OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 7 — Apr. 8, 2013
  • pp: 8025–8043
« Show journal navigation

Assessing the performance of a method of simultaneous compression and encryption of multiple images and its resistance against various attacks

A. Alfalou, C. Brosseau, N. Abdallah, and M. Jridi  »View Author Affiliations


Optics Express, Vol. 21, Issue 7, pp. 8025-8043 (2013)
http://dx.doi.org/10.1364/OE.21.008025


View Full Text Article

Acrobat PDF (2888 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We introduce a double optimization procedure for spectrally multiplexing multiple images. This technique is adapted from a recently proposed optical setup implementing the discrete cosine transformation (DCT). The new analysis technique is a combination of spectral fusion based on the properties of DCT, specific spectral filtering, and quantization of the remaining encoded frequencies using an optimal number of bits. Spectrally multiplexing multiple images defines a first level of encryption. A second level of encryption based on a real key image is used to reinforce encryption. A set of numerical simulations and a comparison with the well known JPEG (Joint Photographic Experts Group) image compression standard have been carried out to demonstrate the improved performances of this method. The focus here will differ from the method of simultaneous fusion, compression, and encryption of multiple images (SFCE) [Opt. Express 19, 24023 (2011)] in the following ways. Firstly, we shall be concerned with optimizing the compression rate by adapting the size of the spectral block to each target image and decreasing the number of bits required to encode each block. This size adaptation is achieved by means of the root-mean-square (RMS) time-frequency criterion. We found that this size adaptation provides a good tradeoff between bandwidth of spectral plane and number of reconstructed output images. Secondly, the encryption rate is improved by using a real biometric key and randomly changing the rotation angle of each block before spectral fusion. By using a real-valued key image we have been able to increase the compression rate of 50% over the original SFCE method. We provide numerical examples of the effects for size, rotation, and shifting of DCT-blocks which play noteworthy roles in the optimization of the bandwidth of the spectral plane. Inspection of the results for different types of attack demonstrates the robustness of our procedure.

© 2013 OSA

1. Introduction

In the last decade optical encryption has emerged as a framework for studying information processing [1

1. A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon. 1(3), 589 (2009). [CrossRef]

3

3. P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20(7), 767–769 (1995). [CrossRef] [PubMed]

]. However, it is well established that the standard double random phase encryption (DRP) exhibits vulnerability to various attacks [4

4. Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express 15(16), 10253–10265 (2007). [CrossRef] [PubMed]

,5

5. P. Kumar, J. Joseph, and K. Singh, “Known-plaintext attack-free double random phase-amplitude optical encryption: vulnerability to impulse function attack,” J. Opt. 14(4), 045401 (2012). [CrossRef]

]. Several approaches have been reported to improve the encryption efficiency of DRP, see, e.g. Refs [1

1. A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon. 1(3), 589 (2009). [CrossRef]

8

8. A. Alfalou and A. Mansour, “All optical video-image encryption enforced security level using independent component analysis,” J. Opt. A, Pure Appl. Opt. 9, 787 (2007). [CrossRef]

]. One possible route towards a multiple-image optical encryption method is based on the modified Gerchberg-Saxton algorithm (MGSA) and the Fresnel transform [6

6. J.-J. Huang, H.-E. Hwang, C.-Y. Chen, and C.-M. Chen, “Lensless multiple-image optical encryption based on improved phase retrieval algorithm,” Appl. Opt. 51(13), 2388–2394 (2012). [CrossRef] [PubMed]

]. Recently, Alfalou and Mansour [8

8. A. Alfalou and A. Mansour, “All optical video-image encryption enforced security level using independent component analysis,” J. Opt. A, Pure Appl. Opt. 9, 787 (2007). [CrossRef]

] found that an approach based on independent component analysis produces a significantly enhanced resistance of the DRP method against specific attacks. In a different context, polarized light and a gyrator transform are used to validate optical encryption methods [9

9. Z. Liu, Q. Guo, L. Xu, M. A. Ahmad, and S. Liu, “Double image encryption by using iterative random binary encoding in gyrator domains,” Opt. Express 18(11), 12033–12043 (2010). [CrossRef] [PubMed]

,10

10. A. Alfalou and C. Brosseau, “Dual encryption scheme of images using polarized light,” Opt. Lett. 35(13), 2185–2187 (2010). [CrossRef] [PubMed]

]. More recently, Wang and co-workers [7

7. X. Wang and D. Zhao, “Double images encryption method with resistance against the specific attack based on an asymmetric algorithm,” Opt. Express 20(11), 11994–12003 (2012). [CrossRef] [PubMed]

] suggested an alternative double-image encryption resistance method. Another encryption method for videos relying on DRP and a specific merging procedure in the output plane was put forward by Mosso et al. [11

11. F. Mosso, J. F. Barrera, M. Tebaldi, N. Bolognini, and R. Torroba, “All-optical encrypted movie,” Opt. Express 19(6), 5706–5712 (2011). [PubMed]

]. It is worth observing that this method leads to good performances even if its compression part is not optimized. However, the method proposed by Mosso and co-workers does not consider the issue of spectral overlapping in the output plane. Consequently it requires a large number of bits to encode the output plane. In addition, their quantization procedure leads to a decrease of performances when the images are reconstructed.

