Ex) Article Title, Author, Keywords
Current Optics
and Photonics
Ex) Article Title, Author, Keywords
Curr. Opt. Photon. 2021; 5(2): 155-163
Published online April 25, 2021 https://doi.org/10.3807/COPP.2021.5.2.155
Copyright © Optical Society of Korea.
Seok Hee Jeon^{1}, Sang Keun Gil^{2}
Corresponding author: skgil@suwon.ac.kr, ORCID 0000-0002-3828-0939
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
We propose a novel optical encryption scheme for cipher-feedback-block (CFB) mode, capable of encrypting two-dimensional (2D) page data with the use of two-step phase-shifting digital interferometry utilizing orthogonal polarization, in which the CFB algorithm is modified into an optical method to enhance security. The encryption is performed in the Fourier domain to record interferograms on charge-coupled devices (CCD)s with 256 quantized gray levels. A page of plaintext is encrypted into digital interferograms of ciphertexts, which are transmitted over a digital information network and then can be decrypted by digital computation according to the given CFB algorithm. The encryption key used in the decryption procedure and the plaintext are reconstructed by dual phase-shifting interferometry, providing high security in the cryptosystem. Also, each plaintext is sequentially encrypted using different encryption keys. The random-phase mask attached to the plaintext provides resistance against possible attacks. The feasibility and reliability of the proposed CFB method are verified and analyzed with numerical simulations.
Keywords: CFB mode, Digital holography, Optical encryption, Phase-shifting interferometry, Symmetric block encryption
OCIS codes: (060.4785) Optical security and encryption; (070.1170) Analog optical signal processing; (070.4560) Data processing by optical means; (090.1995) Digital holography; (090.2880) Holographic interferometry
Information security has increasingly become an important issue in many information societies. Compared to conventional electronic data-security methods, optical data security provides much freedom to encrypt data using the amplitude, phase, polarization, or wavelength of light. Since Refregier and Javidi firstly reported the optical encryption method of double random-phase encoding (DRPE) [1], lots of researchers have investigated optical encryption methods in information-security applications, because of their high-speed and parallel processing potential. In 2009, Matoba
In this paper, we propose an optical encryption scheme for cipher-feedback-block (CFB) mode by means of two-step phase-shifting interferometry and orthogonal polarization. Fourier-domain optical encryption is obtained by the interference of two waves in a phase-shifting interferometer of the Mach-Zehnder architecture. The interferometer consists of binary input data attached to a random-phase mask in the object beam, and a randomly distributed phase pattern with an encryption key in the reference beam, with the resulting interferograms being recorded on CCDs. The encryption key used in the decryption process is also achieved by phase-shifting interferometry. Ciphertexts of the digital interferograms are transmitted over an information network and can easily be decrypted by digital computation. In Section II the CFB mode is briefly reviewed and the proposed optical encryption method for the CFB algorithm is explained, and in Section III the feasibility of the proposed method is verified by the results of numerical simulations and security analysis. Conclusions are summarized in Section IV.
In the conventional cryptographic encryption of digital data, called a block, there are four standard modes: Electronic Codebook (ECB), CBC, CFB and Output Feedback (OFB) in the data-encryption standard (DES) protocol. Among these block-encryption modes, CFB mode introduces a feedback operation into the cryptographic process. In this mode, the previous ciphertext block is fed back and used to encrypt the subsequent plaintext block. Figure 1(a) shows the algorithm for CFB mode encryption, and the encryption procedure is described as follows:
where
Recently, electronic digital cryptographic algorithms have been analyzed by applying optical encryption techniques in which the ciphertext is no longer in digital information, but rather is in an analog random pattern, such as white noise. Inherently, an optical system carries out fast parallel processing with 2D array data, so it can have a very large key space, thereby enhancing security strength. In this paper, the concept of the CFB-mode algorithm is modified to propose an optical encryption scheme using phase-shifting interferometry. Figure 1(b) shows the proposed CFB method, and the encryption procedure is described as follows:
where
The optical architecture for two-step phase-shifting digital holography using orthogonal polarization [20] can also be used for the proposed CFB encryption method. Figure 2 schematically shows the proposed optical encryption architecture, which contains dual Mach-Zehnder interferometers. The collimated laser beam passes through a linear polarizer P1, the polarization direction of which is 45° with respect to the horizontal axis, and is divided by beam splitters into two linear-polarized plane waves traveling in different paths. When shutters S1 and S2 are open and S3 is closed, the inner interferometer is operated to encrypt a previous ciphertext
where Δ
The outer interferometer, with shutters S1 and S3 open and S2 closed, is operated to encrypt a plaintext by another holographic encryption key, which is also the same previous ciphertext. The object-beam path has an amplitude-type SLM3 multiplied by another random-phase mask RPM2, which displays a plaintext
where Δ
In the proposed method, a plaintext is encrypted by phase-shifting interferometry such that we should know the complex hologram function generated from interferometry to decrypt the plaintext. If the complex hologram function in the outer interferometer is assumed to be
To reconstruct the complex distribution
The complex distribution
where * denotes the complex conjugate and IFT{∙} denotes inverse Fourier transformation.
