<p>This paper introduces a medical image cryptosystem founded on a conservative hyper-chaotic system integrated with finite-field operations. An enhanced conservative hyper-chaotic model is first developed, exhibiting superior dynamical complexity while preserving both energy and volume invariants. Comprehensive dynamical analyses and statistical evaluations confirm its strong ergodicity and pseudo-randomness. Building on this foundation, a multi-stage encryption framework is proposed, incorporating SHA-256-based dynamic key generation, modulo-addition diffusion, non-repetitive permutation, and finite-field <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\textrm{GF}(257)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>GF</mtext> <mo stretchy="false">(</mo> <mn>257</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> operations. This hybrid design ensures high security, computational efficiency, and full reversibility for encryption–decryption processes. The scheme demonstrates strong clinical applicability, effectively securing diverse medical image types while preserving diagnostic integrity upon decryption. Experimental results validate its robustness against common cryptographic attacks, with performance comparable to state-of-the-art methods. Achieved metrics include NPCR > 99.58%, UACI: 33.35–33.53%, near-zero correlation (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$< 0.008$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo><</mo> <mn>0.008</mn> </mrow> </math></EquationSource> </InlineEquation>), and near-ideal entropy (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$> 7.996$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>></mo> <mn>7.996</mn> </mrow> </math></EquationSource> </InlineEquation> bits). The proposed architecture provides a reliable and provably secure solution for medical image transmission and processing, addressing critical requirements for healthcare data protection in clinical environments.</p>

A hybrid cryptosystem for medical image security: integrating finite fields with conservative hyperchaos

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发表日期：

2026年1月20日

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Yanbin Zhang,
Ping Lin,
Jiale Chen,
Weigang Sun

摘要

This paper introduces a medical image cryptosystem founded on a conservative hyper-chaotic system integrated with finite-field operations. An enhanced conservative hyper-chaotic model is first developed, exhibiting superior dynamical complexity while preserving both energy and volume invariants. Comprehensive dynamical analyses and statistical evaluations confirm its strong ergodicity and pseudo-randomness. Building on this foundation, a multi-stage encryption framework is proposed, incorporating SHA-256-based dynamic key generation, modulo-addition diffusion, non-repetitive permutation, and finite-field $\textrm{GF}(257)$ $GF (257)$ operations. This hybrid design ensures high security, computational efficiency, and full reversibility for encryption–decryption processes. The scheme demonstrates strong clinical applicability, effectively securing diverse medical image types while preserving diagnostic integrity upon decryption. Experimental results validate its robustness against common cryptographic attacks, with performance comparable to state-of-the-art methods. Achieved metrics include NPCR > 99.58%, UACI: 33.35–33.53%, near-zero correlation ( $< 0.008$ $< 0.008$ ), and near-ideal entropy ( $> 7.996$ $> 7.996$ bits). The proposed architecture provides a reliable and provably secure solution for medical image transmission and processing, addressing critical requirements for healthcare data protection in clinical environments.