While a large body of work has been reported on encryption, the prevailing opinion is that the compression stage is not a main concern in the field of optical encryption. Following existing published work, the real and imaginary parts of the output image following DRP [1

1. A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon. 1(3), 589 (2009). [CrossRef]

3

3. P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20(7), 767–769 (1995). [CrossRef] [PubMed]

] have been considered separately. On the other hand, many digital hologram (DH) studies have been performed for decreasing the amount of data to be processed. For example, Paturzo and co-workers [12

12. M. Paturzo, P. Memmolo, L. Miccio, A. Finizio, P. Ferraro, A. Tulino, and B. Javidi, “Numerical multiplexing and demultiplexing of digital holographic information for remote reconstruction in amplitude and phase,” Opt. Lett. 33(22), 2629–2631 (2008). [CrossRef] [PubMed]

] investigated the possibility to multiplexing and demultiplexing numerically DHs with the aim of optimizing their storage and/or transmission process. The holograms are multiplexed and demultiplexed thanks to the unique property of the DHs to numerically manage the complex wavefields. They showed that it is possible to correctly retrieve quantitative information about the amplitude and phase of one hundred DHs. Their approach can be useful to transmit efficiently, in terms of reduced amount of data, the DHs from the recording head to a remote display unit. Other recent papers dealing with compression of DHs are worthy of note since the methods they describe can be implemented optically and can be adapted to our issue of simultaneous compression and encryption. For example, a compression and multiplexing architecture of multiple images was reported in [13

13. A. Alfalou and C. Brosseau, “Exploiting root-mean-square time-frequency structure for multiple-image optical compression and encryption,” Opt. Lett. 35(11), 1914–1916 (2010). [CrossRef] [PubMed]

].This method, which is based upon a specific spectral multiplexing (fusion without overlapping) of the multiple images, aims to achieve a single encrypted image, at the output plane of our system, that contains all information needed to reconstruct the target images. For that purpose, the Fourier plane of the image to transmit is divided into two types of area, i.e., specific and common areas to each target image. A segmentation criterion taking into account the RMS criterion is proposed. This approach, which consists of merging the input target images together (in the Fourier plane) allows us to reduce the information to be stored and/or transmitted (compression) and induce noise on the output image (encryption). In the same vein, Darakis and Soraghan [14

14. E. Darakis and J. J. Soraghan, “Reconstruction domain compression of phase-shifting digital holograms,” Appl. Opt. 46(3), 351–356 (2007). [CrossRef] [PubMed]

] carried out a compression scheme of data, based on phase-shifting interferometry digital holography (PSIDH) that is performed at the reconstruction plane. These authors have shown how the increased spatial correlation apparent at the reconstruction plane can be effectively exploited to obtain high compression even with relatively simple methods such as the quantization followed by lossless coding. Naughton et al. [15

15. T. J. Naughton, J. B. McDonald, and B. Javidi, “Efficient compression of fresnel fields for Internet transmission of three-dimensional images,” Appl. Opt. 42(23), 4758–4764 (2003). [CrossRef] [PubMed]

] compressed PSDH for the transmission of three dimensional images. For real-time networking applications, the time required to compress can be as critical as the compression rate. They achieved lossy compression through quantization of both the real and imaginary streams, followed by a bit packing operation. They verified transmission speedup due to compression using a special-purpose Internet-based networking application. In [16

16. T. J. Naughton, Y. Frauel, B. Javidi, and E. Tajahuerce, “Compression of digital holograms for three-dimensional object reconstruction and recognition,” Appl. Opt. 41(20), 4124–4132 (2002). [CrossRef] [PubMed]

], Naughton and co-workers also presented the results of applying lossless and lossy data compression to a three-dimensional object reconstruction and recognition technique based on PSDH. The lossy techniques are based on subsampling, quantization, and DCT. Dealing with a face recognition application, Wijaya et al. [17

17. S. L. Wijaya, M. Savvides, and B. V. K. Vijaya Kumar, “Illumination-tolerant face verification of low-bit-rate JPEG2000 wavelet images with advanced correlation filters for handheld devices,” Appl. Opt. 44(5), 655–665 (2005). [CrossRef] [PubMed]

] suggested using the image compression standard JPEG2000, which is a wavelet-based compression engine used to compress the face images to low bit rates suitable for transmission over low-bandwidth communication channels. Ding et al. [18

18. L. Ding, Y. Yan, Q. Xue, and G. Jin, “Wavelet packet compression for volume holographic image recognition,” Opt. Commun. 216(1-3), 105–113 (2003). [CrossRef]

] also reported a wavelet-based method to recognize target images. In addition, Sekwom et al. [19

19. S. Yeom, A. Stern, and B. Javidi, “Compression of 3D color integral images,” Opt. Express 12(8), 1632–1642 (2004). [CrossRef] [PubMed]

] proposed a compression method designed for color images based on standard MPEG-2.

As mentioned above, in contrast with optical encryption, optical compression techniques have not received the amount of attention they deserve and were not mentioned in the above mentioned analysis [1

1. A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon. 1(3), 589 (2009). [CrossRef]

11

11. F. Mosso, J. F. Barrera, M. Tebaldi, N. Bolognini, and R. Torroba, “All-optical encrypted movie,” Opt. Express 19(6), 5706–5712 (2011). [PubMed]

,20

20. A. Alfalou, C. Brosseau, N. Abdallah, and M. Jridi, “Simultaneous fusion, compression, and encryption of multiple images,” Opt. Express 19(24), 24023–24029 (2011). [CrossRef] [PubMed]

,21

21. M. Johnson, P. Ishwar, V. Prabhakaran, D. Schonberg, and K. Ramchandran, “On compressing encrypted data,” IEEE Trans. Signal Process. 52(10), 2992–3006 (2004). [CrossRef]

]. However, our ability to develop new technologies in communication systems, secure local storage and network-transmission of images will largely depend on our understanding of encryption and compression methods. Thus, combining compression and encryption is important for most applications in communications. Further, such approaches are often achieved either in cascade or independently. Motivated by these observations and in anticipation of wide uses for optical communications, we set out to investigate how one of these operations can affect the other.

