Investigation on optical image encryption using fourier and fractional fourier domain techniques

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INVESTIGATIONS ON OPTICAL IMAGE ENCRYPTION USING FOURIER AND

FRACTIONAL FOURIER DOMAIN TECHNIQUES

NAVEEN KUMAR NISHCHAL Department of Physics

Thesis submitted

in fulfilment ofthe requirements for the degree ofDoctor of Philosophy to the

INDIAN INSTITUTE OF TECHNOLOGY, DELHI

NEW DELHI-lb0 016 (INDIA)

April 2004

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CERTIFICATE

This is to certify that the thesis entitled,

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'Investigations on Optical image Encryption using Fourier and Fractional Fourier Domain Techniques

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', being submitted by Mr. Naveen Kumar Nishchal, to the Indian Institute of Technology, Delhi, New Delhi, for the award of Degree of Doctor of Philosophy in Physics is a record of bonaffide research work carried out by him under our supervision and guidance. He has fuiffihled the requirements for submission of the thesis, which to the best of our knowledge has reached the requisite standard.

The material contained in the thesis has not been submitted in part or full to any other University or Institute for the award of any degree or diploma.

(JOBY JOSEPH) (KEHAR SINGH)

Assistant Professor Professor

Department of Physics Department of Physics

I. I. T. Delhi I.I.T Delhi

New Delhi-i 10 016 NewDelhi.-110 016

April, 2004

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ACKNOWLEDGEMENT

I am very grateful to my thesis advisors Professor Kehar Singh and Dr. Joby Joseph for introducing me to this fascinating area of research. Their devotion to research has been a constant source of inspiration to me during the course of my research work. I would like to imbibe this quality fflom them in my future career. I express my profound sense of gratitude towards them for their valuable guidance and encouragement.

I acknowledge Professor Jitendra Behani of Jawaharlal Nehru University for always encouraging me in my academic endeavors.

I am very grateful to Dr. Arvind Kumar for his encouragement and moral support during the course of my research work. He has always been more than willing to help me, whenever I have approached him.

I have been fortunate in having a person like Dr. G. Unnikrishnan as my senior. I had numerous discussions with him on various aspects of my research especially on optical encryption and pattern recognition, which have beneffited me immensely. I have enjoyed working in the Photonics Group all through the years. I thank all the group members for creating a pleasant working environment. I thank Dinesh, Aloka, Rajashekhar, Renu, Madhusudan, Anith, Shailly, Rakesh, and Madan Singh for all their valuable help.

I would like to thank all my friends Vishwajit, Awadhesh, Jitendra, Rajeev, Arun, PaulRaj, Binod, and Ajit for all their help and moral support. It is certainly not enough to thank all my friends Dipanjan, Manoj, Amarendra, Rakesh, Somnath, Pushpendra, Ajay, and Tarsem who made my stay in IITD a pleasant one.

I acknowledge my Mausaji who taught me physics and helped me develop a love for the subject. Words fail to express the profound sense of gratitude I feel for my beloved Babuji, Phua and Phuphaji, Bhaiya and Bhabhi, sister, brother-in-law, Rupak, Meghali, Arsh, Rupali, Shantanu, Ishita, and late grandparents for all the love and affection they have showered on me. But for their affection and encouragement all this would not have been possible.

I dedicate this thesis to the loving memory of my late mother.

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ABSTRACT

'Data security' has become of utmost concern in the present age which is oifien termed as 'information age'. With the advent of Internet tecimology, there has been a phenomenal increase in the rate at which information is being disseminated. Information fraud is increasingly becoming a serious problem for many banks, businesses, and consumers. Each year, commerce and industry worldwide spend billions of dollars on checking information fraud. Therefore, there is a need to develop new methods for security applications.

Cryptography is one of the tools that ensures security, integrity, and authentication of electronic data. Traditional methods have relied on the principles of cryptography [Stallings 2000] to build systems providing the different security services. The security of these cryptosystems is being enhanced by using more powerful algorithms and larger key lengths, which in turn would require more computing time and power. When large amounts of data are to be encoded, these requirements may turn out to be the system bottleneck.

