Abstract
In a general (k, n) scalable secret image sharing (SSIS) scheme, the secret image is shared by n participants and any k or more than k participants have the ability to reconstruct it. The scalability means that the amount of information in the reconstructed image scales in proportion to the number of the participants. In most existing SSIS schemes, the size of each image shadow is relatively large and the dealer does not has a flexible control strategy to adjust it to meet the demand of differen applications. Besides, almost all existing SSIS schemes are not applicable under noise circumstances. To address these deficiencies, in this paper we present a novel SSIS scheme based on a brand-new technique, called compressed sensing, which has been widely used in many fields such as image processing, wireless communication and medical imaging. Our scheme has the property of flexibility, which means that the dealer can achieve a compromise between the size of each shadow and the quality of the reconstructed image. In addition, our scheme has many other advantages, including smooth scalability, noise-resilient capability, and high security. The experimental results and the comparison with similar works demonstrate the feasibility and superiority of our scheme.
Highlights
To safeguard cryptographic keys, Shamir [1] and Blakley [2] presented a novel method for constructing secure and robust key management schemes, called secret sharing (SS), which can overcome many vulnerabilities when one possesses a single master key for a certain cryptosystem
The dealer first generates a k − 1 degree polynomial by letting the k coefficients be the gray values of k pixels in the image and computes the corresponding shadow for each participant according to the polynomial
From a high-level perspective, the reconstruction phase in Shamir-type (k, n)-secret image sharing (SIS) schemes [1, 5, 8, 12] can be regarded as the process of solving the secret image I from Y = AI generated by the available shadows of participants, where A 2 Rk1Âk is the known Vandermonde coefficient matrix and k1 denotes the number of available participants
Summary
Shamir [1] and Blakley [2] presented a novel method for constructing secure and robust key management schemes, called secret sharing (SS), which can overcome many vulnerabilities when one possesses a single master key for a certain cryptosystem. In 2002, Thien and Lin [5] proposed a (k, n) secret image sharing (SIS) scheme based on Shamir’s (k, n) threshold SS scheme. In their scheme, the dealer first generates a k − 1 degree polynomial by letting the k coefficients be the gray values of k pixels in the image and computes the corresponding shadow for each participant according to the polynomial. From a high-level perspective, the reconstruction phase in Shamir-type (k, n)-SIS schemes [1, 5, 8, 12] can be regarded as the process of solving the secret image I from Y = AI generated by the available shadows of participants, where A 2 Rk1Âk is the known Vandermonde coefficient matrix and k1 denotes the number of available participants.
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