<p>This system uses the Hessenberg decomposition (HD) and Chaotic structured phase masks (CSPMs) to propose a phase image encryption algorithm. HD makes the cryptosystem asymmetric. The use of CSPMs enhances the security of the proposed cryptosystem. The approach is further secured by the parameters of the Fresnel transform (FrT). The effectiveness of this method is examined using noise and occlusion attacks. To bolster its legitimacy, key sensitivity results were also included. The obtained values of mean squared error (MSE) is 1.68 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\times 10^{ - 31}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>31</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> for grey image and 1.62 <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\times 10^{ - 31}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>31</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> for binary image which represents the effectiveness of the proposed cryptosystem. Parameters of Fresnel transform (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$z_{1} = 25\;{\text{mm}}, z_{2} = 35\;{\text{mm}}, \lambda = 632.8\;{\text{nm}})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>25</mn> <mspace width="0.277778em" /> <mtext>mm</mtext> <mo>,</mo> <msub> <mi>z</mi> <mn>2</mn> </msub> <mrow> <mo>=</mo> <mn>35</mn> <mspace width="0.277778em" /> <mtext>mm</mtext> <mo>,</mo> <mi>λ</mi> <mo>=</mo> <mn>632.8</mn> <mspace width="0.277778em" /> <mtext>nm</mtext> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> are used to enhance the security of the proposed scheme. This outcome exhibits that the method is effective in obtaining safe image encryption, providing excellent image reconstruction with minimal information loss.</p>

Hybrid image encryption based on Hessenberg decomposition and chaotic structured phase masks in Fresnel transform domain

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发表日期：

2026年1月20日

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R. Girija,
Kapil Shankar Gaur,
Hukum Singh

摘要

This system uses the Hessenberg decomposition (HD) and Chaotic structured phase masks (CSPMs) to propose a phase image encryption algorithm. HD makes the cryptosystem asymmetric. The use of CSPMs enhances the security of the proposed cryptosystem. The approach is further secured by the parameters of the Fresnel transform (FrT). The effectiveness of this method is examined using noise and occlusion attacks. To bolster its legitimacy, key sensitivity results were also included. The obtained values of mean squared error (MSE) is 1.68 $\times 10^{ - 31}$ $\times 10^{- 31}$ for grey image and 1.62 $\times 10^{ - 31}$ $\times 10^{- 31}$ for binary image which represents the effectiveness of the proposed cryptosystem. Parameters of Fresnel transform ( $z_{1} = 25\;{\text{mm}}, z_{2} = 35\;{\text{mm}}, \lambda = 632.8\;{\text{nm}})$ $z_{1} = 25 mm, z_{2} = 35 mm, λ = 632.8 nm)$ are used to enhance the security of the proposed scheme. This outcome exhibits that the method is effective in obtaining safe image encryption, providing excellent image reconstruction with minimal information loss.