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Image encryption using quantum 3-D Baker map and generalized gray code coupled with fractional Chen’s chaotic system

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Abstract

In our efforts to construct a secure quantum image encryption algorithm, we first propose a quantum 3-D Baker map to scramble a 3-D quantum representation of an image. To have this 3-D quantum representation, we harness the NEQR model for a \(2^n \times 2^n\) grayscale image. In the second step of the proposed encryption scheme, we implement a substitution routine which starts by implementing the generalized gray code on the permuted image and concludes with selected intra bit-XOR-ing and XOR-ing with the pseudorandom sequence generated by the Fractional Chen’s system. The encryption scheme utilizes the basic quantum gates like C-NOT, Toffoli, and Ripple-carry adder due to their computational efficiency. The theoretical and numerical simulation results show that the algorithm has the potential to be used as an image encryption algorithm on quantum computers.

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Acknowledgements

One of the authors, Farhan Musanna, is grateful to the Ministry of Human Resource Development, India, and the Indian Institute of Technology, Roorkee, for being the funding agency of this work, with grant number MHR-01-23-200-428.

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  1. Department of Mathematics, IIT Roorkee, Roorkee, India

    Farhan Musanna & Sanjeev Kumar

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  1. Farhan Musanna
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  2. Sanjeev Kumar
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Correspondence to Sanjeev Kumar.

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Musanna, F., Kumar, S. Image encryption using quantum 3-D Baker map and generalized gray code coupled with fractional Chen’s chaotic system. Quantum Inf Process 19, 220 (2020). https://doi.org/10.1007/s11128-020-02724-3

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