Abstract
In this paper, we introduce two new image-sharing types to extend the applicability of sharing. Type 1 is our so-called forbidden type. In its sharing system, any t of the n shares can recover the secret image, unless the t shares form a forbidden group listed in a forbidden list. Type 2 is our so-called cross-department support type. If a government has 3 departments {DEPH, DEPM, DEPL}, then 3 thresholds (tH, tM and tL) exist. Any tH number of officers from department DEPH can unveil the secret image, and likewise for any tM and tL number of officers from departments DEPM and DEPL, respectively. Type 2 image sharing allows a secret to be disclosed not only in an intra-department meeting but also in a cross-department meeting. In this study, both types are implemented through two approaches: the polynomial and linear-equations approaches. Hackers can be confused when two approaches are mixed. As for the applications, use Type 1 to protect sensitive information in medical or military images or legal documents; and use type 2 to support cross-department crime investigation, industrial production, etc.
Highlights
Secret sharing was introduced by Shamir [1] and Blakley [2] in 1979
The first is visual cryptography (VC) [3], which is used for black-and-white (2-levels) images, and the second is polynomial-based sharing [4], which is used for gray-value or color images
The linear-equations approach can be mapped from the polynomial approach
Summary
Secret sharing was introduced by Shamir [1] and Blakley [2] in 1979. In secret sharing, a given secret is encoded and divided into n shares, and two requirements must be met before a secret can be disclosed: a) any t of the n shares can cooperate to unveil the given secret, and b) less than t shares cannot unveil. 2002, Thien and Lin [4] proposed a (t, n) threshold scheme for sharing 256-level secret images. This is because the resultant protection of the image will be extremely weak, the n shares of the key will be smaller in size than the n shares of the secret image. We attempt to extend our previous foundational study [4] on sharing to introduce two other types of sharing: the forbidden type and cross-department support type We implement these two types first by using a polynomial approach and by using a linear-equations approach. The secret image can be divided into several parts, where odd-numbered parts use the polynomial approach, and the even-numbered parts use the linear-equations approach.
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