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Quantum multiple gray scale images encryption scheme in the bit plane representation model

Claire I. Levaillant

TL;DR

The paper proposes a quantum multi-image encryption framework (BRQMI) that encodes $M$ grayscale images across $L$ bit planes into a compact quantum representation on $2n$ spatial qubits plus $\lceil\log_2 M\rceil$ and $\lceil\log_2 L\rceil$ qubits. It combines two-stage scrambling with a discrete quantum baker map to permute both image/bit-plane indices and pixel positions, followed by a diffusion step (CHS chaotification) that generates per-pixel secret keys from plaintext-dependent chaotic sequences and Chebyshev polynomials; encryption uses XOR with these keys and decryption applies inverse gates. The scheme leverages a bit-plane-based representation to reduce qubit overhead and enable independent scrambling of planes and images, while diffusion via a sine-enhanced Henon map broadens chaotic behavior and strengthens security against brute-force attacks. By design, BRQMI supports multiple images in a single quantum state and offers potential advantages in storage and security over prior MQIE/NEQR-based approaches; the authors also discuss future cryptanalytic evaluation and possible extensions to higher-dimensional baker maps and related diffusion schemes.

Abstract

After introducing a bit-plane quantum representation for a multi-image, we present a novel way to encrypt/decrypt multiple images using a quantum computer. Our encryption scheme is based on a two-stage scrambling of the images and of the bit planes on one hand and of the pixel positions on the other hand, each time using quantum baker maps. The resulting quantum multi-image is then diffused with controlled CNOT gates using a sine chaotification of a two-dimensional Hénon map as well as Chebyshev polynomials. The decryption is processed by operating all the inverse quantum gates in the reverse order.

Quantum multiple gray scale images encryption scheme in the bit plane representation model

TL;DR

The paper proposes a quantum multi-image encryption framework (BRQMI) that encodes grayscale images across bit planes into a compact quantum representation on spatial qubits plus and qubits. It combines two-stage scrambling with a discrete quantum baker map to permute both image/bit-plane indices and pixel positions, followed by a diffusion step (CHS chaotification) that generates per-pixel secret keys from plaintext-dependent chaotic sequences and Chebyshev polynomials; encryption uses XOR with these keys and decryption applies inverse gates. The scheme leverages a bit-plane-based representation to reduce qubit overhead and enable independent scrambling of planes and images, while diffusion via a sine-enhanced Henon map broadens chaotic behavior and strengthens security against brute-force attacks. By design, BRQMI supports multiple images in a single quantum state and offers potential advantages in storage and security over prior MQIE/NEQR-based approaches; the authors also discuss future cryptanalytic evaluation and possible extensions to higher-dimensional baker maps and related diffusion schemes.

Abstract

After introducing a bit-plane quantum representation for a multi-image, we present a novel way to encrypt/decrypt multiple images using a quantum computer. Our encryption scheme is based on a two-stage scrambling of the images and of the bit planes on one hand and of the pixel positions on the other hand, each time using quantum baker maps. The resulting quantum multi-image is then diffused with controlled CNOT gates using a sine chaotification of a two-dimensional Hénon map as well as Chebyshev polynomials. The decryption is processed by operating all the inverse quantum gates in the reverse order.
Paper Structure (7 sections, 3 theorems, 44 equations)

This paper contains 7 sections, 3 theorems, 44 equations.

Table of Contents

  1. Introduction
  2. The BRQMI: a bit-plane representation for quantum multiple images
  3. The quantum baker map used for scrambling
  4. The CHS chaotification model used for diffusion
  5. The encryption/decryption scheme
  6. An example of quantum implementation for the scrambling
  7. Conclusion

Key Result

Theorem 1

(Due to Hou-Liu-Feng, $2020$BAK0). Let $B=B_{(2^{q_1},\dots,2^{q_k})}$ with $2^n=2^{q_1}+\dots+2^{q_k}$ be a discrete Baker map. If for every integer $i$ with $1\leq i\leq k$ we have $2^{q_i}|2^{q_1}+\dots+2^{q_{i-1}}$, then $B$ has a quantum implementation using quantum SWAP and controlled SWAP gat

Theorems & Definitions (3)

  • Theorem
  • Lemma 1
  • Lemma 2