random phase codes. The encoding is done in the fractional Fourier domain. The optical distribution in any two planes of a quadratic phase system (QPS) are related by fractional Fourier transform of the appropriately scaled distribution in the two input planes. Thus a QPS offers a continuum of planes in which encoding can be done. The six parameters that characterize the QPS in addition to the random phase codes form the key to the encrypted image. The proposed method has an enhanced security value compared with earlier methods. Experimental results in support of the proposed idea are presented.

Optical encryption by double-random phase encoding in the fractional Fourier domain.

Over the years extensive studies have been carried out to apply coherent optics methods in real-time communications and image transmission. This is especially true when a large amount of information needs to be processed, e.g., in high-resolution imaging. The recent progress in data-processing networks and communication systems has considerably increased the capacity of information exchange. However, the transmitted data can be intercepted by nonauthorized people. This explains why considerable effort is being devoted at the current time to data encryption and secure transmission. In addition, only a small part of the overall information is really useful for many applications. Consequently, applications can tolerate information compression that requires important processing when the transmission bit rate is taken into account. To enable efficient and secure information exchange, it is often necessary to reduce the amount of transmitted information. In this context, much work has been undertaken using the principle of coherent optics filtering for selecting relevant information and encrypting it. Compression and encryption operations are often carried out separately, although they are strongly related and can influence each other. Optical processing methodologies, based on filtering, are described that are applicable to transmission and/or data storage. Finally, the advantages and limitations of a set of optical compression and encryption methods are discussed.

https://hal.archives-ouvertes.fr/docs/00/51/69/80/PDF/20.pdf

Optical image compression and encryption methods

Several attacks are proposed against the double random phase encryption scheme. These attacks are demonstrated on computer-generated ciphered images. The scheme is shown to be resistant against brute force attacks but susceptible to chosen and known plaintext attacks. In particular, we describe a technique to recover the exact keys with only two known plain images. We compare this technique to other attacks proposed in the literature.

Resistance of the double random phase encryption against various attacks

An optical double random-phase encryption method using a joint transform correlator architecture is proposed. In this method, the joint power spectrum of the image to be encrypted and the key codes is recorded as the encrypted data. Unlike the case with classical double random-phase encryption, the same key code is used to both encrypt and decrypt the data, and the conjugate key is not required. Computer simulations and optical experimental results using a photorefractive- crystal-based processor are presented. © 2000 Society of Photo-Optical Instru- mentation Engineers. (S0091-3286(00)03508-X)

Optical encryption using a joint transform correlator architecture

Information security and authentication are important challenges facing society. Recent attacks by hackers on the databases of large commercial and financial companies have demonstrated that more research and development of advanced approaches are necessary to deny unauthorized access to critical data. Free space optical technology has been investigated by many researchers in information security, encryption, and authentication. The main motivation for using optics and photonics for information security is that optical waveforms possess many complex degrees of freedom such as amplitude, phase, polarization, large bandwidth, nonlinear transformations, quantum properties of photons, and multiplexing that can be combined in many ways to make information encryption more secure and more difficult to attack. This roadmap article presents an overview of the potential, recent advances, and challenges of optical security and encryption using free space optics. The roadmap on optical security is comprised of six categories that together include 16 short sections written by authors who have made relevant contributions in this field. The first category of this roadmap describes novel encryption approaches, including secure optical sensing which summarizes double random phase encryption applications and flaws [Yamaguchi], the digital holographic encryption in free space optical technique which describes encryption using multidimensional digital holography [Nomura], simultaneous encryption of multiple signals [Perez-Cabre], asymmetric methods based on information truncation [Nishchal], and dynamic encryption of video sequences [Torroba]. Asymmetric and one-way cryptosystems are analyzed by Peng. The second category is on compression for encryption. In their respective contributions, Alfalou and Stern propose similar goals involving compressed data and compressive sensing encryption. The very important area of cryptanalysis is the topic of the third category with two sections: Sheridan reviews phase retrieval algorithms to perform different attacks, whereas Situ discusses nonlinear optical encryption techniques and the development of a rigorous optical information security theory. The fourth category with two contributions reports how encryption could be implemented at the nano- or micro-scale. Naruse discusses the use of nanostructures in security applications and Carnicer proposes encoding information in a tightly focused beam. In the fifth category, encryption based on ghost imaging using single-pixel detectors is also considered. In particular, the authors [Chen, Tajahuerce] emphasize the need for more specialized hardware and image processing algorithms. Finally, in the sixth category, Mosk and Javidi analyze in their corresponding papers how quantum imaging can benefit optical encryption systems. Sources that use few photons make encryption systems much more difficult to attack, providing a secure method for authentication.

http://diposit.ub.edu/dspace/bitstream/2445/118388/1/664334.pdf

Roadmap on optical security

We implement an optical encryption system based on double-random
phase encoding of the data at the input and the Fourier planes. In
our method we decrypt the image by generating a conjugate of the
encrypted image through phase conjugation in a photorefractive
crystal. The use of phase conjugation results in
near-diffraction-limited imaging. Also, the key that is used during
encryption can also be used for decrypting the data, thereby
alleviating the need for using a conjugate of the key. The effect
of a finite space–bandwidth product of the random phase mask
on the encryption system’s performance is discussed. A theoretical
analysis is given of the sensitivity of the system to misalignment
errors of a Fourier plane random phase mask.

Optical encryption system that uses phase conjugation in a photorefractive crystal.

Optical encryption using quadratic phase systems

We propose a new method to encrypt and decrypt a two-dimensional amplitude image, which uses a jigsaw transform and a localized fractional Fourier transform. The jigsaw transform is applied to the original image to be encrypted, and the image is then divided into independent nonoverlapping segments. Each image segment is encrypted using different fractional parameters and two statistically independent random phase codes. The random phase codes, along with the set of fractional orders and jigsaw transform index, form the key to the encrypted data. Results of computer simulation are presented to verify the proposed idea and analyze the performance of the method. We also propose an optical implementation, which may find application for encrypting data stored in holographic memory.

Optical encryption using a localized fractional Fourier transform

Multichannel image addition and subtraction using joint-transform correlator architecture

We implemented an optical encryption system that uses random Fourier plane encoding as the encryption method. In this method, data is encrypted by using a random phase function in the Fourier plane. In the earlier systems, the random phase function has been mostly implemented by fabricating random phase mask using photolithographic technique or by photographic bleaching process. We implement the binary random phase function using a Ferroelectric spatial light modulator (SLM). The use of SLM eliminates the need of fabricating the random phase mask which makes the SLMs suitable candidates in the encryption systems. The encrypted image which is a complex function is holographically recorded in a photorefractive BaTiO3 crystal.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

G. Unnikrishnan

Papers

Optical encryption system that uses phase conjugation in a photorefractive crystal.

Optical encryption using quadratic phase systems

Optical encryption using a localized fractional Fourier transform

Multichannel image addition and subtraction using joint-transform correlator architecture

Optical encryption system using a spatial light modulator