Optical Cryptosystems. Naveen K. Nishchal

transformed and the order of transformation.

      % PT is the plaintext% Phase_mask1 and Phase_mask2 are the two random phase masks to be used as the keys.PT=imread(’D:\Program\images\godisgreat.bmp’);%reading the image to be encryptedPT=double(PT(:,:,1));PT=PT./max(max(PT));figure;imagesc(abs(PT));colormap(gray);title(’original input image’);%defining the two random phase masks for the two keys[M,N]=size(PT);phase_values1=rand(M);phase_values2=rand(M);phase_mask1=exp(j*2*pi*phase_values1);%First Keyphase_mask2=exp(j*2*pi*phase_values2);%Second Key%%%%%Encryption%First Fractional Fourier transform with fractional order 0.25A=PT.*phase_mask1;A=frt(A,0.25);%Second Fractional Fourier transform with fractional order 0.45B=A.*phase_mask2;B=frt(B,0.45);%ciphertextfigure;imagesc(abs(B));colormap(gray);title(’encrypted image’);%%%%%decryptionD=frt(frt(B,−0.45).*conj(phase_mask2),−0.25);figure;imagesc(abs(D));colormap(gray);title(’decrypted image’);

       IV. Gyrator transform

      functionqt=gyrator(q,a)% Matlab code for fast algorithm of discrete gyrator transform%qis an input signal and a is rotation angle% Direct DGT[M,N]=size(q);mm=((0:M−1)-(M)/2)/sqrt(M);nn=((0:N−1)-(N)/2)/sqrt(N);[x,y]=meshgrid(nn,fliplr(mm));[u,v]=meshgrid(mm,fliplr(nn));p1=exp(−2*j*pi*x.*y*tan(a/2));p2=fftshift(exp(−2*j*pi*u.*v*sin(a)));qt=p1.*(ifft2(fft2(p1.*q).*p2));end

References

[1] Refregier P and Javidi B 1995 Optical image encryption using input plane and Fourier plane random encoding Proc. SPIE 2565 62–8

      [2] Refregier P and Javidi B 1995 Optical image encryption based on input plane encoding and Fourier plane random encoding Opt. Lett. 20 767–9

[3] Javidi B and Ahouzi E 1998 Optical security system with Fourier plane encoding Appl. Opt. 3 6247–55

[4] Goodman J W 2007 Introduction to Fourier Optics 3rd edn (New Delhi: Viva Books)

[5] Alfalou A and Brosseau C 2009 Optical image compression and encryption methods Adv. Opt. Photon. 1 589–636

      [6] Liu S, Guo C and Sheridan J T 2014 A review of optical image encryption techniques Opt. Laser Technol. 57 327–42

      [7] Chen W, Javidi B and Chen X 2014 Advances in optical security systems Adv. Opt. Phot. 6 120–55

[8] Javidi B et al 2016 Roadmap on optical security J. Opt. 18 083001

[9] Javidi B and Horner J L 1994 Optical pattern recognition for validation and security verification Opt. Eng. 33 1752–6

[10] J J Healy, M A Kutay, H M Ozaktas and J T Sheridan 2015 Linear Canonical Transform: Theory and Applications (Berlin: Springer)

[11] Unnikrishnan G, Joseph J and Singh K 1998 Optical encryption system that uses phase conjugation in a photorefractive crystal Appl. Opt. 37 8181–5

[12] Lohmann A W 1993 Image rotation, Wigner rotation, and the fractional Fourier transform J. Opt. Soc. Am. A 10 2181–6

[13] Ozaktas H M, Arikan O, Kutay M A and Bozdagi G 1996 Digital computation of the fractional Fourier transform IEEE Trans. Signal Process. 44 2141–50

      [14] Garcia J, Mas D and Dorsch R G 1996 Fractional Fourier transform calculation through the fast Fourier transform algorithm Appl. Opt. 35 7013–8

[15] Khan G S, Nishchal N K, Jospeh J and Singh K 2001 Fractional Fourier transform and its applications: a bibliographic review Asian J. Phys. 10 251–99

[16] Ozaktas H M, Zalevsky Z and Kutay M A 2001 The Fractional Fourier Transform with Applications in Optics and Signal Processing (Chichester: Wiley)

[17] Unnikrishnan G and Singh K 2000 Double random fractional Fourier-domain encoding for optical security Opt. Eng. 39 2853–9

      [18] Unnikrishnan G, Joseph J and Singh K 2000 Optical encryption by double-random phase encoding in the fractional Fourier domain Opt. Lett. 25 887–9

      [19] Unnikrishnan G, Joseph J and Singh K 2001 Fractional Fourier domain encrypted holographic memory by use of an anamorphic optical system Appl. Opt. 40 299–306

[20] Unnikrishnan G and Singh K 2001 Optical encryption using quadratic phase systems Opt. Commun. 193 51–67

[21] Hua J, Liu L and Li G 1997 Extended fractional Fourier transforms J. Opt. Soc. Am. A 14 3316–22

[22] Nishchal N K, Joseph J and Singh K 2003 Optical encryption using cascaded extended fractional Fourier transform Opt. Memory Neural Net. 12 139–45

[23] Situ G and Zhang J 2004 Double random phase encoding in the Fresnel domain Opt. Lett. 29 1584–6

[24] Shi Y, Situ G and Zhang J 2007 Multiple-image hiding in the Fresnel domain Opt. Lett. 32 1914–6

[25] Rodrigo J A, Alieva T and Calvo M L 2006 Optical system design for orthosymplectic transformations in phase space J. Opt. Soc. Am. A 23 2494–500

[26] Rodrigo J A, Alieva T and Calvo M L 2007 Applications of gyrator transform for image processing Opt. Commun. 278 279–84

[27] Singh H, Yadav A K, Vashisth S and Singh K 2014 Fully phase image encryption using double random-structured phase masks in gyrator domain Appl. Opt. 53 6472–81

[28] Mallat S 2008 A Wavelet Tour of Signal Processing 3rd edn (New York: Academic)

[29] Chen L and Zhao D 2005 Optical image encryption based on fractional wavelet transform Opt. Commun. 254 361–7

[30] Vilardy J M, Useche J, Torres C O and Mattos L 2011 Image encryption using the fractional wavelet transform J. Phys.: Conf. Ser. 274