To obtain the feedback ciphertext
Flowcharts of the encryption and decryption procedures are shown in Fig. 3, where EXP denotes an exponential function to generate the phase distribution, FT and IFT represent the Fourier transform and inverse Fourier transform, Σ denotes a function to perform phase-shifting interferometry, TH denotes a threshold function to generate binary data using a proper threshold value, DH denotes a function to calculate a complex hologram, and ABS denotes the absolute-value function.
To verify the feasibility of the proposed optical encryption scheme for CFB mode shown in Figs. 1(b) and 2, numerical simulations are carried out using Mathlab. 256 × 256-pixel binary images are used for simulation; the size of the data depends on the display capability of the SLM. For visual convenience, binary images are used as input plaintexts. Figures 4(a)–4(c) show the consecutive plaintexts of binary images to be encrypted in CFB mode. Figure 5 shows intensity distributions of ciphertexts for encrypting the 1st plaintext
Figure 6 shows the results of reconstruction and decryption of the consecutive plaintexts
To examine the reliability and sensitivity of the proposed method, the decryption error is analyzed. The mean squared error (MSE) between the decrypted plaintext and the original plaintext is calculated as
where
To discuss the resistance against attacks in the aspect of security, it is assumed that the attacker has a
We propose a novel optical encryption scheme for CFB mode, capable of encrypting large two-dimensional (2D) page data compared to the conventional one-dimensional block data, which is carried out by two-step phase-shifting digital interferometry based on orthogonal polarization, using a quarter-wave plate in the reference beam. The encryption is performed in the Fourier domain to record interferograms on CCDs with 256 gray levels, which generates a noiselike random distribution in the ciphertext. In the proposed optical CFB scheme, a page of plaintext is encrypted into 2D ciphertexts by applying the dual interferometry to the previous ciphertext, while the conventional CFB method encrypts bits of block plaintext. Ciphertexts are transmitted over a digital information network and then decrypted by digital computation according to the given CFB algorithm. Sequential page encryption is possible in the cryptosystem with a different encryption key. The use of a random-phase mask in the encryption system protects against several types of attack, such as KPA, CPA and CCA, and then the proposed method provides higher security with many more degrees of freedom than the conventional method. Furthermore, the proposed method has an additional security advantage because the feedback ciphertext is determined by a specific XOR combination algorithm of ciphertexts known only by the transmitter, which is kept secret from attackers. Numerical simulations verify that the proposed optical CFB encryption scheme shows the feasibility of the highly secure CFB mode, due to its reliability against attacks.
This work was supported by Incheon National University (International Cooperative) Research Grant in 2018.
Curr. Opt. Photon. 2021; 5(2): 155-163
Published online April 25, 2021 https://doi.org/10.3807/COPP.2021.5.2.155
Copyright © Optical Society of Korea.
Seok Hee Jeon^{1}, Sang Keun Gil^{2}
^{1}Department of Electronic Engineering, Incheon National University, Incheon 22012, Korea
^{2}Department of Electronic Engineering, The University of Suwon, Hwaseong, Suwon 18323, Korea
Correspondence to:skgil@suwon.ac.kr, ORCID 0000-0002-3828-0939
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
We propose a novel optical encryption scheme for cipher-feedback-block (CFB) mode, capable of encrypting two-dimensional (2D) page data with the use of two-step phase-shifting digital interferometry utilizing orthogonal polarization, in which the CFB algorithm is modified into an optical method to enhance security. The encryption is performed in the Fourier domain to record interferograms on charge-coupled devices (CCD)s with 256 quantized gray levels. A page of plaintext is encrypted into digital interferograms of ciphertexts, which are transmitted over a digital information network and then can be decrypted by digital computation according to the given CFB algorithm. The encryption key used in the decryption procedure and the plaintext are reconstructed by dual phase-shifting interferometry, providing high security in the cryptosystem. Also, each plaintext is sequentially encrypted using different encryption keys. The random-phase mask attached to the plaintext provides resistance against possible attacks. The feasibility and reliability of the proposed CFB method are verified and analyzed with numerical simulations.
Keywords: CFB mode, Digital holography, Optical encryption, Phase-shifting interferometry, Symmetric block encryption
Information security has increasingly become an important issue in many information societies. Compared to conventional electronic data-security methods, optical data security provides much freedom to encrypt data using the amplitude, phase, polarization, or wavelength of light. Since Refregier and Javidi firstly reported the optical encryption method of double random-phase encoding (DRPE) [1], lots of researchers have investigated optical encryption methods in information-security applications, because of their high-speed and parallel processing potential. In 2009, Matoba
In this paper, we propose an optical encryption scheme for cipher-feedback-block (CFB) mode by means of two-step phase-shifting interferometry and orthogonal polarization. Fourier-domain optical encryption is obtained by the interference of two waves in a phase-shifting interferometer of the Mach-Zehnder architecture. The interferometer consists of binary input data attached to a random-phase mask in the object beam, and a randomly distributed phase pattern with an encryption key in the reference beam, with the resulting interferograms being recorded on CCDs. The encryption key used in the decryption process is also achieved by phase-shifting interferometry. Ciphertexts of the digital interferograms are transmitted over an information network and can easily be decrypted by digital computation. In Section II the CFB mode is briefly reviewed and the proposed optical encryption method for the CFB algorithm is explained, and in Section III the feasibility of the proposed method is verified by the results of numerical simulations and security analysis. Conclusions are summarized in Section IV.
