Asymmetric image encryption based on the Discrete Cosine Transform ...

Asymmetric image encryption based on the Discrete Cosine Transform using Random Phase Masks. Anshula CSE and IT Department The NorthCap University, Gurugram, India [email protected]

Hukum Singh Applied Science Department The NorthCap University, Gurugram , India [email protected]

extended sequence and is also very similar to Discrete Fourier Transform (DFT) i.e. is related to Fourier series. It uses N X N real base vectors which are components of cosine.

Abstract ± This paper includes image encryption

describing Discrete Cosine Transform (DCT) using Double Random Phase Masks (DRPE), which is implemented on MATLAB (2008a). The computed value of mean-squared-error between the retrieved and the input images shows the efficacy of scheme.

2. Proposed Optical Security Scheme

Asymmetric cryptosystem [15, 16] uses two public keys in the cryptosystem, making is very secure. Random phase mask as RPM1 i.e.

Keywords- Discrete Cosine Transform (DCT) and Double Random Phase Encoding (DRPE).

ሾ݆݁ሺʹߨ݊ͳ ሺ‫ݔ‬ǡ‫ݕ‬ሻ ሿ is tried on the original image‫ܫ‬ଵ ሺ‫ݔ‬ǡ ‫ݕ‬ሻ. The discrete cosine transform is then tried to the RPM1. The image obtained is amplitude and phase truncated for encryption. The obtained amplitude-truncated (AT) value then helps out in generating the first decryption Another mask RPM2 key (DK1). ݆ሺʹߨ݊ ሺ‫ݑ‬ǡ‫ݒ‬ሻ ʹ i.e.ሾ݁ ሿ is applied on the phase

1. Introduction With the increase in use of internet and multimedia applications it has become very important to secure the data available in any form like audio, video, document, image etc. Asymmetric cryptosystems are more secure when compared to symmetric cryptosystems as the later are linear in nature. Also asymmetric cryptosystem bases on the DRPE method which was introduced by Refregier and Javidi [1]. DRPE has been extended in several transform for increasing the security of several data forms like fractional Fourier [2, 3], Fresnel [4-6, 12], gyrator wavelet [7] and gyrator [8-11]. The Discrete Cosine Transform is the technique specially used for the JPEG standard for the lossy compression. DCT [13-14] is a symmetrically

c 978-1-5386-0627-8/17/$31.00 2017 IEEE

truncated vale (PT) and then the inverse discrete cosine transform to finally achieve the encrypted image which is amplitude-truncated to originate second decryption key (DK2). The, ݊ଵ ሺ‫ݔ‬ǡ ‫ݕ‬ሻ and ݊ଶ ሺ‫ݑ‬ǡ ‫ݒ‬ሻ are statistically independent which are irregularly distributed in [0, 1]. Selecting the wrong or improper parameters during decryption gives out negative results. The encryption keys make the system more secure opposite the unaccredited attacker.

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The steps (Fig. 1) of encrypting of the input image ‫ܫ‬ଵ ሺ‫ݔ‬ǡ ‫ݕ‬ሻ can be indicated as ݃ሺ‫ݑ‬ǡ ‫ݒ‬ሻ ൌ ܲܶൣ‫ܶܥܦ‬൛ሼ‫ܫ‬ଵ ሺ‫ݔ‬ǡ ‫ݕ‬ሻ ൈ ݁

௝ሺଶగ௡భ ሺ௫ǡ௬ሻ

DK1

DK2

E(x, y)

DCT

PT

g(u, v)

IDCT

ൟ൧

PT

f(x, y)

(1)

&ŝŐƵƌĞϮĞĐƌǇƉƚŝŽŶƉƌŽĐĞƐƐ

݂ሺ‫ݔ‬ǡ ‫ݕ‬ሻ ൌ ܲܶൣ‫ܶܥܦܫ‬൛݃ሺ‫ݑ‬ǡ ‫ݒ‬ሻ ൈ ݁

௝ሺଶగ௡మ ሺ௫ǡ௬ሻ

ൟ൧

(2)