1.1. Optical DCT: motivation and background

In Ref [13

13. A. Alfalou and C. Brosseau, “Exploiting root-mean-square time-frequency structure for multiple-image optical compression and encryption,” Opt. Lett. 35(11), 1914–1916 (2010). [CrossRef] [PubMed]

], we proposed a simultaneous compression and encryption method of multiple images based on a spectral fusion of target images in the Fourier domain. Additionally, Alfalou and Brosseau recently examined a new SFCE method by using DCT and information fusion in the spectral domain, which is appropriate for dealing with multiple images of a video sequence [20

20. A. Alfalou, C. Brosseau, N. Abdallah, and M. Jridi, “Simultaneous fusion, compression, and encryption of multiple images,” Opt. Express 19(24), 24023–24029 (2011). [CrossRef] [PubMed]

]. Two advantages of this method are noteworthy. Firstly, only real-valued spectra are dealt with. Secondly, the use of DCT allows the grouping of the information for reconstructing the image in the upper left corner of its spectral plane. Such a grouping of real-valued information does not require the storage and/or transmission of complex-valued data as is the case of most DRP-based techniques [1

1. A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon. 1(3), 589 (2009). [CrossRef]

]. Previously, we have proposed and validated [22

22. A. Alfalou, A. Mansour, M. Elbouz, and C. Brosseau, “Optical compression scheme to multiplex & simultaneously encode images”, in Optical and Digital Image Processing Fundamentals and Applications, G. Cristobal (Ed.), P. Schelkens (Ed.), and H. Thienpont (Ed.), (Wiley, 2011) pp. 463–483.

] an all-optical setup which allows optical implementing of the DCT. However, the quality of the reconstructed images remains poor because the data encoding uses a number of bits which is not adapted to the dynamics in the spectral domain. The motivation of the present study is to remedy this situation by introducing a detailed double optimization procedure for spectrally multiplexing multiple images.

1.2. Optimization of the method

In this work we adopt the optimization strategy recently proposed in [20

20. A. Alfalou, C. Brosseau, N. Abdallah, and M. Jridi, “Simultaneous fusion, compression, and encryption of multiple images,” Opt. Express 19(24), 24023–24029 (2011). [CrossRef] [PubMed]

]. Its main advantage in our context is that it offers a way to increase both compression (section 3) and encryption (section 4) rates. Interestingly, the SFCE method has a strong ability to merge different information from target images in the DCT spectral plane. Its underlying principle is to decompose the spectral plane into many independent areas. One information block corresponding to a target image is affected to each area. We follow the RMS time-frequency criterion [13

13. A. Alfalou and C. Brosseau, “Exploiting root-mean-square time-frequency structure for multiple-image optical compression and encryption,” Opt. Lett. 35(11), 1914–1916 (2010). [CrossRef] [PubMed]

] introduced by Alfalou and Brosseau to determine the useful spectral size of target images. As a consequence, the size of each block is adapted to the target image. We wish to point out that this procedure differs from that which was considered by us in an earlier work [20

20. A. Alfalou, C. Brosseau, N. Abdallah, and M. Jridi, “Simultaneous fusion, compression, and encryption of multiple images,” Opt. Express 19(24), 24023–24029 (2011). [CrossRef] [PubMed]

] where each block was set at a fixed size leading to degradation in performance for image reconstruction. We found that this size adaptation provides a good tradeoff between bandwidth of spectral plane and compression rate. In addition we include the idea of using a real key for increasing the encryption rate of our method. This leads to a decrease of the amount of encrypted information to store and/or to transmit compared to the SFCE method which uses both real and imaginary components (section 4). The present results will allow us to investigate the effects of quantization and several types of attack on compression rate.

The paper is organized as follows. First we briefly review the SFCE method by focusing on the block selection and encryption methods. In section 3 we discuss the phenomenology of the SFCE method in the context of increasing compression rates. A comparison of the error in the reconstructed object following our procedure with others, e.g. JPEG image compression standard, reveals its good performance. Section 4 is devoted to improvement of the encryption performance. To test the robustness of our procedure and illustrate better the implications of our findings, we simulate several types of attack. We summarize and conclude in section 5.

2. Simultaneous fusion, compression, and encryption of multiple images

Figure 1 (a)
Fig. 1 Principle of the SFCE method: (a) synoptic diagram, (b) compression technique scheme.
schematizes the basic principle of fusion underlying the SFCE method. A detailed description of this method can be found in Ref [20

20. A. Alfalou, C. Brosseau, N. Abdallah, and M. Jridi, “Simultaneous fusion, compression, and encryption of multiple images,” Opt. Express 19(24), 24023–24029 (2011). [CrossRef] [PubMed]

]. Here, only the salient features relevant to this analysis will be highlighted. In this figure, I(1), I(2), ..., I(Ni) are the target images at the input of the SFCE system. Firstly we apply separately the DCT transform separately to each of these images. Secondly, each spectrum of size (N,N) pixels is multiplied by a low-pass filter (N',N') with N'<N. In this way, a block of size (N',N'), containing the relevant information for reconstructing each target image, is obtained. An example of such block (filtered DCT) is shown in Fig. 1(b).Each spectral plane is multiplied by a low-pass filter, of size set to (N',N') pixels, positioned in its upper left corner. Then, four of these blocks to which are applied one of the four rotations with angle 0°, 90°, 180°, 270° are grouped together. This leads to a domain of size (2N’,2N’) pixels as shown in Fig. 1(a) (first 4 filtered DCTs). To avoid information overlap these blocks are returned and shifted. Then, quantization to each block of size (N’,N’) pixels is realized, as displayed in Fig. 1 (b). This permits to divide each block in several areas which are further quantized. This quantization is realized by normalizing each DCT to its maximum value. Following this quantization, we get the block shown in the right-side of Fig. 1(b). By reducing the maximum value in a given area we reduce the number of bits required to encode it.

According to the above discussion, we have a real-valued spectral plane containing relevant information for reconstructing the Ni target images. The use of a first encryption-key (a specific image among those used in the input plane of SFCE), the specific fusion after rotation and the quantification constitute the first level of encryption. Then, a digital fingerprint encrypted with the classical DRP system is added to the fusion spectrum to avoid the second encryption level.

Further, we note that even if the SFCE approach has proved to be an effective technique [20

20. A. Alfalou, C. Brosseau, N. Abdallah, and M. Jridi, “Simultaneous fusion, compression, and encryption of multiple images,” Opt. Express 19(24), 24023–24029 (2011). [CrossRef] [PubMed]

], it has limitations because a simple low-pass filter of size (N’,N’) is insufficient to optimize the bandwidth of the spectral plane. In addition, we remark that using a unique and constant filter size for each block and image would not be optimized. It should also be noted that the number of bits for encoding frequencies is not optimized when only the maximum value of the given area is considered. In addition the encryption technique developed in [20

20. A. Alfalou, C. Brosseau, N. Abdallah, and M. Jridi, “Simultaneous fusion, compression, and encryption of multiple images,” Opt. Express 19(24), 24023–24029 (2011). [CrossRef] [PubMed]

] requires the storage and/or transmission of complex data. As already stated in the Introduction section, the problem we address now is to propose specific optimizations for each limitation mentioned.

