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Security of Digital Images Based on 3D Arnold Cat Map and Elliptic Curve

Anand B. Joshi

Department of Mathematics and Astronomy, University of Lucknow, Lucknow 226007, Uttar Pradesh, India

E-mail Address: anandiitd.joshi@gmail.com

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Dhanesh Kumar

Department of Mathematics and Astronomy, University of Lucknow, Lucknow 226007, Uttar Pradesh, India

E-mail Address: dhaneshkumar.lu@gmail.com

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D. C. Mishra

Department of Mathematics, Govt. P. G. College, Jaiharikhal 246193, Uttrakhand, India

E-mail Address: deepiitdelhi@gmail.com

Corresponding author.

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https://doi.org/10.1142/S0219467821500066Cited by:10 (Source: Crossref)

Abstract

Security of digital data is an important task in the present era. In this paper, we propose a new scheme of digital image encryption and decryption method based on three-dimensional (3D) Arnold cat map (ACM) and elliptic curve. In this proposed encryption method, we have applied 3D ACM on the digital color image which performs the dual encryption first, it performs the permutation and second, it performs the substitution of image pixels. After that, elliptic curve cryptography (ECC) is used to encrypt the image, for this a mapping method is proposed to convert the pixels of the image as points on the elliptic curve. Further, a mapping inverting method is proposed for decryption and then 3D inverse Arnold cat map (iACM) is applied to get the original image. The statistical and security analyses are done on various images and the experimental results show the robustness of the proposed method.

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