Optical-digital encryption systems

As an alternative approach of encryption techniques, optical-digital system approach is worth of noting. Such systems introduce optically a known distortion in a registered image. Then such introduced distortion can be compensated digitally.

All of such encryption systems can be divided in three category: optical, digital, and hybrid optical-digital systems. A brief survey of them is presented further.

Digital encryption systems

Digital encryption systems are performing all operations in numerical form in computer [1] so there is no need of optical systems to be created. There are several systems that are mostly digital such as Virtual Optics system [2] and virtual-optical-holography (VOH) [3] that are characterized by high cryptography resistance. Other digital systems that are worth noting are using fractional wavelet transform [4] or fractional Fourier transform [5].

One of the most widespread digital encryption technique is virtual-optical imaging scheme, VOIS [2] that simulates an optical imaging system in a computer model. As a computation model, Fresnel approach is used; encryption parameters are the wavelength of coherent ``virtual'' light LAMBDA , the distance between the image to be encoded and ``lens'' d0 , focal distance of the ``lens'' f , and distance between the ``lens'' and observing plane d_i (see Fig. 1).

Figure 1: The key diagram of the Virtual Optics.

Fourier-spectrum of an image to be encoded is multiplied by Fourier-spectrum of coding mask, so one need to know exact parameters of LAMBDA, d0 , d_i , and f in order to decrypt the image.

Optical encryption systems

In optical encryption techniques are utilized high speed and parallelism of optical images processing. As encryption keys, diffractive optical elements (DOEs) are used that are synthesized and outputted to ferroelectric [6] or LCD-modulators [7]. For example, such systems use lensless approach [8], 4-f based systems [9], fractional Fourier transform [10,11,12] or systems based on double random phase mask [13]. Apart from these systems, toroidal zone plates encryption systems is worth mention [14].

The most widespread approach in optical encryption systems is double random phase mask [13,15,16,17]. As it shortly described in [18], the image to be encrypted P is immediately followed by a first random phase mask, which is the first key X . Both the image and the mask are located in the object focal plane of a first lens (see Fig. 2).

Figure 2: DRPE coding scheme

In the image focal plane of this lens is therefore obtained the Fourier transform (FT) of the product P*X. This product is then multiplied by another random phase mask that is the second key Y. Lastly, another FT is performed by a second lens to return to the spatial domain. Since the last FT does not add anything to the security of the system, we will perform all our analyses in the Fourier plane. The ciphered image C is then:

C = Y * FT(P*X)

(1)

where F stands for the Fourier transform operation. In most of the paper, we will assume that P is a grey-level image.

Such systems allow obtaining encrypted images that are characterized by high cryptography resistance. Images are being encrypted in a very short time because of parallel optical processing is performed. Complexity of optical key diagram and expensiveness are drawbacks of such systems. Moreover, several vulnerabilities of double random phase mask were reported recently [19,20,21].

Hybrid optical-digital systems

Hybrid optical-digital systems allow to combine advantages of optical processing (high speed and parallelism) and digital processing (flexibility of digital image processing methods). Application of digital methods in optical coding allow to reduce weight and cost of devices.

As a most widespread optical-digital paradigms, ``wavefront coding'' [22] and ``pupil engineering'' [23] are worth mention. Systems based on these paradigms are used in enhancing depth of field in microscopic imaging [24], aberrations compensation [25], depth-of-field improvement in MEMS-systems [26], and enhancing of tomography images [27].

Coding diffractive element (DOE) is introduced in the imaging scheme of such devices; hence optical convolution of input object and point spread function (PSF) of the DOE is performed optically. As a result, the image registered is blurred but a blur is the same across the image. Digital images deconvolution is performed in order to reconstruct the image and compensate introduced distortion. An example of hybrid optical-digital device is shown in Fig. 3.

Figure 3: Hybrid optical-digital imaging system: a photo sensor and a kinoform (DOE).

Hybrid optical-digital systems based on ``wavefront coding'' and ``pupil engineering'' paradigms can be used not only for encryption but for depth-of-field enhancing, too.

Such systems are advantageous because of their inexpensiveness, flexibility, and reliability (may be used not only for data encryption). But after image decryption, visual quality of the image is degraded slightly that is a disadvantage.

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