Cryptanalysis of Image Cryptosystem via Finite-Time Projective Synchronization in Fractional-Order Inertial Memristive Neural Networks
7 affiliations
- 1University of Electronic Science and Technology of China Zhongshan Institute, Zhongshan 528402, China
- 2Guangdong Provincial/Zhuhai Key Laboratory of Interdisciplinary Research and Application for Data Science, Beijing Normal-Hong Kong Baptist University, Zhuhai 519087, China
- 3Department of Computer Science, Hong Kong Baptist University, Hong Kong, China
- 4Faculty of Information Technology, Macau University of Science and Technology, Macao, China
- 5School of Artificial Intelligence, Guangzhou Institute of Science and Technology, Guangzhou 510540, China
- 6School of Computer, Zhuhai College of Science and Technology, Zhuhai 519041, China
- 7University of Electronic Science and Technology of China, Chengdu 611731, China
Abstract
This paper presents a systematic structural cryptanalysis of a color-image cryptosystem based on finite-time projective synchronization in fractional-order inertial memristive neural networks. By examining the algebraic structure and plaintext–ciphertext dependencies of its encryption pipeline, several attack-relevant structural properties are identified, including plaintext-independent sequence reuse, algebraically redundant XOR operations, shared encryption material across RGB channels, and the absence of interpixel diffusion. Under a fixed secret configuration and a bijective spatial disruption map, the complete encryption process is shown to reduce to Cc(i)=Pc(π(i))⊕K(i), where π denotes a reusable spatial permutation and K is an equivalent XOR mask obtained by combining the two nominal diffusion sequences. At the image layer, this representation shows that encryption is determined by the induced permutation and equivalent mask. Exploiting these properties, a chosen-plaintext attack is developed to recover the equivalent mask using an all-zero image and reconstruct the spatial permutation through base-256 position encoding. The implemented two-query construction supports up to 224 pixels, whereas an optimal two-query design supports up to 240 pixels; one query suffices for at most 216 pixels. A differential chosen-plaintext attack further recovers the equivalent key by eliminating the mask through related plaintext differences. In addition, a known-plaintext attack reconstructs the permutation using mask-invariant positional fingerprints under explicit uniqueness conditions, while chosen-ciphertext attacks enable direct plaintext recovery with one nonchallenge query or equivalent-key recovery with two queries. The two-query CPA is also evaluated through an encryption-oracle-only interface. Experimental results on 512×512 RGB images confirm exact equivalent-key recovery and lossless plaintext reconstruction. All eight tested image cases yield exact recovery under the fixed context, with seven repeated runs per case used to summarize timing, and six heterogeneous known plaintext–ciphertext pairs suffice for exact recovery in the principal experiment. In general, known-plaintext recovery identifies the permutation when the positional fingerprints are unique. Finally, an invertible, module-wise proof-of-concept design is specified for context-dependent sequence generation, cross-channel coupling, bijective spatial disruption, and independent bidirectional feedback diffusion; its relation to the attacks analyzed in this paper is assessed structurally.
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BibTeX
@article{lin2026cryptanalysis,
title = {{Cryptanalysis of Image Cryptosystem via Finite-Time Projective Synchronization in Fractional-Order Inertial Memristive Neural Networks}},
author = {Yiting Lin and Xiyuan Cheng and Yaokang Li and Yunan Wei and Wenbin Cheng},
journal = {Fractal and Fractional},
year = {2026},
month = nov,
doi = {10.3390/fractalfract10110770},
url = {https://www.mdpi.com/2504-3110/10/11/770},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Cryptanalysis of Image Cryptosystem via Finite-Time Projective Synchronization in Fractional-Order Inertial Memristive Neural Networks
AU - Yiting Lin
AU - Xiyuan Cheng
AU - Yaokang Li
AU - Yunan Wei
AU - Wenbin Cheng
PY - 2026
DA - 2026/11/04
JO - Fractal and Fractional
DO - 10.3390/fractalfract10110770
UR - https://www.mdpi.com/2504-3110/10/11/770
AB - This paper presents a systematic structural cryptanalysis of a color-image cryptosystem based on finite-time projective synchronization in fractional-order inertial memristive neural networks. By examining the algebraic structure and plaintext–ciphertext dependencies of its encryption pipeline, several attack-relevant structural properties are identified, including plaintext-independent sequence reuse, algebraically redundant XOR operations, shared encryption material across RGB channels, and the absence of interpixel diffusion. Under a fixed secret configuration and a bijective spatial disruption map, the complete encryption process is shown to reduce to Cc(i)=Pc(π(i))⊕K(i), where π denotes a reusable spatial permutation and K is an equivalent XOR mask obtained by combining the two nominal diffusion sequences. At the image layer, this representation shows that encryption is determined by the induced permutation and equivalent mask. Exploiting these properties, a chosen-plaintext attack is developed to recover the equivalent mask using an all-zero image and reconstruct the spatial permutation through base-256 position encoding. The implemented two-query construction supports up to 224 pixels, whereas an optimal two-query design supports up to 240 pixels; one query suffices for at most 216 pixels. A differential chosen-plaintext attack further recovers the equivalent key by eliminating the mask through related plaintext differences. In addition, a known-plaintext attack reconstructs the permutation using mask-invariant positional fingerprints under explicit uniqueness conditions, while chosen-ciphertext attacks enable direct plaintext recovery with one nonchallenge query or equivalent-key recovery with two queries. The two-query CPA is also evaluated through an encryption-oracle-only interface. Experimental results on 512×512 RGB images confirm exact equivalent-key recovery and lossless plaintext reconstruction. All eight tested image cases yield exact recovery under the fixed context, with seven repeated runs per case used to summarize timing, and six heterogeneous known plaintext–ciphertext pairs suffice for exact recovery in the principal experiment. In general, known-plaintext recovery identifies the permutation when the positional fingerprints are unique. Finally, an invertible, module-wise proof-of-concept design is specified for context-dependent sequence generation, cross-channel coupling, bijective spatial disruption, and independent bidirectional feedback diffusion; its relation to the attacks analyzed in this paper is assessed structurally.
SN - 2504-3110
ER -