3. Simulation Experiments

Here ܲܶሼሽ denotes a phase truncation operator,‫ܶܥܦ‬ሾሿ and ‫ܶܥܦܫ‬ሾሿ denoted the Discrete Cosine Transform and inverse Discrete Cosine Transform, respectively. The main intention of PTDCT-based asymmetric cryptosystem is to smash the linearity of ordinary system. The value of cryptosystem is when dissimilar phase masks are taken for dissimilar plaintexts during each encryption as the decryption keys which are generated in the encryption process and are directly associated to the plaintext and encryption keys. The expressions for obtaining the decryption keys (DKs) are as follows:

For performing the scheme we used a 256 X 256 pixel greyscale image, Lena (Fig. 3). The scheme is performed on MATLAB (2008a)

‫ܭܦ‬ଵ ሺ‫ݑ‬ǡ ‫ݒ‬ሻ ൌ ‫ ܶܣ‬ቂ‫ܶܥܦ‬ቄሼ‫ܫ‬ଵ ሺ‫ݔ‬ǡ ‫ݕ‬ሻ ൈ ݆݁ሺʹߨ݊ͳ ሺ‫ݔ‬ǡ‫ݕ‬ሻ ቅቃ (3)

‫ܭܦ‬ଶ ሺ‫ݔ‬ǡ ‫ݕ‬ሻ ൌ ‫ܶܣ‬ሾ‫ܶܥܦܫ‬ሼ‫ ܶܥܦ‬ሼ‫ܫ‬ଵ ሺ‫ݔ‬ǡ ‫ݕ‬ሻ ൈ ݁ ௝ሺଶగ௡భ ሺ௫ǡ௬ሻ ሽ ൈൈ ݁ ௝ሺଶగ௡మ ሺ௫ǡ௬ሻ ሿ

(a)

(4)

For decrypting the image we follow complete inverse of the process we did for the encryption that is we use the DK2 for the DCT and DK1 for the inverse Discrete Cosine Transform. RPM1 f(x, y)

RPM2 PT

DCT AT DK1

g(u, v)

IDCT

PT

E(x, y)

AT DK2

&ŝŐƵƌĞϭŶĐƌǇƉƚŝŽŶƉƌŽĐĞƐƐ͘

(b)

2017 International Conference on Computing and Communication Technologies for Smart Nation (IC3TSN)

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4. Conclusion It is concluded that the system becomes very secure with the use of two keys. The proposed strategy has been ratified in the DCT domain. MSE showed the efficiency of the scheme. References 1. ZĞĨƌĞŐŝĞƌ W͕ :ĂǀŝĚŝ ͕ KƉƚŝĐĂů ŝŵĂŐĞ ĞŶĐƌǇƉƚŝŽŶ ďĂƐĞĚ ŽŶ ŝŶƉƵƚ ƉůĂŶĞ ĂŶĚ &ŽƵƌŝĞƌ ƉůĂŶĞ ƌĂŶĚŽŵ ĞŶĐŽĚŝŶŐ͕ KƉƚ >Ğƚƚ͕ ϮϬ;ϭϵϵϱͿϳϲϳͲϲϵ͘

(c)

Ϯ͘ hŶŶŝŬƌŝƐŚŶĂŶ'͕:ŽƐĞƉŚ:͕^ŝŶŐŚĞƚƚ͕Ϯϱ;ϮϬϬϬͿϴϴϳͲϴϴϵ͘ 3. Dahiya M, Sukhija S, Singh H,(2014) Image Encryption using Quad Masks in Fractional Fourier Domain and Case Study, IEEE International Advance Computing Conference (IACC), 1048-1053. (d) &ŝŐ͘ϯ ZĞƐƵůƚƐ ĨŽƌ ŐƌĞǇƐĐĂůĞ ŝŵĂŐĞƐ͗ ;ĂͿ ŝŶƉƵƚ ŝŵĂŐĞƐŽĨ ϮϱϲпϮϱϲ ƉŝǆĞůƐ͖ ;ďͿ ŶĐƌǇƉƚĞĚ /ŵĂŐĞ ;ĐͿ ĞĐƌǇƉƚŝŽŶ ǁŝƚŚ ǁƌŽŶŐ ƉĂƌĂŵĞƚĞƌ ;ĚͿ ĞĐƌǇƉƚĞĚŝŵĂŐĞ