3. Compression optimization

Our optimization scheme begins with choosing the size of the filter used in the spectral plane of each target image. In our proposed optimization scheme, we used and adapted the RMS criterion to determine the minimal size for each target image.

3.1. Adaptation of the block size according RMS criterion

Optimizing the spectral bandwidth, that is increasing the multiplexing capability of the SFCE method, requires finding a criterion which allows us to adapt the block size (set for the moment to (N’,N’) pixels) for each target image. Let us estimate the minimum size of the spectrum of a given target image. For that purpose we have adapted the RMS duration criterion to DCT. Following [13

13. A. Alfalou and C. Brosseau, “Exploiting root-mean-square time-frequency structure for multiple-image optical compression and encryption,” Opt. Lett. 35(11), 1914–1916 (2010). [CrossRef] [PubMed]

], we define the RMS criterion

t=n++(u2+v2)|SI(u,v)|2dudv,
(1)

where tis the block size expressed in pixels for a given target image, |SI(u,v)| is the normalized DCT of target image I, and n is a constant ranging from 0 and 2, e.g. n=1represents the minimum size required for reconstructing a given image.

The value of 2 was achieved by trial and error and by considering that the useful information contained in a DCT spectrum is contained in a space less than two times the useful size defined by the RMS criterion. Hence, the filter size which is used in the spectral plane (i.e. block’s size) is not constant but depends on the amount of information. We present in Table 1

Table 1. Example of a reconstructed image corresponding to several sizes of block(t,t)

table-icon
View This Table
| View All Tables
the reconstructed images corresponding to several sizes of block(t,t) with n ranging between 0 and 2. Table 1 shows that the reconstruction of the target image does not require the information contained in all pixels. If n = 1, i.e. for a block of size 88×88 pixels (panel (e) of Table 1), the algorithm was able to reconstruct satisfactorily the target image (panel (a) of Table 1). However, the algorithm performs poorly for n<1 (panels (b-c-d) of Table 1). In contrast a good performance can be achieved for n>1 (panels (f-g) of Table 1).

Changing n from 1.5 to 2 improves the quality of the reconstructed image. Beyond n = 2 there is no visible improvement of the quality of the reconstructed image. In the following n is set to 2. For the purpose of later comparison of the numerically derived effect of block size on the quality of the reconstructed image and compression rate, two different metrics will be used: the mean-square error (MSE), and the peak signal-to-noise ratio (PSNR).

3.2. Effect of the block size on the quality of reconstructed images

Here no quantization is applied and the compression rate Tc_pixel (expressed in pixels) is evaluated as follows. Assume that we consider Ni target images of size (tx,ty)pixels, where tx and ty denote the size in pixels of each image (in this work we assume that tx=ty=N). Then, the total size of the image is Nitxty=NiN2 pixels. After multiplexing (Fig 1(a)), a single spectral plane of size (tx,ty)needs to be stored instead of the Ni images each of size (tx,ty)pixels. Since the DCT spectrum is real, this size is equal to txty=N2 As a result, we find that
Tc_pixel=1sizeofmultiplexedDCTspectralplanesizeofNiinputimages=1N2Ni×N2=11Ni
(2)
To illustrate this point, we consider Table 2

Table 2. Effect of the compression rate (Tc_pixel) in pixels on the quality of the reconstructed images

table-icon
View This Table
| View All Tables
which shows a comparison of the reconstructed images and compression rates as a function of block size: The first column of this table is concerned with the block size obtained from Eq. (1). The second column corresponds to the compression rates (in pixels) for a given block size, e.g. if N=256 (image size equal to 256×256 pixels) and n=1.5, 4 blocks of size (132×132) pixels can be merged in a (256×256 pixels) spectral plane. The third column lists the MSE and PSNR values. The fourth column shows an example of a reconstructed image. The fifth column shows the number of target images that can be merged for a given n. Not surprisingly, the effect of increasing the number of multiplexed images is to increase Tc_pixel but significantly impacts the quality of the reconstructed images. Increasing Tc_pixel (while keeping a good quality of the reconstructed images) can be realized by adapting quantization such as using the smallest number of bits.

3.3. Calculation of the compression rate without quantization

For a further comparison of the effect of quantization on Tc, we first consider the special case in the absence of quantization. The compression rate Tc (in bits) is determined with respect to the input images (images to transmit and/or to store) and the filtered multiplexed spectra. It is given by
Tc=1sizeout/sizein,
(3)
where size=in8Nitxty is defined as the length (in its bit description) of the sequence of images to store and/or transmit (gray scale images encoded over 8 bits are considered here), and sizeout denotes its counterpart at the output of Fig. 1(a). The number of bits used in each block can be written as log{max(block)min(block)}2t2, where max(block) and min (block) denote respectively the maximal and minimal value in the blocks, and t is calculated from Eq. (1).

It is interesting to point out that without taking into account the decimal part of the DCT (without quantization) the encoding is realized with less than 16 bits compared with 65 bits when the decimal part is considered. Without quantization Tc in bits is not optimized. That is, it is smaller than Tc in pixels (Table 3

Table 3. Comparison of the compression rate expressed in bits and in pixels

table-icon
View This Table
| View All Tables
). This is due in part to the rapidly varying spectra which necessitate a large number of encoding bits. To remedy this situation we propose to quantify the DCT blocks to obtain a fixed number of bits.

