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<p>A large amount of digital data is produced and distributed across the network on a daily basis. This has raised security concerns of data storage and its transmission over vulnerable networks. A variety of solutions have been proposed to address these security concerns such as encryption schemes, Steganography, Watermarking. However, these methods are only effective for concealing a limited amount of data. To handle these issues, we look into another class of solutions known as secret sharing schemes to encrypt secret data. In this paper, we proposed a new approach to image encryption based on the concept of a (<i>k</i>,&#xa0;<i>n</i>) secret image sharing scheme. The proposed scheme, namely <i>“Linear Algebra based Threshold Secret Image Sharing (LATSIS) scheme"</i>, is a polynomial-based secret image sharing (PSIS) variant. Most of the existing polynomial based secret sharing variants work efficiently only for cryptographic keys and those proposed for images are based on the extension of Shamir’s scheme (Communications of the ACM, 22(11):612–613 1979), which uses a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((k-1)\)</EquationSource> </InlineEquation> degree polynomial and Lagrange’s interpolation. The proposed scheme, therefore, provides an alternative polynomial based approach that uses linear algebra principles for image encryption and decryption. The proposed scheme can be used with both grayscale and color images. The effectiveness of the scheme is evaluated through various experiments and different qualitative and quantitative measures. The strength and resilience of the algorithm are evaluated against attacks such as few-shares attack, cropping attack, and salt-and-pepper attack. The limitation of this work is that the scheme is not completely lossless, as it truncates pixel values greater than 251 and is only applicable for a single secret.</p>

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(k, n) Threshold Secret Image Sharing using linear algebra for secure multimedia transmission

  • 期刊论文

  • 发表日期：

    2025年9月20日

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  • Maroti Deshmukh,
  • Arjun Singh Rawat

摘要

A large amount of digital data is produced and distributed across the network on a daily basis. This has raised security concerns of data storage and its transmission over vulnerable networks. A variety of solutions have been proposed to address these security concerns such as encryption schemes, Steganography, Watermarking. However, these methods are only effective for concealing a limited amount of data. To handle these issues, we look into another class of solutions known as secret sharing schemes to encrypt secret data. In this paper, we proposed a new approach to image encryption based on the concept of a (k, n) secret image sharing scheme. The proposed scheme, namely “Linear Algebra based Threshold Secret Image Sharing (LATSIS) scheme", is a polynomial-based secret image sharing (PSIS) variant. Most of the existing polynomial based secret sharing variants work efficiently only for cryptographic keys and those proposed for images are based on the extension of Shamir’s scheme (Communications of the ACM, 22(11):612–613 1979), which uses a \((k-1)\) degree polynomial and Lagrange’s interpolation. The proposed scheme, therefore, provides an alternative polynomial based approach that uses linear algebra principles for image encryption and decryption. The proposed scheme can be used with both grayscale and color images. The effectiveness of the scheme is evaluated through various experiments and different qualitative and quantitative measures. The strength and resilience of the algorithm are evaluated against attacks such as few-shares attack, cropping attack, and salt-and-pepper attack. The limitation of this work is that the scheme is not completely lossless, as it truncates pixel values greater than 251 and is only applicable for a single secret.