In an encryption system, we wish to encode information in such a fashion that, even if it is viewed or recorded, only the application of the correct key will reveal the original information. Optical systems have many features, which make them attractive for data security applications [Refregier and Javidi i 995a,b; Javidi i 997a,b; Yu and Jutamulia 1998; Unnikrishnan et al. 1998,2000a,b,2001;Unnikrishnan and Singh 200 1 a,b]. For example, an intensity-sensing device cannot copy information encoded using phase of the light. Optical signals are two-dimensional compared to electrical signals which are one- dimensional. This fact makes optical devices inherently capable of processing two- dimensional data such as images. Moreover, most of the electronic processors are limited to serial processing. Hence, optical systems can process and transmit large amount of

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information in parallel and have higher throughput rate compared to their electronic counterparts. It is believed that optical encryptioli technologies provide a more complex environment and are more resistant to attacks than are digital electronic systems. Optical security systems can be classiffied into two categories based on the type of application, namely security veriffication, and encryption of data. With the rapid advancement in computers, CCD technology, image processing hardware and soifiware, printers, scanners and copiers, it has become increasingly possible to reproduce very authentic looking pictures, logos, symbols, patterns, and holograms. The holographic pattern can be photographed or captured by a CCD camera and a new hologram can be synthesized.

Optical pattern recognition techniques [Yu and Jutamulia 1998] have been used to develop foolproof security systems [Javidi and Homner 1994a,b; Abookasis et al. 2001;

Javidi 2002; Abookasis and Rosen 2003a,b]. One of the ffirst proposed methods [Javidi and Homer i 994a,b] uses a scheme of complex phase/amplitude patterns that cannot be copied by an intensity detector such as CCD camera. A phase mask is bonded permanently and irretrievably to a primary identiffication amplitude pattern such as a ffingerprint or a signature. The veriffication of the document is done by a nonlinear joint transform correlator. Optical processing systems have been used to encrypt data [Javidi and Homner 1994a,b; Javidi et al. 1994a,b; Refflegier and Javidi 1995a,b; Homer et al.

1996; Volodin et al. 1996; Javidi 1997a,b; Yu and Jutamulia 1998; Unnikrislman et al.

i 998,2000a,b,200 I;Unnikrishnan and Singh 2000,2001a,b; Matoba and Javidi 2000a,b;

Tajahuerce and Javidi 2000; Tajahuerce et al. 2000,2001;Tan et al. 2000, 2001a,b; Peng et al. 2002a-c,2003;Hennelly and Sheridan 2003a-d; Poon et al. 2003; Seo and Kim 2003a,b; Janucki and Owsik 2003a,b]. In

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double random phase encoding method' [Refflegier and Javidi 1995a,b], a VanderLugt 4-f optical system encrypts a primary image to a noise like image by using two random phase masks in the input and Fourier plane.

The random phase masks serve as the key to the encrypted data. One needs to know the

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random phase mask used for encryption to decode the data. The keys used in optical encryption methods, are more diffficult to break due to the requirement of using sophisticated optical techniques. Thus optical encoding techniques provide safety ifiorn attacks used in digital methods.

Optical methods are more advantageous when data is to be encrypted in the optical domain as in a holographic memory. Encrypted optical memory is emerging as one of the major applications of optical encryption. Many optical encryption techniques have been proposed to secure data stored in holographic memories [Heanue et al. 1995; Javidi 1997b; Matoba and Javidi 1999a-c,2000b; Unni

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ishnan et al. 2001;Tan et al. 200 la,b;

Nomura et al. 2003]. Encrypted optical memory restricts the use of the stored data to people having, a knowledge of the key. Matoba and Javidi [1999a] proposed an encrypted optical memory, which uses double random encoding with the two random phase codes in the Fresnel domain. The knowledge ofthe random codes and their position is essential for the successful decryption of data. Hence the two-dimensional random phase codes along with their positional information, is referred to as three-dimensional key. Matoba and Javidi [ 1 999e] demonstrated an encrypted optical memory based on double-random phase encoding using angular multiplexing. The encrypted images were stored in a photorefractive iron doped lithium niobate crystal using angular multiplexing. The bit- error rate as a function of optical system bandwidth is also numcrically evaluated.