3.4. Fixed quantization

A natural question is this: what is the influence of the number of bits m which is required to encode the coefficients of the DCT blocks? There are several ways in which this question might be answered, but here, we first assume that m=log2(max(block)) is fixed. The results showing the reconstructed images, Tc, and PSNR are summarized in Table 4

Table 4. Compression rate, PSNR, and quality of the reconstructed images when using a number of bits set to m=log2(max(block))

table-icon
View This Table
| View All Tables
.A notable feature of Table 4 is that obtaining a good compression rate requires a small block t, i.e. a large number of images to be multiplexed. According to these numbers, the quality of the reconstructed images degrades rapidly. For example, if Ni is set to 16, the attained Tc=88% corresponding to a 10 dB loss. In addition, one sees that the values of Tc remain quite limited.

The data in Table 5

Table 5. Effect of uniform quantization of the DCT blocks on the compression rate and reconstructed image quality

table-icon
View This Table
| View All Tables
show that compression rate can be fixed by choosing the number of bits which is necessary to encode the values of each block. This corresponds to a compression rate of 80% for a number of bits set to 4 (with only two images Ni=2; second line). This value of Tc is significantly larger than the 2.5% obtained for the case of two images (Table 4). But, it should be noted that the quality of the reconstructed images remains poor. Thus, if the latter is over 8 bits this method leads to a high degradation in reconstructed image quality due to the uniform quantization.

Comparing Table 4 (good quality of reconstructed images) and Table 5 (large Tcs) indicates that a compromise between the two ways of calculating m should be found. We suggest that a convenient measure of m is given by
m=log2(V'),
(5)
where m is the maximum number of bits used for encoding the DCT coefficients of a given block, and V' is the normalized value of the DCT coefficient within the range [0, max]. It is worth noting that Eq. (5) can be applied to every block size (t×t), and even to areas smaller than (t×t)as depicted in Fig. 1(b).

3.5. Quantization by block optimization and normalization between 0 and max

To overcome the issue of image quality (Table 5), we adopt the following strategy. We decompose a DCT block into several areas, and quantize each area using to Eq.(4). However, the number of bits is not optimized. This reflects the fact that only the maximum value of the quantified-DCT is considered in Eq.(4) without knowledge of its minimum value. The optimization which is proposed consists in calculating a new block of the quantized DCT taking into account of the minimum value (Fig. 1). The number of bits which is used to encode each area of the DCT blocks is fixed and set to m. The DCT is first divided in several areas according to a given step (Fig. 1). Next, each area is quantized (each area is represented by a specific color in Fig. 1 by considering both maximum and minimum values in this area.

Table 6

Table 6. Comparison of the compression rate and PSNR with or without optimization of the number of bits m

table-icon
View This Table
| View All Tables
compares the quality of the reconstructed images and Tc with or without optimization. From left to right, the first column indicates the number of images to be multiplexed in the spectral plane. PSNR is shown in the second column. The reconstructed images without optimization [20

20. A. Alfalou, C. Brosseau, N. Abdallah, and M. Jridi, “Simultaneous fusion, compression, and encryption of multiple images,” Opt. Express 19(24), 24023–24029 (2011). [CrossRef] [PubMed]

] are displayed in the third column, while those with optimization are considered in the fourth column. In this column, the number of bits used for each area of the DCT blocks of size (t,t) is calculated with respect to the range between these two values, i.e. log2(max-min), instead of using the range from 0 to the maximum value, i.e. log2(max-0). The net effect is a decrease of m for the following reason. Assume that in a given area the maximum and minimum value as are respectively set to 255 and 128. Using log2(max-0) requires 8 bits for encoding these values. Now normalizing values between 0 and max [0-128] and using log2(max-min) involves only 7 bits. Another notable feature of Table 6 is that as the PSNR is decreased the quality of the reconstructed image decreases gently while the compression rate (in bits) increases. For a given PSNR value, the compression rate is always larger when our optimization method is employed. This scheme permits a compression rate close to 97% to be obtained with good quality of reconstructed images (Ni=16).

3.6. Comparison with JPEG

The efficiency of our optimized method will be demonstrated by adapting a number of pixels to each image and DCT quantization in order to reduce the number of bits required for encoding DCT blocks (t,t). Table 7

Table 7. A comparison of the compression performance between JPEG (left) and SFCE (right) methods

table-icon
View This Table
| View All Tables
shows a comparison of the results (gray-level images) obtained from our method with those obtained with the JPEG image compression standard for several compression rates. The data in Table 7 shows that the optimized SFCE method proved to be a very effective technique to control Tc. This is due to the adapted quantization and choice of the size of the DCT block. The key feature is that our technique does not suffer from the pixellization as is observed with the JPEG compression method. It is anticipated that this can be improved further by applying different geometric forms to define each DCT block as used in the Tetrolet transform [23

23. J. Krommweh, “Tetrolet transform: A new adaptive Haar wavelet algorithm for sparse image representation,” J. Vis. Commun. Image R. 21(4), 364–374 (2010). [CrossRef]

]. Overall, these simulations confirm the importance of the optimized SFCE method. As shown in Table 5, for a compression rate of 94%, the attained PSNR is 27.7, while for a compression rate of 93% JPEG leads to a PSNR value of 25.6%.

In Fig. 2(a)
Fig. 2 Compression rate as a function of the number of multiplexed images without optimization. (b) As in (a) for the PSNR. (c) A comparison of the PSNR values versus the compression rate with our optimized method (squares) and the JPEG method (circles). The circled values indicate that our scheme may not have better compression performances than JPEG in the high PSNR case. The dashed line corresponds to the case of five multiplexed images. The solid lines are guides for the eye.
and Fig. 2(b) we present respectively the compression rate and the PSNR values as a function of the number of multiplexed images without optimization. Figure 2(c) compares the PSNR as a function of compression rate for the optimized SFCE and JPEG methods. With the former, we get Tc=62% and PSNR= 32.5 dB.

Visual observation indicates that the quality of images is good and is better than the one obtained with JPEG as shown in the bottom lines of Table 6 and Table 7. However, our calculations show that our method may not have better compression performances than JPEG in the high PSNR case.

