An Implementation of Image Secret Sharing Scheme Based on Matrix Operations

Zihan Ren, Peng Li and Xin Wang
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Zihan Ren: Department of Mathematics and Physics, North China Electric Power University, Baoding 071003, China
Peng Li: Department of Mathematics and Physics, North China Electric Power University, Baoding 071003, China
Xin Wang: Department of Mathematics and Physics, North China Electric Power University, Baoding 071003, China

Mathematics, 2022, vol. 10, issue 6, 1-18

Abstract: The image secret sharing scheme shares a secret image as multiple shadows. The secret image can be recovered from shadow images that meet a threshold number. However, traditional image secret sharing schemes generally reuse the Lagrange’s interpolation in the recovery stage to obtain the polynomial in the sharing stage. Since the coefficients of the polynomial are the pixel values of the secret image, it is able to recover the secret image. This paper presents an implementation of the image secret sharing scheme based on matrix operations. Different from the traditional image secret sharing scheme, this paper does not use the method of Lagrange’s interpolation in the recovery stage, but first identifies the participants as elements to generate a matrix and calculates its inverse matrix. By repeating the matrix multiplication, the polynomial coefficients of the sharing stage are quickly derived, and then the secret image is recovered. By theoretical analysis and the experimental results, the implementation of secret image sharing based on matrix operation is higher than Lagrange’s interpolation in terms of efficiency.

Keywords: image secret sharing; linear algebra; matrix operations; Lagrange’s polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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