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Single Secret Sharing Scheme Using Chinese Remainder Theorem, Modified Shamir’s Scheme and XOR Operation

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Abstract

The existing scheme uses lightweight modular arithmetic and Boolean operations for the secret sharing scheme by compromising minor degradation in security with less computation overhead. In this paper, we proposed the computation efficient (n, n)-single secret sharing scheme using the Chinese Remainder Theorem (CRT), modified Shamir’s scheme, and Boolean XOR operation with perfect security. The share generation process follows the lightweight, computationally efficient reverse CRT, modified Shamir’s scheme, and XOR operation, which generates the highly randomized shares and does not reveal any information. The secret reconstruction process follows the CRT, modified Shamir’s scheme, and XOR operation. To reconstruct the secret, all n distributed shares are required. The proposed scheme is attack resistant to an attack on any shares. The estimated values of NPCR and UACI, which are 99.99 and 33.33 respectively, demonstrate that the proposed approach is significantly more secure against differential attack than the existing schemes. Additional statistical measures, such as correlation, RMSE, and PSNR, with better approximate values compared to existing schemes, respectively as 0, 97, and 8 dB, are used to evaluate an algorithm’s performance in terms of similarity. To check th robustness of an algorithm, different levels of salt and pepper noise are performed on distributed shares. The experiment results show that the approach is more efficient and secure than existing schemes. The experimental findings demonstrate that the shared images are more randomized, do not reveal any sensitive information, and can be recovered without introducing any loss to the original image. The limitation of the proposed scheme is that it is suitable for a single secret.

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  1. National Institute of Technology, Uttarakhand, Srinagar, India

    Dinesh Pande, Arjun Singh Rawat, Maroti Deshmukh & Maheep Singh

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  1. Dinesh Pande
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Correspondence to Maroti Deshmukh.

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Pande, D., Rawat, A.S., Deshmukh, M. et al. Single Secret Sharing Scheme Using Chinese Remainder Theorem, Modified Shamir’s Scheme and XOR Operation. Wireless Pers Commun 130, 957–985 (2023). https://doi.org/10.1007/s11277-023-10315-5

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