4. Optimized encryption adapted to the SFCE method

The spectral plane resulting from the fusion of the different DCT blocks constitutes a first encryption level (Fig. 1). Without knowledge of the size of each block, its rotation, shape, and position, it remains difficult to reconstruct the target images. Additionally, if DRP is applied to the JPEG implementation, compression rate is limited, i.e. Tc47%, since the encrypted images are complex valued. Hence, a second level of encryption will be added without degradation either in reconstructed image quality or in compression rate.

4.1 Optimization using real key image

Figure 3
Fig. 3 Synoptic diagram illustrating the optimized encryption method.
shows the basic principle used to add a second encryption level. For that we used a real key image (a single personal fingerprint). The second encryption key is found offline. We start by Fourier transforming the biometric image, i.e. fingerprint, multiplied by a first random phase mask. Next, only the real part of the spectrum is selected. Using the encrypted real-part, the maximum value (max) is calculated. Then, a random mask with real values within the range [0, max] is performed. Then, the real part of the encrypted spectrum of this fingerprint is added to the second mask. It is interesting to notice that introduction of this random real mask allows us to smoothen the values in the spectral multiplexed plane. Finally, the random amplitude values are used to encrypt the spectral plane containing the different multiplexed spectra. Thus, compressed and encrypted output plane is obtained.

We start by fabricating the decryption mask. This requires the knowledge of the key image (fingerprint) and the procedure. The reverse procedure which is illustrated in Fig. 1 is then performed. Here, the encryption rate is calculated via the PSNR between the target image and the decrypted image without knowledge of keys. The PSNR should be larger than 15 dB for reconstruction integrity. The technique achieves PSNR< 4 up to 16 images indicating a good performance of encryption (PSNR<<30 dB i.e. the value of reconstructed image without compression). Table 8

Table 8. Encryption using a real key image: PSNR as function of the number of multiplexed images

table-icon
View This Table
| View All Tables
shows the PSNR corresponding to the encryption results as a function of the number of multiplexed input images. Our calculations indicate that PSNR< 4dB.

For comparison, we also show calculations of Tc with encryption (Table 9

Table 9. Compression rate with m = 5

table-icon
View This Table
| View All Tables
) and m=5. The performances are good since Tc is decreased by only 8% compared to the case where no encryption is performed.

4.2 Resistance against attacks

We confine our attention in this subsection to quantify the performance of our algorithm against several plaintext-chosen attacks. Attack 1 is the most probable since the cipher does not have any information about the target images, the used technique, and the encryption keys.Attack 1: Our first test is conducted with the cipher having no information about our technique. We assume that he or she has no knowledge of the number of target images, their rotation and quantization, the encryption keys, and the encryption protocol. To accomplish his or her goal, the cipher needs all this information which renders his or her task arduous. Indeed, within the optimized SFCE algorithm that is presented here one needs to have the fingerprint, random phase mask, quantization matrix, block sizes, their rotations and shapes to decrypt the input information. The size of the random matrix and fingerprint is tx×ty. To show how it is difficult to retrieve this information contained in a quantization matrix whose size is equal to txNi let us consider an example. We now briefly discuss how the combination number scales for the case of an image of size 256×256: 256256×256 for the fingerprint and (1015)256×256 for the random matrix. The quantization matrix (for an image of size 256×256) has size 256×1. The latter includes maximum values of the DCT of the image. The simulation of this matrix seems to be unlikely. In this case, testing all keys is discouraging.Attack 2: The second test considers that the cipher now knows the principle of the optimized SFCE. For simplicity, a single image was used in this test. Since the cipher has access to our system, he or she can send an image corresponding to the inverse DCT (IDTC) of a matrix whole elements are all equal to 1. Matrix quantization is realized such that each value is m-bit encoded, i.e. every value is multiplied by (2m-1 – 1). Then, encryption block is realized. This block is the sum of the real part of the Fourier transform of the fingerprint and of the maximum value of the latter multiplied by a random matrix. The cipher can guess the encryption block in suppressing a matrix of the same dimension as the image sent but for which all the values are equal to 2m11 in the output plane of SFCE resulting from encryption. Thus, for another sent image, he or she already knows the block which allows encryption of this image. He or she suppresses it from the encrypted image and since the quantization matrix is unknown to him or her, only the IDCT needs to be carried out. In Fig. 4
Fig. 4 Example of attack with knowledge of the fingerprint and random matrix: (a) target image, (b) compressed and encrypted image following the SFCE algorithm, (c) the cipher result.
, we show an example of what can be obtained by the cipher following his or her attack. As displayed in Fig. 4(c), the resulting reconstructed image differs from the target image. However, the latter shows some part of the information contained in the former.Optimization against attack 2: To get better results and enhance the robustness of our system against such attack (2), one elegant idea for addressing the flaw is to divide the key image into several parts, see, e.g. Fig. 5(a)
Fig. 5 (a) Key image, (b) key image decomposed in several parts which have been permuted.
and Fig. 5(b). Then, we introduce the number of the part sent in the encryption process in such a way that the encryption block changes at each sending. Consequently, even if the cipher knows the encryption block following this method, he or she could not decrypt images sent later. The solution to this defect consists in changing the numbered parts (Fig. 5(b)) according to the considered image. This implies a change of the Fourier transform and of the encryption block with which the image is encrypted. Interestingly, the number of the part can be easily introduced in the fingerprint. The output encrypted image resembles to that shown in Fig. 4(b). However, only low values of PSNR were obtained, e.g. after 5000 trials and using two of the four parts of the key image (Fig. 5(b)), PSNR7.3 dB.Thirdly, we assume that the cipher knows that a specific image exists among those to be sent. He or she knows also that the second key is a fingerprint. If he or she finds a satisfactory PSNR between the result he or she recovers the image to be sent (PSNR>18 dB), then the algorithm stops. Otherwise, the cipher changes the value of the fingerprint considered using 4×4 blocks, then using 2×2 blocks, and finally pixel by pixel. At each change, the PSNR is calculated and the algorithm stops if the PSNR is larger than 18 dB. The result of this attack has not permitted recovery of the image.

