A New Lossless Secret Image Sharing Scheme for Grayscale Images with Small Shadow Size
The current paper offers a lossless (k, n)-threshold scheme with reduced shadow size using the algebraic properties of the polynomial ring \(\mathbb {Z}_{251}[x]\) over the field \(\mathbb {Z}_{251}\) . Unlike most of the existing secret image sharing sch
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Abstract The current paper offers a lossless (k, n)-threshold scheme with reduced shadow size using the algebraic properties of the polynomial ring Z251 [x] over the field Z251 . Unlike most of the existing secret image sharing schemes, our scheme does not require any preprocessing steps in order to transform the image into a random image to avoid data leakage from the shares of the secret image. Moreover, the efficiency of our proposed scheme is explained through security analysis and demonstrated through simulation results. Keywords Polynomial-based secret sharing · Lossless recovery · Finite field
1 Introduction Security is one of the most important issues when storage or transmission of secret image is considered. Secret sharing (SS) can resolve this issue. A (k, n)-SS scheme encodes the secret data into shares and distributes such shares to n participants in such a manner that in the recovery phase, when k or more participants pool their shares, the secret is recovered. On the other hand, fewer than k participants, even if collect their shares, no extra information is revealed. The notion of secret sharing was further extended to visual cryptography [1, 3–5] by Noar and Shamir [6]. In 2002, Thien and Lin [8] used the polynomial secret image sharing scheme of Shamir to share secret images in Z251 . Instead of using the first coefficient, they [8] used all the coefficients of the k − 1 degree polynomial in Shamir (k, n)-scheme. As a 1 result, the size of shadow images reduced to times the secret image. However, in k Md. K. Sardar (B) Department of Pure Mathematics, University of Calcutta, Kolkata, India e-mail: [email protected] A. Adhikari Presidency University, Kolkata, West Bengal, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 D. Bhattacharjee et al. (eds.), Proceedings of International Conference on Frontiers in Computing and Systems, Advances in Intelligent Systems and Computing 1255, https://doi.org/10.1007/978-981-15-7834-2_65
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[8] all gray values greater than 250 were truncated. As a result, the scheme becomes lossy. However, to achieve the lossless recovery, Thien and Lin [8] split those pixels whose values are larger than 250 into two pixels, resulting in the increase of the share size. In 2013, Yang et al. [9] developed Lin et al.’s [8] model to achieve a lossless scheme by using Galois Field GF(28 ). Ding et al. [2] successfully proposed a lossless (k, n)-scheme in Z251 without pixel expansion. But, in this scheme, the share size remains same with the original secret image. We have successfully overcome these issues. Using the algebraic properties of the polynomial ring Z251 [x] over the field Z251 , in the present paper, we propose a lossless (k, n)-scheme with diminished shadow size. The main advantage of our scheme is that, unlike most of the existing scheme, it requires no preprocessing to transform the secret image into a random-looking image, resulting in our scheme an efficient one. The arrangement of the rest of the p
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