Digital holography for optical information security is an active research topic [Javidi and Nomura 2000a; Lai and Neifeld 2000; Tajahuerce and Javidi 2000; Tajahuerce et al. 2000; Kishk and Javidi 2003a; Arizaga et al. 2003; Yu and Caj 2003; Zhu et al.

2003]. The digital hologram is a convenient form for data transmission and object recognition. Techniques based on digital holography in the fleld of information security have important beneffits as they enable digital storage, transmission, and decryption of encrypted data. Javidi and Nomura [2000a] demonstrated an optical security system using

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digital holography. An encrypted image is stored as a digital hologram. The decryption key is also stored as a digital hologram. The encrypted image can be electrically decrypted by use of the key hologram. This security technique provides secure storage and data transmission.

The present thesis reports the results of investigations on some new optical architecture for data encryption. These architectures use the degrees of ffleedom offered by an optical system to encode information, resulting in enhanced security. A fully phase encryption system has been demonstrated that uses an electrically addressed SLM. Secure holographic storage using cascaded FRT has been demonstrated. Theoretical analysis and simulation studies of an optical encryption algorithm to encode data using jigsaw transform and a localized fractional Fourier transform (FRT) [Ozaktas et al. 2001], has been presented. An encryption system based on digital holography has also been demonstrated.

Chapter 1 contains an introduction and overview of the research in the area of optical security using optical information processing techniques. It includes a discussion on various techniques used for data encryption, and secure holographic memories. The chapter also contains a brief introduction to fractional Fourier transforms and the concept of fractional Fourier domains for encryption. A discussion on digital holography and its application to information security is given.

Chapter 2 reports the experimental realization of a fully phase encryption system based on use of a photorefflactive crystal and an electrically addressed SLM. This chapter is divided into two sections. Section I discusses the encryption using Fourier domain random phase encoding, and section II discusses the encryption using fractional domain random phase encoding. The encrypted image is holographically recorded in a barium titanate photorefractive crystal. Generating a conjugate of the encrypted image through phase conjugation does the decryption of the image. The FRT parameters along with the

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random phase codes constitute the key to the encrypted data. The knowledge of the key is essential to the successful decryption of data. The use of phase conjugation results in near diffflaction-lirnited 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 decrypted phase image is converted into an amplitude image using an electrically addressed SLM as a phase contrast fllter (PCF). Use of an SLM in the ffilter plane does not require manual fabrication of a PCF and it offers the ffleedom of the generation of PCF of different phase shiifis and sizes.

Chapter 3 reports the optical implementation of cascaded extended FRT and its application in amplitude and fully phase encryption. This chapter is divided into two sections. Section I discusses the amplitude image encryption using cascaded extended FRT and section II discusses the phase image based encryption using cascaded extended FRT. The original amplitude or phase image to be encrypted is fflactional Fourier transformed three times and random phase masks are placed in the two intermediate planes. Performing the FRT three times increases the key size, at an added complexity of one more lens. The encrypted image is recorded holographically in a barium titanate crystal and is then decrypted, by generating through phase conjugation, a conjugate of the encrypted image. Experimental results are presented of the optical implementation of cascaded extended FRT. A lithium niobate crystal is used as a PCF to reconstruct the decrypted phase image, in case of fully phase encryption, alleviating the need of alignment of a physical PCF in the Fourier plane making the system rugged.

Chapter 4 discusses a new method to encrypt and decrypt a two-dimensional amplitude image that uses jigsaw transform and localized FRT. The jigsaw transform is applied to the original image to be encrypted and the image is then divided into independent non-overlapping segments. Each image segment is encrypted using different fflactional parameters and two statistically independent random codes. The random phase

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codes along with the set of fractional orders and jigsaw transform index, form key to the ener

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ted data. Results of computer simulation have been presented in support of the proposed idea and to analyze the performance of the method. An optical implementation, which may ffind application for encrypting data stored in holographic memory, has also been proposed.

