Researchers develop image encryption using quantum walks and achieve near-zero pixel correlations with robust sensitivity exceeding 99.6%

Image encryption relies on scrambling data to protect it from unauthorised access, and researchers continually seek methods that offer both security and efficiency. Lukasz Pawela, from the Institute of Theoretical and Applied Informatics at the Polish Academy of Sciences, and colleagues demonstrate a new image encryption protocol that utilises the principles of quantum walks, a quantum analogue of random walks. This work is significant because it explicitly investigates how a counterintuitive phenomenon known as the Parrondo paradox, where alternating losing strategies can unexpectedly yield an overall winning outcome, can both enhance and undermine the security of the encryption scheme. By carefully analysing the interplay between quantum walk parameters and the Parrondo paradox, the team not only presents a potentially robust cipher, but also identifies specific conditions under which the paradox weakens encryption, offering valuable guidance for practical implementation and parameter selection.

Researchers employ an efficient circuit realisation of discrete-time quantum walks, based on quantum Fourier transform diagonalisation and coin-conditioned phase layers, which yields low circuit depth for both position and step operations. When tested, the scheme suppresses adjacent-pixel correlations to near zero after encryption and produces nearly uniform histograms, achieving high ciphertext entropy close to the 8-bit ideal value. The data demonstrates strong diffusion and confusion, with normalized pixel change rate exceeding 99% and unified average intensity change around 30%, consistent with robust sensitivity to small plaintext changes.

Quantum Walks and the Parrondo Paradox for Encryption

This research explores a novel quantum image encryption algorithm leveraging discrete-time quantum walks and the intriguing phenomenon of the Parrondo paradox. The core idea is to use quantum walks on cyclic graphs to generate cryptographic keys, offering a sensitive and secure method for quantum image encryption. Key findings include a new encryption scheme and strong security features. The encryption scheme effectively obscures correlations between adjacent pixels, exhibits uniform pixel intensity distributions, demonstrates near-maximal sensitivity to minor changes in the plaintext, and approaches the theoretical maximum entropy, indicating minimal information leakage.

The research identifies that the Parrondo paradox can negatively impact encryption performance if not carefully managed, as specific coin parameter combinations can lead to encryption failure. Careful parameter selection is essential to ensure reliable encryption. The researchers used discrete-time quantum walks on cyclic graphs to generate cryptographic keys, a novel enhanced quantum representation for image encoding, and extensive simulations to evaluate the algorithm’s performance. Standard cryptographic metrics like pixel change rate, unified average changing intensity, and entropy were used to assess security.

The research demonstrates the potential of discrete-time quantum walks and the Parrondo paradox for quantum image encryption, while highlighting the importance of careful parameter selection. Imagine a complex maze (the quantum walk) that scrambles your image. The way the maze is built (the parameters) is crucial. If the maze is built in a special, paradoxical way, it can actually weaken the encryption. This research shows how to build the maze correctly to create a strong and secure encryption method for images.

Parrondo Paradox Secures Quantum Image Encryption

Researchers have developed a novel quantum image encryption protocol that leverages discrete-time quantum walks on cycles and examines the role of the Parrondo paradox in enhancing security. The team designed a system where a quantum walk generates a probability mask, transformed into a key image and applied via a controlled-NOT operation to encrypt grayscale images, demonstrating a performant approach to quantum image cryptography. This method utilizes an efficient circuit realisation of discrete-time quantum walks, based on quantum Fourier transform diagonalisation and coin-conditioned phase layers, achieving low circuit depth for both position and step operations. Experiments reveal that the encryption scheme effectively suppresses adjacent-pixel correlations to near zero, producing nearly uniform histograms and achieving high ciphertext entropy close to the ideal 8-bit value.

Differential analyses confirm strong diffusion and confusion properties, with normalized pixel change rate exceeding 99% and unified average change intensity around 30%, indicating robust sensitivity to even minor alterations in the plaintext. The researchers identified specific parameter regimes where alternating coin operations induce the Parrondo paradox, paradoxically degrading security by raising correlations, lowering entropy, and reducing both pixel change rate and unified average changing intensity, thereby creating practical failure modes. This work delivers both a high-performance quantum image cipher based on discrete-time quantum walks and clear guidance on selecting coin and message parameters to avoid these paradox-dominated regimes. The team’s efficient circuit design, utilizing quantum Fourier transform diagonalisation without swap gates, achieves a significant reduction in multi-qubit gate count and circuit depth compared to previous approaches, paving the way for potential hardware implementations and extensions to higher-dimensional walks. Data confirms the potential of this method for secure transmission and storage of digital images, especially in the face of emerging quantum computing threats.

Quantum Walks Secure Grayscale Image Encryption

This research introduces a new quantum image encryption algorithm based on discrete-time quantum walks, demonstrating a method for securely encoding grayscale images. The algorithm utilizes quantum walks on cyclic graphs to generate cryptographic keys, effectively suppressing correlations between adjacent pixels in the encrypted images and producing histograms closely resembling random distributions. Performance metrics, including pixel change rate and unified average changing intensity, indicate a high degree of sensitivity to even minor alterations in the original image, suggesting strong resistance to cryptanalytic attacks. The study also identifies specific parameter combinations within the quantum walk that can trigger the Parrondo paradox, a phenomenon that paradoxically degrades the encryption process.

This results in reduced entropy, increased pixel correlations, and lower sensitivity to plaintext changes, highlighting the importance of careful parameter selection. While the research demonstrates the potential of this approach for secure quantum image storage and transmission, it acknowledges that avoiding these paradox-dominated regimes is crucial for reliable performance. Future work could focus on extending the algorithm to higher-dimensional quantum walks and exploring practical hardware implementations.