HYBRID OPTICAL CRYPTOGRAPHY AND COMPRESSIVE SENSING BASED ON ORTHOGONAL MATCHING PURSUIT

Compressive sensing (CS) is a technique that allows a signal vector to be reconstructed with a number of linear measurements far fewer than its size. In this study, optical hybrid cryptography with simultaneous compressive sensing based on orthogonal matching pursuit (OMP) is proposed as an alternative solution to the two important problems in communications, namely, effective / efficient / signal processing and secure encryption/decrypton. The whole system is able to both compress and encrypt data with attack immunity.


INTRODUCTION
Many signals used in practise such as audio, image, radar, and video signals are highly correlated and can be represented as sparse signals [1].Compressive sensing theory shows how to restore the original signal from the compressed signal [2], [3].
The number of measurements (M) required for signal recovery depends on the signal length (N), and the number of nonzero sparse signal elements (K).The most commonly used relation is given by [4][5][6] M≥(K x log (N)) (1) Cryptography involves methods used to encrypt and decrypt information.Studies on mathematical methods dealing with information security such as reliability, data integrity, and authentication are important topics of cryptography [7][8].Cryptoanalysis involves methods to investigate the strengths and weaknesses of cryptographic systems.
Symmetric encryption algorithms use the same key for encryption and decryption operations.
Symmetric encryption is very fast and easy to implement in electronic devices.In asymmetric encryption, one general key is used for encryption, and another special key is used for decryption.
Asymmetric encryption algorithms are usually developed with very large prime numbers.

LITERATURE SUMMARY
Amir and Ester proposed that EEG signals can be encrypted by using the measurement vector of the EEG signal [9].Minal and Rajankar proposed to change the rows and columns of the detection matrix for encryption [10].

HYBRID OPTICAL CRYPTOGRAPHY WITH COMPRESSIVE SENSING BASED ON ORTHOGONAL MATCHING PURSUIT
Orthogonal Matching Pursuit (OMP) is an iterative method to recover the non-zero elements of a sparse signal from the measured signal.If the length m of the measurement vector is larger than k, the number of nonzero elements of the sparse signal, the sparse signal can be recovered by OMP with a very large probability [18,19].
In the proposed work, the detection matrix was generated by using a fast transform such as discrete while not converged, do In the proposed method, the RSA algorithm was used for asymmetric encryption of the keys [7,8,20,21].In this method, two very large prime numbers p and q with N=pq as well as bit length n are selected.N does not exceed n bits in length.The algorithm generates two keys e, the public key, and d, the private key.e being an integer less than and coprime to Q=(p-1)(q-1).d is found by A message M is coded as an integer such that 0 M N   , and M is prime to N. The message is encrypted as a ciphertext C by Decryption is achieved by recovering M from C by using Using asymmetric and symmetric encryptions together is named hybrid cryptography.It increases the advantages and decreases the disadvantages of the asymmetric and symmetric encryptions [7,8,20,21].
The fllow diagram for simultaneous compressive sensing and optical encryption is shown in Figure 1.In the figure, it is assumed that DFT is used for CS OMP compression with its associated fast algorithm FFT.In the actual implementation, the CS measurement matrix generated by multiplying a fast transform matrix with pre and post random permutation matrices is obtained independently of the input signal.The proposed method is applied per block (vector) as shown in Figure 2. The optical phase/amplitude keys p1 and p2 are generated with random complex numbers.The phase covers 360 degrees.The corresponding 2-f optical encryption system using the Fourier transform is shown in Figure 2 as an optical system.The lens represents the Fourier transformation.This is repeated once more for a 4-f optical encryption system for additional security.The resulting encrypted signal is of smaller size than the original signal.
In order to increase cryptographic security, the optical p1 and p2 phase + amplitude keys are composed of complex random numbers.The use of complex numbers with double random optical phase + amplitude keys and transform processing provides good scattering.In order to apply asymmetric cryptography in our proposed algorithm, the symmetric keys are sent asymmetrically to the receiver by separating the real and imaginary parts of the two optical random phase + amplitude complex keys and the keys are received symmetrically with the RSA.At the receiver, the CS OMP algorithm is used to recover the original signal.We claim that ( * ( )) keys and encryption algorithms including CS OMP makes phase and amplitude recovery virtually impossible.Figure 5 shows the original BABOON image.Figure 6 shows the encrypted image obtained with the SCOSC method and blockwise processing.Figure 7 shows the result obtained after decryption when the correct key was used.The image is essentially the same as the original image.Figure 8 shows the result obtained after decryption when the wrong key was used.The image is totally unrecognizable.

CONCLUSIONS
In this study, a method for simultaneous compressive sensing using OMP and optical cryptography using double random phase/amplitude keys was proposed.The RSA algorithm involving asymmetric cryptography was used to encrypt/decrypt the optical keys.

Fourier
transform (DFT), discrete cosine transform (DCT), real sinusoidal transform (RST), Haar wavelet transform, Hadamard transform, discrete sine transform (DST) and discrete cosine-III transform (DC3T) [21].In the experiments discussed in Section 6, the ranking of transforms in terms of accuracy of results were DC3T, DCT, DFT, RST, DST, Hadamard and Haar.In addition, DC3T has fewer number of multiplications than DCT.The procedure for the OMP is as follows: Given: A = measurement matrix, y = measurement vector Define: l  =index set at the lth iteration x l = sparse signal vector estimate at the lth iteration r l = residual signal vector at the lth iteration 2

Figure 1 .
Figure 1.Flow diagram of the proposed method.

Figure 7 .
Figure 7. Decrypted image when the correct key was used.

Figure 8 .
Figure 8. Decrypted image when the wrong key was used.
Rachlin et al. and Dwork et al. proposed using CS for data security and