Chapter 5 describes a fully digital technique for optical data encryption. This chapter is divided into two sections. Section I discusses amplitude image encryption using double random encoding using Fourier and fractional Fourier transforms. Section II discusses the phase image based encryption using Fourier and Fresnel transforms. The input amplitude image (to be encrypted) is multiplied by a random phase mask, and either its Fourier or fractional transform is obtained. In case of fully phase encryption, the input phase image is Fourier or Fresnel transformed. Using interference with a wave from another random phase mask, the encrypted data (Fourier/fractional/Fresnel hologram) is recorded digitally. The decryption key is also recorded as a digital hologram. An electronic key (random code) is generated and the encrypted hologram is then multiplied by this key and another Fourier or fractional transform (encrypted image) is obtained. The decryption key hologram, the electronic key, and the encrypted image, all can be transmitted through communication channels. The retrieval is carried out by all-digital means using the fast Fourier transform algorithm.

Chapter 6 contains a summary of important conclusions and scope for future work in the area ofoptical security.

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TABLE OF CONTENTS

List of Figures

Chapter 1

AN OVERVIEW OF OPTICAL PROCESSING TECHNIQUES USED FOR SECURITY APPLICATIONS

i.i Introduction

i .2 Security systems for authentication and veriffication using optical pattern recognition tecimiques

i .3 Optical encryption

I .3. 1 Double random Fourier plane encoding (i) Algorithm

(ii) Statistical properties ofthe encoded image

(iii) Influence of coded image perturbations in the decoding process

(iv) Noise robustness (v) Optical implementation

1.3.2 Double random fractional Fourier domain encoding i .3.3 Fully phase encryption

1.3.4 Optical encryption systems using digital holographic techniques

1.3.5 Polarization encoding

1 .3.6 Encryption using digital optical systems i .3.7 Digital watermarking

i .3.8 Other encryption techniques

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i .4 Liquid crystal spatial light modulators and their use in optical encryption

i .5 Photorefractive effect and its use in optical encryption

Chapter 2

OPTICAL PHASE ENCRYPTION USING PHASE CONTRAST TECHNIQUE

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Introduction Phase imaging

2.3 Phase encryption using Fourier domain encoding 2.3.1 Computer simulation

2.3 .2 Experimental results

2.4 Optical encryption using fflactional domain encoding 2.5 Fully phase encryption using FRT

2.5. 1 Experimental results and discussion

2.6 Conclusion

Chapter 3

OPTICAL ENCRYPTION USING CASCADED EXTENDED FRACTIONAL FOURIER TRANSFORM

Introduction

Amplitude encryption using cascaded FRT 3 .2. 1 Experimental results

Fully phase encryption using cascaded extended FRT 3.3.i Phase contrast using photorefractive crystals

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Chapter 4

OPTICAL ENCRYPTION USING A FRACTIONAL FOURIER TRANSFORM 4.1 Introduction

4.2 Principle

4.3 Algorithm for encryption and decryption 4.4 Optical implementation

4.5 Numerical simulation results

4.6 Robustness ofthe algorithm to blind decryption 4.7 Jigsaw transformed LFRT encryption

4.8 Conclusion

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Chapter 5

DATA SECURITY USING DIGITAL HOLOGRAPHY 5 . 1 Introduction

5.2 Amplitude encryption using digital holography 5.2.1 Double random Fourier plane encoding

5.2.2 Double random fflactional Fourier plane encoding 5.2.3 Experimental results

3 Fully phase encryption using digital holography 5.3.i Fourier encryption

5.3.2 Fresnel encryption

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5 . 3 . 3 Experimental results 5.4 Discussion

5.5 Conclusion

Chapter 6

CONCLUSION AND SCOPE FOR FUTURE STUDIES 6. 1 Conclusions

6.2 Scope for future studies

REFERENCES

LIST OF PUBLICATIONS AUTHOR'S BIOGRAPHY

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