Attack 3: Finally, we consider that the cipher knows a part of the image to be sent (part (P×P)of the target image depicted in Fig. 6
Fig. 6 For the attack 3, the part of the image framed in red is known by the cipher.
) and where it is located. Once again, we assume that the cipher knows the principle of the encryption method. So, he or she tries to decrypt the image thanks to a given fingerprint. The algorithm stops when PSNR>18 dB. The PSNR is calculated between the image reconstructed by the attack for which the image part and its position are known. It is important to point out that we were unable to decrypt the target image after trials lasting more than three weeks (P=64 pixels, image size=256 pixels). In conclusion, this set of tests demonstrates the robustness of our algorithm against such kind of attacks since even with knowledge of much data the original target image cannot be decrypted.

5. Summary and conclusions

In conclusion, we have investigated several ways of optimization of the SFCE method originally suggested in [13

13. A. Alfalou and C. Brosseau, “Exploiting root-mean-square time-frequency structure for multiple-image optical compression and encryption,” Opt. Lett. 35(11), 1914–1916 (2010). [CrossRef] [PubMed]

]. The presented technique has great potential to achieve compression and encryption of images simultaneously in a dependent way. The motivation for much of this research was the premise that control of the size, rotation, and shifting of DCT-blocks can be achieved to optimize the bandwidth of the spectral plane. Finally, we stress that the results presented here provide strong evidence that the use of an encryption method based on real keys allows us to increase the robustness of this method against several types of attack while maintaining a satisfactory compression rate. These results will hopefully stimulate more theoretical efforts to obtain a greater understanding of efficient simultaneous compression and encryption of multiple images, which, in turn, could stimulate the optical implementation of these procedures.

Acknowledgment

We thank the reviewers of this manuscript for enhancing the quality of our work. This work was supported by the Lab-STICC which is Unité Mixte de Recherche CNRS 6285. This paper is dedicated to the memory of Alfalou’s mother, Mrs. Fatma Bayda.

References and links

1.

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon. 1(3), 589 (2009). [CrossRef]

2.

B. Javidi, ed., Optical and Digital Techniques for Information Security (Springer Verlag, New York, 2005).

3.

P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20(7), 767–769 (1995). [CrossRef] [PubMed]

4.

Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express 15(16), 10253–10265 (2007). [CrossRef] [PubMed]

5.

P. Kumar, J. Joseph, and K. Singh, “Known-plaintext attack-free double random phase-amplitude optical encryption: vulnerability to impulse function attack,” J. Opt. 14(4), 045401 (2012). [CrossRef]

6.

J.-J. Huang, H.-E. Hwang, C.-Y. Chen, and C.-M. Chen, “Lensless multiple-image optical encryption based on improved phase retrieval algorithm,” Appl. Opt. 51(13), 2388–2394 (2012). [CrossRef] [PubMed]

7.

X. Wang and D. Zhao, “Double images encryption method with resistance against the specific attack based on an asymmetric algorithm,” Opt. Express 20(11), 11994–12003 (2012). [CrossRef] [PubMed]

8.

A. Alfalou and A. Mansour, “All optical video-image encryption enforced security level using independent component analysis,” J. Opt. A, Pure Appl. Opt. 9, 787 (2007). [CrossRef]

9.

Z. Liu, Q. Guo, L. Xu, M. A. Ahmad, and S. Liu, “Double image encryption by using iterative random binary encoding in gyrator domains,” Opt. Express 18(11), 12033–12043 (2010). [CrossRef] [PubMed]

10.

A. Alfalou and C. Brosseau, “Dual encryption scheme of images using polarized light,” Opt. Lett. 35(13), 2185–2187 (2010). [CrossRef] [PubMed]

11.

F. Mosso, J. F. Barrera, M. Tebaldi, N. Bolognini, and R. Torroba, “All-optical encrypted movie,” Opt. Express 19(6), 5706–5712 (2011). [PubMed]

12.

M. Paturzo, P. Memmolo, L. Miccio, A. Finizio, P. Ferraro, A. Tulino, and B. Javidi, “Numerical multiplexing and demultiplexing of digital holographic information for remote reconstruction in amplitude and phase,” Opt. Lett. 33(22), 2629–2631 (2008). [CrossRef] [PubMed]

13.

A. Alfalou and C. Brosseau, “Exploiting root-mean-square time-frequency structure for multiple-image optical compression and encryption,” Opt. Lett. 35(11), 1914–1916 (2010). [CrossRef] [PubMed]

14.

E. Darakis and J. J. Soraghan, “Reconstruction domain compression of phase-shifting digital holograms,” Appl. Opt. 46(3), 351–356 (2007). [CrossRef] [PubMed]

15.

T. J. Naughton, J. B. McDonald, and B. Javidi, “Efficient compression of fresnel fields for Internet transmission of three-dimensional images,” Appl. Opt. 42(23), 4758–4764 (2003). [CrossRef] [PubMed]

16.

T. J. Naughton, Y. Frauel, B. Javidi, and E. Tajahuerce, “Compression of digital holograms for three-dimensional object reconstruction and recognition,” Appl. Opt. 41(20), 4124–4132 (2002). [CrossRef] [PubMed]

17.

S. L. Wijaya, M. Savvides, and B. V. K. Vijaya Kumar, “Illumination-tolerant face verification of low-bit-rate JPEG2000 wavelet images with advanced correlation filters for handheld devices,” Appl. Opt. 44(5), 655–665 (2005). [CrossRef] [PubMed]

18.

L. Ding, Y. Yan, Q. Xue, and G. Jin, “Wavelet packet compression for volume holographic image recognition,” Opt. Commun. 216(1-3), 105–113 (2003). [CrossRef]

19.

S. Yeom, A. Stern, and B. Javidi, “Compression of 3D color integral images,” Opt. Express 12(8), 1632–1642 (2004). [CrossRef] [PubMed]

20.

A. Alfalou, C. Brosseau, N. Abdallah, and M. Jridi, “Simultaneous fusion, compression, and encryption of multiple images,” Opt. Express 19(24), 24023–24029 (2011). [CrossRef] [PubMed]

21.

M. Johnson, P. Ishwar, V. Prabhakaran, D. Schonberg, and K. Ramchandran, “On compressing encrypted data,” IEEE Trans. Signal Process. 52(10), 2992–3006 (2004). [CrossRef]

22.

