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A Reversible Secret Image Sharing Scheme in Matrix Projection Using Discrete Haar Wavelet Transform
Abstract
Secret Sharing Schemes have become an important area of research in order to achieve secured communication over communication networks. Secrets may be of any form i.e. it can be textual data, an image itself, a sound signal or a video. They are encrypted in carrier images or secret images, carrier signals or carrier video and transmitted. At receiver end they are decrypted and the secrets are revealed. In this paper various secret sharing schemes are discussed. The Matrix Projection Secret Image Sharing Scheme (MPSISS) and application of Discrete Haar Wavelet Transform (DHWT) for secret image sharing for secure communication is presented in the paper.
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This paper deals with using discrete wavelet transform derived features used for digital image texture analysis. Wavelets appear to be a suitable tool for this task, because they allow analysis of images at various levels of resolution. The proposed features have been tested on images from standard Brodatz catalogue.
A new grayscale image encryption algorithm based on (k,n) threshold secret sharing is proposed. The scheme allows a secret image to be transformed into n shares, where any k ≤ n shares can be used to reconstruct the secret image, while the knowledge of k-1 or fewer shares leaves no sufficient information about the secret image and it becomes hard to decrypt the transmitted image. In the proposed scheme, the pixels of the secret image are first permuted and then encrypted by using quadratic residues. In the final stage, the encrypted image is shared into n shadow images using polynomials of Shamir scheme. The proposed scheme is provably secure and the experimental results shows that the scheme performs well while maintaining high levels of quality in the reconstructed image.
A "secret sharing system" permits a secret to be shared among n trustees in such a way that any k of them can recover the secret, but any k-1 have complete uncertainty about it. A linear coding scheme for secret sharing is exhibited which subsumes the polynomial interpolation method proposed by Shamir and can also be viewed as a deterministic version of Blakley's probabilistic method. Bounds on the maximum value of n for a given k and secret size are derived for any system, linear or nonlinear. The proposed scheme achieves the lower bound which, for practical purposes, differs insignificantly from the upper bound. The scheme may be extended to protect several secrets. Methods to protect against deliberate tampering by any of the trustees are also presented.
The Haar Wavelet Transformation is a simple form of compression in-volved in averaging and differencing terms, storing detail coefficients, elim-inating data, and reconstructing the matrix such that the resulting matrix is similar to the initial matrix. The Haar Wavelet Transform is a corner-stone in compressing computer images.
We proposed a fast secret image sharing based on Haar wavelet transform and Shamir's method. Many researchers develop secret image sharing method with Shamir's algorithm in one whole image. We employ discrete Haar wavelet transform to reduce the secret image to its quarter size firstly, i.e. the 1-level LL subband. Then only apply the modified Shamir's algorithm to this LL subband to generate the shadow images. Lagrange method exploits the enough numbers of the shadow images in the retrieval step. Due to the Shamir's and Lagrange algorithms consume a lot of time during the processing of the secret image sharing. Our method only processes a quarter size of image that can decrease computation time, and still achieve to recover the secret image reversible. The experiment results demonstrate our method is fast and retrieve secret image lossless.
In a secret sharing scheme, a datumd is broken into shadows which are shared by a set of trustees. The family {P′⊆P:P′ can reconstructd} is called the access structure of the scheme. A (k, n)-threshold scheme is a secret sharing scheme having the access structure {P′⊆P: |P′|≥k}. In this paper, by observing a simple set-theoretic property of an access structure, we propose its mathematical definition.
Then we verify the definition by proving that every family satisfying the definition is realized by assigning two more shadows
of a threshold scheme to trustees.
In this paper, we propose a method such that a secret image is shared by n shadow images, and any r shadow images (r⩽n) of them can be used to restore the whole secret image. The size of each shadow image is smaller than the secret image in our method. This property gives the benefit in further process of the shadow images, such as storage, transmission, or image hiding.
This paper presents a strong (k,n) threshold-based ramp secret sharing scheme with k access levels. The secrets are the elements represented in a square matrix S. The secret matrix S can be shared among n different participants using a matrix projection technique where: i) any subset of k participants can collaborate together to reconstruct the secret, and ii) any subset of (k-1) or fewer participants cannot partially discover the secret matrix. The primary advantages are its large compression rate on the size of the shares and its strong protection of the secrets
This paper presents a reliable image secret sharing method which incorporates two k-out-of-n secret sharing schemes: i) Shamir's secret sharing scheme and ii) matrix projection secret sharing scheme. The technique allows a colored secret image to be divided as n image shares so that: i) any k image shares (k les n) are sufficient to reconstruct the secret image in the lossless manner and ii) any (k - 1) or fewer image shares cannot get enough information to reveal the secret image. It is an effective, reliable and secure method to prevent the secret image from being lost, stolen or corrupted. In comparison with other image secret sharing methods, this approach's advantages are its large compression rate on the size of the image shares, its strong protection of the secret image and its ability for the realtime processing
In this paper we show how to divide data D into n pieces in such a way that D is easily reconstructable from any k pieces, but even complete knowledge of k - 1 pieces reveals absolutely no information about D. This technique enables the construction of robust key management schemes for cryptographic systems that can function securely and reliably even when misfortunes destroy half the pieces and security breaches expose all but one of the remaining pieces.
An Image Secret Sharing Scheme With The Capability Of Previewing The Secret Image
- Ching-Nung Yang
- Tse-Shih Chen
Ching-Nung Yang and Tse-Shih Chen "An Image Secret Sharing
Scheme With The Capability Of Previewing The Secret Image",
National Dong Hwa University, Taiwan.