### Mathematical Biosciences and Engineering

2019, Issue 5: 4802-4817. doi: 10.3934/mbe.2019242
Research article Special Issues

# Reducing file size and time complexity in secret sharing based document protection

• Received: 24 January 2019 Accepted: 25 April 2019 Published: 28 May 2019
• Recently, Tu and Hsu proposed a secret sharing based document protecting scheme. In their scheme, a document is encrypted into $n$ shares using Shamir's $(k, n)$ secret sharing, where the $n$ shares are tied in with a cover document. The document reconstruction can be accomplished by acknowledgement of any $k$ shares and the cover document. In this work, we construct a new document protecting scheme which is extended from Tu-Hsu's work. In Tu-Hsu's approach, each inner code of secret document takes one byte length, and shares are generated from all inner codes with the computation in $GF(257)$, where $257$ is a Fermat Prime that satisfies $257 = 2^{2^{3}}+1$. However, the share size expands when it equals to $255$ or $256$. In our scheme, each two inner codes of document is combined into one double-bytes inner code, and shares are generated from these combined inner codes with the computation in $GF(65537)$ instead, where $65537$ is also a Fermat Prime that satisfies $65537 = 2^{2^{4}}+1$. Using this approach, the share size in our scheme can be reduced from Tu-Hsu's scheme. In addition, since the number of combined inner codes is half of the inner codes number in Tu-Hsu's scheme, our scheme is capable of saving almost half running time for share generation and document reconstruction from Tu-Hsu's scheme.

Citation: Yan-Xiao Liu, Ya-Ze Zhang, Ching-Nung Yang. Reducing file size and time complexity in secret sharing based document protection[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 4802-4817. doi: 10.3934/mbe.2019242

### Related Papers:

• Recently, Tu and Hsu proposed a secret sharing based document protecting scheme. In their scheme, a document is encrypted into $n$ shares using Shamir's $(k, n)$ secret sharing, where the $n$ shares are tied in with a cover document. The document reconstruction can be accomplished by acknowledgement of any $k$ shares and the cover document. In this work, we construct a new document protecting scheme which is extended from Tu-Hsu's work. In Tu-Hsu's approach, each inner code of secret document takes one byte length, and shares are generated from all inner codes with the computation in $GF(257)$, where $257$ is a Fermat Prime that satisfies $257 = 2^{2^{3}}+1$. However, the share size expands when it equals to $255$ or $256$. In our scheme, each two inner codes of document is combined into one double-bytes inner code, and shares are generated from these combined inner codes with the computation in $GF(65537)$ instead, where $65537$ is also a Fermat Prime that satisfies $65537 = 2^{2^{4}}+1$. Using this approach, the share size in our scheme can be reduced from Tu-Hsu's scheme. In addition, since the number of combined inner codes is half of the inner codes number in Tu-Hsu's scheme, our scheme is capable of saving almost half running time for share generation and document reconstruction from Tu-Hsu's scheme.

 [1] Q. D. Sun, N. Wang, Y. D. Zhou, et al., Identification of influential online social network users based on Multi-Features, Int. J. Pattern Recognit. Artif. Intell., 30 (2016), 1–15. [2] Q. D. Sun, N. Wang, S. C. Li, et al., Local spatial obesity analysis and estimation using online social network sensors, J. Biomed. Inform., 83 (2018), 54–62. [3] A. Shamir, How to share a secret, Commun. ACM, 22 (1979), 612–613. [4] G. R. Blakley, Safeguarding cryptographic keys, AFIPS Conference, 48 (1979), 313–317. [5] X. X. Jia, Y. X. Song, D. S. Wang, et al., A collaborative secret sharing scheme based on the Chinese Remainder Theorem, Math. Biosci. Eng., 16 (2019), 1280–1299. [6] X. X. Jia, D. S. Wang, D. X. Nie, et al., A new threshold changeable secret sharing scheme based on the Chinese Remainder Theorem, Inf. Sci., 473 (2019), 13–30. [7] C. C. Thien and J. C. Lin, Secret image sharing, Comput. Graph., 26 (2002), 765–770. [8] Y. X. Liu, C. N. Yang, C. M. Wu, et al. Threshold changeable secret image sharing scheme based on interpolation polynomial, Multimed. Tools Appl., (2019), (DOI: 10.1007/s11042-019-7205-4). [9] Y. X. Liu and C. N. Yang, Scalable secret image sharing scheme with essential shadows. Signal Process. Image, 58 (2017), 49–55. [10] S. F. Tu and C. S. Hsu, Protecting secret documents via a sharing and hiding scheme, Inf. Sci., 279 (2014), 52–59. [11] C. C. Chang and T. X. Yu, Sharing a secret gray image in multiple images, First International Symposium on Cyber Worlds, (2002), 230–237. [12] D. S. Tsai, G. Horng, T. H. Chen, et al., A novel secret image sharing scheme for true-color images with size constraint, Inf. Sci., 179 (2009), 3247–3254. [13] R. Lukac and K.N. Plataniotis, Bit-level based secret sharing for image encryption, Pattern Recognit., 38 (2005), 767–772. [14] Y. X. Liu, C. N. Yang and P. H. Yeh, Reducing shadow size in smooth scalable secret image sharing, Secur. Commun. Netw., 7 (2014), 2237–2244. [15] R. Z. Wang and C. H. Su, Secret image sharing with smaller shadow images, Pattern Recogn. Lett., 27 (2006), 551–555. [16] C. N. Yang, P. Li, C. C Wu, et al., Reducing shadow size in essential secret image sharing by conjunctive hierarchical approach, Signal Process. Image, 31 (2015), 1–9. [17] C. N. Yang, J. F. Ouyang and L. Harn et al., Steganography and authentication in image sharing without parity bits, Opt. Commun., 285 (2012), 1725–1735. [18] C. C. Chen and S. C. Chen, Two-layered structure for optimally essential secret image sharing scheme, J. Vis. Commun. Image R., 38 (2016), 595–601.
• ##### Reader Comments
• © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

2.080 2.1

## Metrics

Article views(952) PDF downloads(447) Cited by(1)

Article outline

## Figures and Tables

Figures(8)  /  Tables(2)

## Other Articles By Authors

• On This Site
• On Google Scholar

/

DownLoad:  Full-Size Img  PowerPoint