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.
Highlights
Shamir [1] first introduced this concept in 1979, in which a secret message is embedded as a constant term of a polynomial of order k − 1, and random numbers are used for the other coefficients of the polynomial
Polynomial based image secret sharing schemes have attracted a lot of attention, and new secret sharing algorithms based on polynomial sharing schemes have been developed
Experiments show that the operation time of the matrix operation-based secret image sharing scheme proposed in this paper is smaller than that of the polynomial interpolation-based secret image sharing scheme
Summary
Secret sharing is an important research direction in the field of modern cryptography. When the attacker has a certain number of shared keys is it possible to recover the original secret information correctly, so the recovery of the original secret information is very difficult. A secret sharing scheme with a threshold of (k, n) means sharing a secret message into n shares, where any k or more shares can recover the secret. Shamir [1] first introduced this concept in 1979, in which a secret message is embedded as a constant term of a polynomial of order k − 1, and random numbers are used for the other coefficients of the polynomial. In 2004, Lin and Tsai [3] used a steganography approach to embed the shadow image in [2] in a steganographic image, which improves the security of the scheme and has verifiable functionality. Polynomial based image secret sharing schemes have attracted a lot of attention, and new secret sharing algorithms based on polynomial sharing schemes have been developed
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