For verification of the credibility of the nominated method of attack, a mean square error (MSE) is calculated as:

ଶହ଺ ଶହ଺

‫ ܧܵܯ‬ൌ ෍ ෍ ௜ୀ଴ ௝ୀ଴

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4. Matoba O, Javidi B, (1999) Encrypted optical memory system using threedimensional keys in the Fresnel domain, Opt Lett, 24:762-764. 5. Situ G, Zhang J,(2004) Double randomphase encoding in the Fresnel domain, Opt Lett, 49:1584-1586. 6. Singh H, Yadav A K, Vashisth S, Singh K, (2015) Optical image encryption using GHYLO¶V YRUWH[ WRURLGDO OHQV LQ WKH IUHVQHO transform domain, International J Opt:926135,1-13. 7. Singh H, (2016) 'HYLO¶VYRUWH[)UHVQHOOHQV phase masks on an asymmetric cryptosystem based on phase-truncated in gyrator wavelet transform, Opt Lasers Eng, 81:125-139.


ϴ͘ ZŽĚƌŝŐŽ : ͕ ůŝĞǀĂ d͕ ĂůǀŽ D >͕ 'ǇƌĂƚŽƌ ƚƌĂŶƐĨŽƌŵ͗ƉƌŽƉĞƌƚŝĞƐĂŶĚĂƉƉůŝĐĂƚŝŽŶƐ͕KƉƚ ǆƉƌĞƐƐ͕ϭϱ͕;ϮϬϬϳͿϮϭϵϬͲϮϮϬϯ͘ 9. Singh H, Yadav A K, Vashisth S, Singh K, Fully-phase image encryption using double random-structured phase masks in gyrator domain, Appl Opt,53(2014) 6472-6481. 10. Singh H, Yadav A K, Vashisth S, Singh K, Double phase-image encryption using gyrator transforms, and structured phase mask in the frequency plane, Opt Lasers Eng 67(2015)145-156. 11. Vashisth S, Yadav A K, Singh H, Singh K, Watermarking in gyrator domain using an asymmetric cryptosystem, Proc. Of SPIE, 9654, 2015, 96542 E- 1/8. 12. Singh H, Cryptosystem for securing image encryption using structured phase masks in Fresnel wavelet transform domain, 3D Research 7, 2016: 34 13. K.H. Chang, C-6 +XDQJ &3 /LQ ³'HVLJQ and implementation of DCT/IDCT chip with QRYHODUFKLWHFWXUH´LQ3URFHHGLQJVRI,((( 2000, pp 741-744. 14. S.F. Hsiao and J.M. Tseng, ³1HZ matrix formulation for two-dimensioned DCT/IDCT computation and its distributedPHPRU\ 9/6, LPSOHPHQWDWLRQV´ ,((( Proceedings, vol. 149, 2002, pp. 97-107. 15. YŝŶ t͕ WĞŶŐ y͕ ƐǇŵŵĞƚƌŝĐ ĐƌǇƉƚŽƐǇƐƚĞŵ ďĂƐĞĚ ŽŶ ƉŚĂƐĞͲƚƌƵŶĐĂƚĞĚ &ŽƵƌŝĞƌ ƚƌĂŶƐĨŽƌŵ͕KƉƚ͘>Ğƚƚ͕ϯϱ;ϮϬϭϬͿϭϭϴͲϭϮϬ͘ 16. Singh H, (2016) Optical cryptosystem of color images using random phase masks in the fractional wavelet transform domain, AIP conf. Proc., 1728: 020063-1/4.


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