In the conventional cryptographic encryption of digital data, called a block, there are four standard modes: Electronic Codebook (ECB), CBC, CFB and Output Feedback (OFB) in the data-encryption standard (DES) protocol. Among these block-encryption modes, CFB mode introduces a feedback operation into the cryptographic process. In this mode, the previous ciphertext block is fed back and used to encrypt the subsequent plaintext block. Figure 1(a) shows the algorithm for CFB mode encryption, and the encryption procedure is described as follows:
where
Recently, electronic digital cryptographic algorithms have been analyzed by applying optical encryption techniques in which the ciphertext is no longer in digital information, but rather is in an analog random pattern, such as white noise. Inherently, an optical system carries out fast parallel processing with 2D array data, so it can have a very large key space, thereby enhancing security strength. In this paper, the concept of the CFB-mode algorithm is modified to propose an optical encryption scheme using phase-shifting interferometry. Figure 1(b) shows the proposed CFB method, and the encryption procedure is described as follows:
where
The optical architecture for two-step phase-shifting digital holography using orthogonal polarization [20] can also be used for the proposed CFB encryption method. Figure 2 schematically shows the proposed optical encryption architecture, which contains dual Mach-Zehnder interferometers. The collimated laser beam passes through a linear polarizer P1, the polarization direction of which is 45° with respect to the horizontal axis, and is divided by beam splitters into two linear-polarized plane waves traveling in different paths. When shutters S1 and S2 are open and S3 is closed, the inner interferometer is operated to encrypt a previous ciphertext
where Δ
The outer interferometer, with shutters S1 and S3 open and S2 closed, is operated to encrypt a plaintext by another holographic encryption key, which is also the same previous ciphertext. The object-beam path has an amplitude-type SLM3 multiplied by another random-phase mask RPM2, which displays a plaintext
where Δ
In the proposed method, a plaintext is encrypted by phase-shifting interferometry such that we should know the complex hologram function generated from interferometry to decrypt the plaintext. If the complex hologram function in the outer interferometer is assumed to be
To reconstruct the complex distribution
The complex distribution
where * denotes the complex conjugate and IFT{∙} denotes inverse Fourier transformation.
To obtain the feedback ciphertext
Flowcharts of the encryption and decryption procedures are shown in Fig. 3, where EXP denotes an exponential function to generate the phase distribution, FT and IFT represent the Fourier transform and inverse Fourier transform, Σ denotes a function to perform phase-shifting interferometry, TH denotes a threshold function to generate binary data using a proper threshold value, DH denotes a function to calculate a complex hologram, and ABS denotes the absolute-value function.
To verify the feasibility of the proposed optical encryption scheme for CFB mode shown in Figs. 1(b) and 2, numerical simulations are carried out using Mathlab. 256 × 256-pixel binary images are used for simulation; the size of the data depends on the display capability of the SLM. For visual convenience, binary images are used as input plaintexts. Figures 4(a)–4(c) show the consecutive plaintexts of binary images to be encrypted in CFB mode. Figure 5 shows intensity distributions of ciphertexts for encrypting the 1st plaintext
Figure 6 shows the results of reconstruction and decryption of the consecutive plaintexts
To examine the reliability and sensitivity of the proposed method, the decryption error is analyzed. The mean squared error (MSE) between the decrypted plaintext and the original plaintext is calculated as
where
To discuss the resistance against attacks in the aspect of security, it is assumed that the attacker has a
We propose a novel optical encryption scheme for CFB mode, capable of encrypting large two-dimensional (2D) page data compared to the conventional one-dimensional block data, which is carried out by two-step phase-shifting digital interferometry based on orthogonal polarization, using a quarter-wave plate in the reference beam. The encryption is performed in the Fourier domain to record interferograms on CCDs with 256 gray levels, which generates a noiselike random distribution in the ciphertext. In the proposed optical CFB scheme, a page of plaintext is encrypted into 2D ciphertexts by applying the dual interferometry to the previous ciphertext, while the conventional CFB method encrypts bits of block plaintext. Ciphertexts are transmitted over a digital information network and then decrypted by digital computation according to the given CFB algorithm. Sequential page encryption is possible in the cryptosystem with a different encryption key. The use of a random-phase mask in the encryption system protects against several types of attack, such as KPA, CPA and CCA, and then the proposed method provides higher security with many more degrees of freedom than the conventional method. Furthermore, the proposed method has an additional security advantage because the feedback ciphertext is determined by a specific XOR combination algorithm of ciphertexts known only by the transmitter, which is kept secret from attackers. Numerical simulations verify that the proposed optical CFB encryption scheme shows the feasibility of the highly secure CFB mode, due to its reliability against attacks.
This work was supported by Incheon National University (International Cooperative) Research Grant in 2018.