Over the past decade, most of secret image sharing schemes have been proposed by using Shamir's technique. It is based on a linear combination polynomial arithmetic. Although Shamir's technique based secret image sharing schemes are efficient and scalable for various environments, there exists a security threat such as Tompa-Woll attack. Renvall and Ding proposed a new secret sharing technique based on nonlinear combination polynomial arithmetic in order to solve this threat. It is hard to apply to the secret image sharing. In this paper, we propose a
In a security system, there is a maintenance tool which must be checked every day. In order to check it, someone must have access to this system. Three senior administrators are engaged, but they do not trust the combination to any individual administrator. Hence, we would like to design a system whereby any two of three administrators can gain access to this system, but an individual administrator cannot do so. In order to design this system, we adapt a concept of secret sharing. A secret sharing is technique for distributing a secret amongst a group of honest participants, and each secret piece is allocated for each participant after the secret is divided into several pieces. This secret can be reconstructed only when a sufficient number, of possibly different types of shares are combined together; an individual share is no use on its own [
With the development of computing and network technologies, in the meantime, multimedia data such as image, audio, and video files have transmitted over the Internet, actively. As a result, multimedia security has emerged as an important issue [
As mentioned above, most of secret image sharing schemes are based on Shamir’s
In sharing procedure for
In this paper, we propose a nonlinear secret image sharing scheme with steganography concept. Although the proposed scheme is based on Renvall and Ding’s sharing and reconstruction methods [
This paper is organized as follows. Section
In this section, Shamir’s
In 1979, Shamir has proposed a secret sharing scheme for the first time [
Let
For the example of
In Shamir’s scheme, the linear combination polynomial and Lagrange’s interpolation arithmetic operations over prime
When
If participants want to reconstruct a
Consider
Lastly, a key can be derived from
In 1996, Renvall and Ding [
Let for any set of indices where for any set of indices
where Consider
where
In sharing process, the secret
In order to distribute the shares,
If participants want to reconstruct the secret
They have completed verification of security for Tompa-Woll attack [
In this section, we illustrate considerations, sharing, and reconstruction algorithms.
In order to propose a new nonlinear secret image sharing scheme, we discuss some considerations such as handing techniques of secret and shadow images and overflow (or underflow).
In previous scheme, they used (
If an arbitrary pixel value in SI is one of 251 to 255, it can occur an overflow or underflow because all arithmetic operations are performed within GF(251). So, we define another variable positive integer
In Renvall and Ding’s scheme,
Suppose that the cover image (
In this procedure, the sharing process is described. Input: A Output:
Convert a
If
Choose
Consider
Calculate a shadow value
Embed the generated
The embedding method by prime
Range | Embedding technique | Pixel block |
---|---|---|
|
LSB1 | per 1 pixel |
|
LSB2 | per 1 pixel |
|
LSB1 and LSB2 | per 2 pixels |
|
LSB2 | per 2 pixels |
|
LSB1 and LSB2 | per 3 pixels |
|
LSB2 | per 3 pixels |
|
LSB1 and LSB2 | per 4 pixels |
|
LSB2 | per 4 pixels |
Distribute the generated
In this procedure, the reconstruction process is described. Input: Output: a reconstructed
Extract a
Calculate a
Convert the calculated
In this section, we analyze the security and efficiency of proposed scheme.
In order to estimate the efficiency and security of secret image sharing schemes, there exist two typical measurement tools: the embedding capacity and
In the experiments, we have performed the experiment for
Eight greyscale test images.
Lena
Baboon
Airplane
Peppers
Boat
Man
Elaine
Woman
In the proposed scheme, PSNR result depends on the embedding method by prime
PSNR result of
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Average |
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11 | 44.08 | 43.92 | 43.93 | 43.96 | 43.97 |
17 | 45.39 | 45.47 | 45.60 | 45.39 | 45.46 |
19 | 45.51 | 45.48 | 45.50 | 45.44 | 45.48 |
29 | 45.49 | 45.38 | 45.43 | 45.35 | 45.41 |
37 | 44.15 | 44.13 | 44.13 | 44.04 | 44.11 |
79 | 45.18 | 45.17 | 45.03 | 45.16 | 45.13 |
113 | 45.08 | 45.11 | 45.12 | 45.10 | 45.10 |
167 | 44.15 | 44.13 | 44.20 | 44.15 | 44.16 |
251 | 44.16 | 44.13 | 44.16 | 44.20 | 44.16 |
In the meantime, we utilized a variable
The relation of PSNR between
The embedding capacity of the proposed scheme was decided with the embedding method by prime
The theoretical embedding capacity of the proposed scheme.
Interval | MEBs |
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In order to verify an excellence of the proposed scheme, we have performed a comparison between our and the previous schemes and the result of it is shown in Table
The comparison result between the proposed and previous schemes for the embedding capacity and PSNR.
Schemes | EC (bpp) | PSNR (dB) |
---|---|---|
Lin and Tsai [ |
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39.17 |
Wang and Shyu [ |
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— |
Chang et al. [ |
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40.92 |
Lin and Chan [ |
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40.01 |
Proposed |
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44.78 |
In this paper, we have proposed a (
The future works are as follows: the studies of nonlinear secret image sharing scheme over
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2012R1A1A2008348) and Brain Korea 21 Plus (BK21+) Project in 2014.