A. Alfalou, A. Mansour, M. Elbouz, and C. Brosseau, “Optical compression scheme to multiplex & simultaneously encode images”, in Optical and Digital Image Processing Fundamentals and Applications, G. Cristobal (Ed.), P. Schelkens (Ed.), and H. Thienpont (Ed.), (Wiley, 2011) pp. 463–483.

23.

J. Krommweh, “Tetrolet transform: A new adaptive Haar wavelet algorithm for sparse image representation,” J. Vis. Commun. Image R. 21(4), 364–374 (2010). [CrossRef]

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(100.0100) Image processing : Image processing
(200.4560) Optics in computing : Optical data processing

ToC Category:
Image Processing

History
Original Manuscript: January 8, 2013
Revised Manuscript: February 21, 2013
Manuscript Accepted: February 28, 2013
Published: March 26, 2013

Citation
A. Alfalou, C. Brosseau, N. Abdallah, and M. Jridi, "Assessing the performance of a method of simultaneous compression and encryption of multiple images and its resistance against various attacks," Opt. Express 21, 8025-8043 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-7-8025


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon.1(3), 589 (2009). [CrossRef]
  2. B. Javidi, ed., Optical and Digital Techniques for Information Security (Springer Verlag, New York, 2005).
  3. P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett.20(7), 767–769 (1995). [CrossRef] [PubMed]
  4. Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express15(16), 10253–10265 (2007). [CrossRef] [PubMed]
  5. P. Kumar, J. Joseph, and K. Singh, “Known-plaintext attack-free double random phase-amplitude optical encryption: vulnerability to impulse function attack,” J. Opt.14(4), 045401 (2012). [CrossRef]
  6. J.-J. Huang, H.-E. Hwang, C.-Y. Chen, and C.-M. Chen, “Lensless multiple-image optical encryption based on improved phase retrieval algorithm,” Appl. Opt.51(13), 2388–2394 (2012). [CrossRef] [PubMed]
  7. X. Wang and D. Zhao, “Double images encryption method with resistance against the specific attack based on an asymmetric algorithm,” Opt. Express20(11), 11994–12003 (2012). [CrossRef] [PubMed]
  8. A. Alfalou and A. Mansour, “All optical video-image encryption enforced security level using independent component analysis,” J. Opt. A, Pure Appl. Opt.9, 787 (2007). [CrossRef]
  9. Z. Liu, Q. Guo, L. Xu, M. A. Ahmad, and S. Liu, “Double image encryption by using iterative random binary encoding in gyrator domains,” Opt. Express18(11), 12033–12043 (2010). [CrossRef] [PubMed]
  10. A. Alfalou and C. Brosseau, “Dual encryption scheme of images using polarized light,” Opt. Lett.35(13), 2185–2187 (2010). [CrossRef] [PubMed]
  11. F. Mosso, J. F. Barrera, M. Tebaldi, N. Bolognini, and R. Torroba, “All-optical encrypted movie,” Opt. Express19(6), 5706–5712 (2011). [PubMed]
  12. M. Paturzo, P. Memmolo, L. Miccio, A. Finizio, P. Ferraro, A. Tulino, and B. Javidi, “Numerical multiplexing and demultiplexing of digital holographic information for remote reconstruction in amplitude and phase,” Opt. Lett.33(22), 2629–2631 (2008). [CrossRef] [PubMed]
  13. A. Alfalou and C. Brosseau, “Exploiting root-mean-square time-frequency structure for multiple-image optical compression and encryption,” Opt. Lett.35(11), 1914–1916 (2010). [CrossRef] [PubMed]
  14. E. Darakis and J. J. Soraghan, “Reconstruction domain compression of phase-shifting digital holograms,” Appl. Opt.46(3), 351–356 (2007). [CrossRef] [PubMed]
  15. T. J. Naughton, J. B. McDonald, and B. Javidi, “Efficient compression of fresnel fields for Internet transmission of three-dimensional images,” Appl. Opt.42(23), 4758–4764 (2003). [CrossRef] [PubMed]
  16. T. J. Naughton, Y. Frauel, B. Javidi, and E. Tajahuerce, “Compression of digital holograms for three-dimensional object reconstruction and recognition,” Appl. Opt.41(20), 4124–4132 (2002). [CrossRef] [PubMed]
  17. S. L. Wijaya, M. Savvides, and B. V. K. Vijaya Kumar, “Illumination-tolerant face verification of low-bit-rate JPEG2000 wavelet images with advanced correlation filters for handheld devices,” Appl. Opt.44(5), 655–665 (2005). [CrossRef] [PubMed]
  18. L. Ding, Y. Yan, Q. Xue, and G. Jin, “Wavelet packet compression for volume holographic image recognition,” Opt. Commun.216(1-3), 105–113 (2003). [CrossRef]
  19. S. Yeom, A. Stern, and B. Javidi, “Compression of 3D color integral images,” Opt. Express12(8), 1632–1642 (2004). [CrossRef] [PubMed]
  20. A. Alfalou, C. Brosseau, N. Abdallah, and M. Jridi, “Simultaneous fusion, compression, and encryption of multiple images,” Opt. Express19(24), 24023–24029 (2011). [CrossRef] [PubMed]
  21. M. Johnson, P. Ishwar, V. Prabhakaran, D. Schonberg, and K. Ramchandran, “On compressing encrypted data,” IEEE Trans. Signal Process.52(10), 2992–3006 (2004). [CrossRef]
  22. A. Alfalou, A. Mansour, M. Elbouz, and C. Brosseau, “Optical compression scheme to multiplex & simultaneously encode images”, in Optical and Digital Image Processing Fundamentals and Applications, G. Cristobal (Ed.), P. Schelkens (Ed.), and H. Thienpont (Ed.), (Wiley, 2011) pp. 463–483.
  23. J. Krommweh, “Tetrolet transform: A new adaptive Haar wavelet algorithm for sparse image representation,” J. Vis. Commun. Image R.21(4), 364–374 (2010). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited