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

Yan-Xiao Liu; Ya-Ze Zhang; Ching-Nung Yang; Yan-Xiao Liu; Ya-Ze Zhang; Ching-Nung Yang

doi:10.3934/mbe.2019242

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 4802-4817. doi: 10.3934/mbe.2019242

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Research article Special Issues

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

1.
Department of Computer Science and Engineering, XI’AN University of Technology, XI’AN, China
2.
Department of CSIE, National Dong Hwa University, Hualien, Taiwan

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.
- document protection,
- secret sharing,
- share size,
- Fermat Prime
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

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Abstract

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.

References

[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.

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