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Multi-image quantum encryption scheme using blocks of bit planes and images

Claire Levaillant

TL;DR

This work addresses secure encryption of large sets of images in a quantum setting by introducing QBBRMI, a block-based quantum block-bit-plane representation that encodes $M$ images into blocks of size $2^{\lceil \log_2 L\rceil}$ to reduce quantum resources. The scheme achieves scrambling via a block-wise quantum baker map and diffusion via a sine chaotification of a $5$-D hyperchaotic map, with plaintext-dependent seeds to ensure strong sensitivity and an effectively infinite key space. A general quantum circuit for the quantum baker map is provided, along with detailed qubit and depth counts, and the authors compare their block-based approach against a non-blocked scheme (LE), highlighting significant qubit savings at the cost of potential depth increases in the most secure variant. The results demonstrate a viable path to scalable, secure quantum multi-image encryption with quantifiable resource trade-offs for different deployment scenarios.

Abstract

We present a multi-image quantum encryption/decryption scheme based on blocks of bit planes and images. We provide a quantum circuit for the quantum baker map.

Multi-image quantum encryption scheme using blocks of bit planes and images

TL;DR

This work addresses secure encryption of large sets of images in a quantum setting by introducing QBBRMI, a block-based quantum block-bit-plane representation that encodes images into blocks of size to reduce quantum resources. The scheme achieves scrambling via a block-wise quantum baker map and diffusion via a sine chaotification of a -D hyperchaotic map, with plaintext-dependent seeds to ensure strong sensitivity and an effectively infinite key space. A general quantum circuit for the quantum baker map is provided, along with detailed qubit and depth counts, and the authors compare their block-based approach against a non-blocked scheme (LE), highlighting significant qubit savings at the cost of potential depth increases in the most secure variant. The results demonstrate a viable path to scalable, secure quantum multi-image encryption with quantifiable resource trade-offs for different deployment scenarios.

Abstract

We present a multi-image quantum encryption/decryption scheme based on blocks of bit planes and images. We provide a quantum circuit for the quantum baker map.

Paper Structure

This paper contains 12 sections, 4 theorems, 43 equations.

Table of Contents

  1. Introduction, novel multi-image quantum representation and cryptographic scheme outline
  2. Introduction
  3. Novel multi-image quantum representation
  4. Cryptographic scheme outline
  5. Paper outline
  6. Encryption and decryption of the multi-image
  7. Scrambling with the quantum baker map
  8. Diffusion using a five dimensional hyperchaotic map
  9. Complexity analysis of the quantum circuit
  10. Quantum circuit for the quantum baker map
  11. Circuit depth
  12. Analysis and some conclusions

Key Result

Theorem 1

Quantum implementation of the discrete baker map. (i) The map defined by has a quantum implementation. (ii) Each subfunction on $\lbrace N_{i-1},\dots,N_i-1\rbrace$ of the discrete baker map is $M_{q_i}$ if and only if $2^{q_i}|2^{q_1}+\dots+2^{q_{i-1}}$.

Theorems & Definitions (8)

  • Definition 1
  • Theorem 1
  • Definition 2
  • Theorem 2
  • Definition 3
  • Definition 4
  • Theorem 3
  • Theorem 4